Statistics Theses
http://hdl.handle.net/10023/101
Sat, 16 Nov 2019 21:13:25 GMT2019-11-16T21:13:25ZEstimating abundance of African great apes
http://hdl.handle.net/10023/18859
All species and subspecies of African great apes are listed by the International Union for the Conservation of Nature as endangered or critically endangered, and populations continue to decline. As human populations and industry expand into great ape habitat, efficient, reliable estimators of great ape abundance are needed to inform conservation status and land-use planning, to assess adverse and beneficial effects of human activities, and to help funding agencies and donors make informed and efficient contributions. Fortunately, technological advances have improved our ability to sample great apes remotely, and new statistical methods for estimating abundance are constantly in development. Following a brief general introduction, this thesis reviews established and emerging approaches to estimating great ape abundance, then describes new methods for estimating animal density from photographic data by distance sampling with camera traps, and for selecting among models of the distance sampling detection function when distance data are overdispersed. Subsequent chapters quantify the effect of violating the assumption of demographic closure when estimating abundance using spatially explicit capture–recapture models for closed populations, and describe the design and implementation of a camera trapping survey of chimpanzees at the landscape scale in Kibale National Park, Uganda. The new methods developed have generated considerable interest, and allow abundances of multiple species, including great apes, to be estimated from data collected during a single photographic survey. Spatially explicit capture–recapture analyses of photographic data from small study areas yielded accurate and precise estimates of chimpanzee abundance, and this combination of methods could be used to enumerate great apes over large areas and in dense forests more reliably and efficiently than previously possible.
Tue, 03 Dec 2019 00:00:00 GMThttp://hdl.handle.net/10023/188592019-12-03T00:00:00ZHowe, Eric JAll species and subspecies of African great apes are listed by the International Union for the Conservation of Nature as endangered or critically endangered, and populations continue to decline. As human populations and industry expand into great ape habitat, efficient, reliable estimators of great ape abundance are needed to inform conservation status and land-use planning, to assess adverse and beneficial effects of human activities, and to help funding agencies and donors make informed and efficient contributions. Fortunately, technological advances have improved our ability to sample great apes remotely, and new statistical methods for estimating abundance are constantly in development. Following a brief general introduction, this thesis reviews established and emerging approaches to estimating great ape abundance, then describes new methods for estimating animal density from photographic data by distance sampling with camera traps, and for selecting among models of the distance sampling detection function when distance data are overdispersed. Subsequent chapters quantify the effect of violating the assumption of demographic closure when estimating abundance using spatially explicit capture–recapture models for closed populations, and describe the design and implementation of a camera trapping survey of chimpanzees at the landscape scale in Kibale National Park, Uganda. The new methods developed have generated considerable interest, and allow abundances of multiple species, including great apes, to be estimated from data collected during a single photographic survey. Spatially explicit capture–recapture analyses of photographic data from small study areas yielded accurate and precise estimates of chimpanzee abundance, and this combination of methods could be used to enumerate great apes over large areas and in dense forests more reliably and efficiently than previously possible.Methods in spatially explicit capture-recapture
http://hdl.handle.net/10023/18233
Capture-recapture (CR) methods are a ubiquitous means of estimating animal abundance from wildlife surveys. They rely on the detection and subsequent redetection of individuals over a number of sampling occasions. It is usually necessary for individuals to be recognised upon redetection. Spatially explicit capture-recapture (SECR) methods generalise those of CR by accounting for the locations at which each detection occurs. This allows spatial heterogeneity in detection probabilities to be accounted for: individuals with home-range centres near the detector array are more likely to be detected. They also permit estimation of animal density in addition to abundance.
One particular advantage of SECR methods is that they can be used when individuals are detected via the cues they produce---examples include birdsongs detected by microphones and whale surfacings detected by human observers. In such situations each cue may be detected by multiple detectors at different fixed locations. Redetections are then spatial (rather than temporal) in nature, and density can be estimated from a single survey occasion.
Existing methods, however, cannot generally be appropriately applied to the resulting cue-detection data without making assumptions that rarely hold. Additionally, they usually estimate cue density rather than animal density, which does not usually have the same biological importance. This thesis extends SECR methodology primarily for the appropriate estimation of animal density from cue-based SECR surveys. These extensions include (i) incorporation of auxiliary survey data into SECR estimators, (ii) appropriate point and variance estimators of animal density for a range of scenarios, and (iii) methods to account for both heterogeneity in detectability and cues that are directional in nature.
Moreover, a general class of methods is presented for the estimation of demographic parameters from wildlife surveys on which individuals cannot be recognised. These can variously be applied to CR and---potentially---SECR.
Fri, 24 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/182332016-06-24T00:00:00ZStevenson, Ben C.Capture-recapture (CR) methods are a ubiquitous means of estimating animal abundance from wildlife surveys. They rely on the detection and subsequent redetection of individuals over a number of sampling occasions. It is usually necessary for individuals to be recognised upon redetection. Spatially explicit capture-recapture (SECR) methods generalise those of CR by accounting for the locations at which each detection occurs. This allows spatial heterogeneity in detection probabilities to be accounted for: individuals with home-range centres near the detector array are more likely to be detected. They also permit estimation of animal density in addition to abundance.
One particular advantage of SECR methods is that they can be used when individuals are detected via the cues they produce---examples include birdsongs detected by microphones and whale surfacings detected by human observers. In such situations each cue may be detected by multiple detectors at different fixed locations. Redetections are then spatial (rather than temporal) in nature, and density can be estimated from a single survey occasion.
Existing methods, however, cannot generally be appropriately applied to the resulting cue-detection data without making assumptions that rarely hold. Additionally, they usually estimate cue density rather than animal density, which does not usually have the same biological importance. This thesis extends SECR methodology primarily for the appropriate estimation of animal density from cue-based SECR surveys. These extensions include (i) incorporation of auxiliary survey data into SECR estimators, (ii) appropriate point and variance estimators of animal density for a range of scenarios, and (iii) methods to account for both heterogeneity in detectability and cues that are directional in nature.
Moreover, a general class of methods is presented for the estimation of demographic parameters from wildlife surveys on which individuals cannot be recognised. These can variously be applied to CR and---potentially---SECR.The statistical development of integrated multi-state stopover models
http://hdl.handle.net/10023/18206
This thesis focusses on the analysis of ecological capture-recapture data and the
estimation of population parameters of interest. Many of the common models applied
to such data, for example the Cormack-Jolly-Seber model, condition on the first capture of an individual or on the number of individuals encountered. A consequence
of this conditioning is that it is not possible to estimate the total abundance
directly. Stopover models remove the conditioning on first capture and instead
explicitly model the arrival of individuals into the population. This permits the
estimation of abundance through the likelihood along with other parameters such
as capture and retention probabilities.
We develop an integrated stopover model capable of analysing multiple years of
data within a single likelihood and allowing parameters to be shared across years.
We consider special cases of this model, writing the likelihood using sufficient statistics
as well as utilising the hidden Markov model framework to allow for efficient
evaluation of the likelihood. We further extend this model to an integrated multistate-stopover model which incorporates any available discrete state information.
The new stopover models are applied to real ecological data sets. A cohort-dependent
single-year stopover model is applied to data on grey seals, Halichoerus
grypus, where the cohorts are determined by birth year. The integrated stopover
model and integrated multi-state stopover model are used to analyse a data set on
great crested newts, Triturus cristatus. A subset of this data is used to explore closed population models that permit capture probabilities to depend on discrete
state information. The final section of this thesis considers a capture-recapture-recovery
data set relating to Soay sheep, a breed of domestic sheep Ovis aries.
These data contain individual time-varying continuous covariates and raise the issue
of dealing with missing data.
Fri, 24 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/182062016-06-24T00:00:00ZWorthington, HannahThis thesis focusses on the analysis of ecological capture-recapture data and the
estimation of population parameters of interest. Many of the common models applied
to such data, for example the Cormack-Jolly-Seber model, condition on the first capture of an individual or on the number of individuals encountered. A consequence
of this conditioning is that it is not possible to estimate the total abundance
directly. Stopover models remove the conditioning on first capture and instead
explicitly model the arrival of individuals into the population. This permits the
estimation of abundance through the likelihood along with other parameters such
as capture and retention probabilities.
We develop an integrated stopover model capable of analysing multiple years of
data within a single likelihood and allowing parameters to be shared across years.
We consider special cases of this model, writing the likelihood using sufficient statistics
as well as utilising the hidden Markov model framework to allow for efficient
evaluation of the likelihood. We further extend this model to an integrated multistate-stopover model which incorporates any available discrete state information.
The new stopover models are applied to real ecological data sets. A cohort-dependent
single-year stopover model is applied to data on grey seals, Halichoerus
grypus, where the cohorts are determined by birth year. The integrated stopover
model and integrated multi-state stopover model are used to analyse a data set on
great crested newts, Triturus cristatus. A subset of this data is used to explore closed population models that permit capture probabilities to depend on discrete
state information. The final section of this thesis considers a capture-recapture-recovery
data set relating to Soay sheep, a breed of domestic sheep Ovis aries.
These data contain individual time-varying continuous covariates and raise the issue
of dealing with missing data.Title redacted
http://hdl.handle.net/10023/16693
Mon, 20 Nov 2017 00:00:00 GMThttp://hdl.handle.net/10023/166932017-11-20T00:00:00ZErichson, N. BenjaminIncorporating animal movement with distance sampling and spatial capture-recapture
http://hdl.handle.net/10023/16467
Distance sampling and spatial capture-recapture are statistical methods to estimate the
number of animals in a wild population based on encounters between these animals and
scientific detectors. Both methods estimate the probability an animal is detected during a
survey, but do not explicitly model animal movement.
The primary challenge is that animal movement in these surveys is unobserved; one must
average over all possible paths each animal could have travelled during the survey. In this
thesis, a general statistical model, with distance sampling and spatial capture-recapture
as special cases, is presented that explicitly incorporates animal movement. An efficient
algorithm to integrate over all possible movement paths, based on quadrature and hidden
Markov modelling, is given to overcome the computational obstacles.
For distance sampling, simulation studies and case studies show that incorporating animal
movement can reduce the bias in estimated abundance found in conventional models and
expand application of distance sampling to surveys that violate the assumption of no animal
movement. For spatial capture-recapture, continuous-time encounter records are used to
make detailed inference on where animals spend their time during the survey. In surveys
conducted in discrete occasions, maximum likelihood models that allow for mobile activity
centres are presented to account for transience, dispersal, and heterogeneous space use.
These methods provide an alternative when animal movement causes bias in standard methods and the opportunity to gain richer inference on how animals move, where they spend
their time, and how they interact.
Thu, 06 Dec 2018 00:00:00 GMThttp://hdl.handle.net/10023/164672018-12-06T00:00:00ZGlennie, RichardDistance sampling and spatial capture-recapture are statistical methods to estimate the
number of animals in a wild population based on encounters between these animals and
scientific detectors. Both methods estimate the probability an animal is detected during a
survey, but do not explicitly model animal movement.
The primary challenge is that animal movement in these surveys is unobserved; one must
average over all possible paths each animal could have travelled during the survey. In this
thesis, a general statistical model, with distance sampling and spatial capture-recapture
as special cases, is presented that explicitly incorporates animal movement. An efficient
algorithm to integrate over all possible movement paths, based on quadrature and hidden
Markov modelling, is given to overcome the computational obstacles.
For distance sampling, simulation studies and case studies show that incorporating animal
movement can reduce the bias in estimated abundance found in conventional models and
expand application of distance sampling to surveys that violate the assumption of no animal
movement. For spatial capture-recapture, continuous-time encounter records are used to
make detailed inference on where animals spend their time during the survey. In surveys
conducted in discrete occasions, maximum likelihood models that allow for mobile activity
centres are presented to account for transience, dispersal, and heterogeneous space use.
These methods provide an alternative when animal movement causes bias in standard methods and the opportunity to gain richer inference on how animals move, where they spend
their time, and how they interact.Title redacted
http://hdl.handle.net/10023/15909
Fri, 23 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/159092017-06-23T00:00:00ZMillar, Colin PearsonIncorporating animal movement into circular plot and point transect surveys of wildlife abundance
http://hdl.handle.net/10023/15612
Estimating wildlife abundance is fundamental for its effective management and conservation.
A range of methods exist: total counts, plot sampling, distance sampling and
capture-recapture based approaches. Methods have assumptions and their failure can
lead to substantial bias. Current research in the field is focused not on establishing new
methods but in extending existing methods to deal with their assumptions' violation.
This thesis focus on incorporating animal movement into circular plot sampling (CPS)
and point transect sampling (PTS), where a key assumption is that animals do not move
while within detection range, i.e., the survey is a snapshot in time. While targeting this
goal, we found some unexpected bias in PTS when animals were still and model selection
was used to choose among different candidate models for the detection function (the
model describing how detectability changes with observer-animal distance). Using a simulation
study, we found that, although PTS estimators are asymptotically unbiased, for
the recommended sample sizes the bias depended on the form of the true detection function.
We then extended the simulation study to include animal movement, and found this
led to further bias in CPS and PTS. We present novel methods that incorporate animal
movement with constant speed into estimates of abundance. First, in CPS, we present
an analytic expression to correct for the bias given linear movement. When movement
is de ned by a diffusion process, a simulation based approach, modelling the probability
of animal presence in the circular plot, results in less than 3% bias in the abundance
estimates. For PTS we introduce an estimator composed of two linked submodels: the
movement (animals moving linearly) and the detection model. The performance of the
proposed method is assessed via simulation. Despite being biased, the new estimator
yields improved results compared to ignoring animal movement using conventional PTS.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/156122018-01-01T00:00:00ZPrieto González, RocíoEstimating wildlife abundance is fundamental for its effective management and conservation.
A range of methods exist: total counts, plot sampling, distance sampling and
capture-recapture based approaches. Methods have assumptions and their failure can
lead to substantial bias. Current research in the field is focused not on establishing new
methods but in extending existing methods to deal with their assumptions' violation.
This thesis focus on incorporating animal movement into circular plot sampling (CPS)
and point transect sampling (PTS), where a key assumption is that animals do not move
while within detection range, i.e., the survey is a snapshot in time. While targeting this
goal, we found some unexpected bias in PTS when animals were still and model selection
was used to choose among different candidate models for the detection function (the
model describing how detectability changes with observer-animal distance). Using a simulation
study, we found that, although PTS estimators are asymptotically unbiased, for
the recommended sample sizes the bias depended on the form of the true detection function.
We then extended the simulation study to include animal movement, and found this
led to further bias in CPS and PTS. We present novel methods that incorporate animal
movement with constant speed into estimates of abundance. First, in CPS, we present
an analytic expression to correct for the bias given linear movement. When movement
is de ned by a diffusion process, a simulation based approach, modelling the probability
of animal presence in the circular plot, results in less than 3% bias in the abundance
estimates. For PTS we introduce an estimator composed of two linked submodels: the
movement (animals moving linearly) and the detection model. The performance of the
proposed method is assessed via simulation. Despite being biased, the new estimator
yields improved results compared to ignoring animal movement using conventional PTS.A continuous-time formulation for spatial capture-recapture models
http://hdl.handle.net/10023/15596
Spatial capture-recapture (SCR) models are relatively new but have become the
standard approach used to estimate animal density from capture-recapture data. It
has in the past been impractical to obtain sufficient data for analysis on species that
are very difficult to capture such as elusive carnivores that occur at low density and
range very widely. Advances in technology have led to alternative ways to virtually
“capture" individuals without having to physically hold them. Some examples of
these new non-invasive sampling methods include scat or hair collection for genetic
analysis, acoustic detection and camera trapping.
In traditional capture-recapture (CR) and SCR studies populations are sampled
at discrete points in time leading to clear and well defined occasions whereas the
new detector types mentioned above sample populations continuously in time. Researchers
with data collected continuously currently need to define an appropriate
occasion and aggregate their data accordingly thereby imposing an artificial construct
on their data for analytical convenience.
This research develops a continuous-time (CT) framework for SCR models by
treating detections as a temporal non homogeneous Poisson process (NHPP) and
replacing the usual SCR detection function with a continuous detection hazard function.
The general CT likelihood is first developed for data from passive (also called
“proximity") detectors like camera traps that do not physically hold individuals. The
likelihood is then modified to produce a likelihood for single-catch traps (traps that
are taken out of action by capturing an animal) that has proven difficult to develop
with a discrete-occasion approach.
The lack of a suitable single-catch trap likelihood has led to researchers using
a discrete-time (DT) multi-catch trap estimator to analyse single-catch trap data.
Previous work has found the DT multi-catch estimator to be robust despite the fact
that it is known to be based on the wrong model for single-catch traps (it assumes
that the traps continue operating after catching an individual). Simulation studies in
this work confirm that the multi-catch estimator is robust for estimating density when
density is constant or does not vary much in space. However, there are scenarios with
non-constant density surfaces when the multi-catch estimator is not able to correctly
identify regions of high density. Furthermore, the multi-catch estimator is known
to be negatively biased for the intercept parameter of SCR detection functions and
there may be interest in the detection function in its own right. On the other hand
the CT single-catch estimator is unbiased or nearly so for all parameters of interest
including those in the detection function and those in the model for density.
When one assumes that the detection hazard is constant through time there is
no impact of ignoring capture times and using only the detection frequencies. This
is of course a special case and in reality detection hazards will tend to vary in time.
However when one assumes that the effects of time and distance in the time-varying
hazard are independent, then similarly there is no information in the capture times
about density and detection function parameters. The work here uses a detection
hazard that assumes independence between time and distance. Different forms for
the detection hazard are explored with the most flexible choice being that of a cyclic
regression spline.
Extensive simulation studies suggest as expected that a DT proximity estimator is
unbiased for the estimation of density even when the detection hazard varies though
time. However there are indirect benefits of incorporating capture times because
doing so will lead to a better fitting detection component of the model, and this can
prevent unexplained variation being erroneously attributed to the wrong covariate.
The analysis of two real datasets supports this assertion because the models with the
best fitting detection hazard have different effects to the other models. In addition,
modelling the detection process in continuous-time leads to a more parsimonious
approach compared to using DT models when the detection hazard varies in time.
The underlying process is occurring in continuous-time and so using CT models
allows inferences to be drawn about the underlying process, for example the timevarying
detection hazard can be viewed as a proxy for animal activity. The CT
formulation is able to model the underlying detection hazard accurately and provides
a formal modelling framework to explore different hypotheses about activity patterns.
There is scope to integrate the CT models developed here with models for space usage
and landscape connectivity to explore these processes on a finer temporal scale.
SCR models are experiencing a rapid growth in both application and method
development. The data generating process occurs in CT and hence a CT modelling
approach is a natural fit and opens up several opportunities that are not possible
with a DT formulation. The work here makes a contribution by developing and
exploring the utility of such a CT SCR formulation.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/155962017-01-01T00:00:00ZDistiller, GregSpatial capture-recapture (SCR) models are relatively new but have become the
standard approach used to estimate animal density from capture-recapture data. It
has in the past been impractical to obtain sufficient data for analysis on species that
are very difficult to capture such as elusive carnivores that occur at low density and
range very widely. Advances in technology have led to alternative ways to virtually
“capture" individuals without having to physically hold them. Some examples of
these new non-invasive sampling methods include scat or hair collection for genetic
analysis, acoustic detection and camera trapping.
In traditional capture-recapture (CR) and SCR studies populations are sampled
at discrete points in time leading to clear and well defined occasions whereas the
new detector types mentioned above sample populations continuously in time. Researchers
with data collected continuously currently need to define an appropriate
occasion and aggregate their data accordingly thereby imposing an artificial construct
on their data for analytical convenience.
This research develops a continuous-time (CT) framework for SCR models by
treating detections as a temporal non homogeneous Poisson process (NHPP) and
replacing the usual SCR detection function with a continuous detection hazard function.
The general CT likelihood is first developed for data from passive (also called
“proximity") detectors like camera traps that do not physically hold individuals. The
likelihood is then modified to produce a likelihood for single-catch traps (traps that
are taken out of action by capturing an animal) that has proven difficult to develop
with a discrete-occasion approach.
The lack of a suitable single-catch trap likelihood has led to researchers using
a discrete-time (DT) multi-catch trap estimator to analyse single-catch trap data.
Previous work has found the DT multi-catch estimator to be robust despite the fact
that it is known to be based on the wrong model for single-catch traps (it assumes
that the traps continue operating after catching an individual). Simulation studies in
this work confirm that the multi-catch estimator is robust for estimating density when
density is constant or does not vary much in space. However, there are scenarios with
non-constant density surfaces when the multi-catch estimator is not able to correctly
identify regions of high density. Furthermore, the multi-catch estimator is known
to be negatively biased for the intercept parameter of SCR detection functions and
there may be interest in the detection function in its own right. On the other hand
the CT single-catch estimator is unbiased or nearly so for all parameters of interest
including those in the detection function and those in the model for density.
When one assumes that the detection hazard is constant through time there is
no impact of ignoring capture times and using only the detection frequencies. This
is of course a special case and in reality detection hazards will tend to vary in time.
However when one assumes that the effects of time and distance in the time-varying
hazard are independent, then similarly there is no information in the capture times
about density and detection function parameters. The work here uses a detection
hazard that assumes independence between time and distance. Different forms for
the detection hazard are explored with the most flexible choice being that of a cyclic
regression spline.
Extensive simulation studies suggest as expected that a DT proximity estimator is
unbiased for the estimation of density even when the detection hazard varies though
time. However there are indirect benefits of incorporating capture times because
doing so will lead to a better fitting detection component of the model, and this can
prevent unexplained variation being erroneously attributed to the wrong covariate.
The analysis of two real datasets supports this assertion because the models with the
best fitting detection hazard have different effects to the other models. In addition,
modelling the detection process in continuous-time leads to a more parsimonious
approach compared to using DT models when the detection hazard varies in time.
The underlying process is occurring in continuous-time and so using CT models
allows inferences to be drawn about the underlying process, for example the timevarying
detection hazard can be viewed as a proxy for animal activity. The CT
formulation is able to model the underlying detection hazard accurately and provides
a formal modelling framework to explore different hypotheses about activity patterns.
There is scope to integrate the CT models developed here with models for space usage
and landscape connectivity to explore these processes on a finer temporal scale.
SCR models are experiencing a rapid growth in both application and method
development. The data generating process occurs in CT and hence a CT modelling
approach is a natural fit and opens up several opportunities that are not possible
with a DT formulation. The work here makes a contribution by developing and
exploring the utility of such a CT SCR formulation.Modelling the spatial dynamics of non-state terrorism : world study, 2002-2013
http://hdl.handle.net/10023/12067
To this day, terrorism perpetrated by non-state actors persists as a worldwide threat, as exemplified by the recent lethal attacks in Paris, London, Brussels, and the ongoing massacres perpetrated by the Islamic State in Iraq, Syria and neighbouring countries. In response, states deploy various counterterrorism policies, the costs of which could be reduced through more efficient preventive measures. The literature has not applied statistical models able to account for complex spatio-temporal dependencies, despite their potential for explaining and preventing non-state terrorism at the sub-national level. In an effort to address this shortcoming, this thesis employs Bayesian hierarchical models, where the spatial random field is represented by a stochastic partial differential equation. The results show that lethal terrorist attacks perpetrated by non-state actors tend to be concentrated in areas located within failed states from which they may diffuse locally, towards neighbouring areas. At the sub-national level, the propensity of attacks to be lethal and the frequency of lethal attacks appear to be driven by antagonistic mechanisms. Attacks are more likely to be lethal far away from large cities, at higher altitudes, in less economically developed areas, and in locations with higher ethnic diversity. In contrast, the frequency of lethal attacks tends to be higher in more economically developed areas, close to large cities, and within democratic countries.
Thu, 07 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/120672017-12-07T00:00:00ZPython, AndréTo this day, terrorism perpetrated by non-state actors persists as a worldwide threat, as exemplified by the recent lethal attacks in Paris, London, Brussels, and the ongoing massacres perpetrated by the Islamic State in Iraq, Syria and neighbouring countries. In response, states deploy various counterterrorism policies, the costs of which could be reduced through more efficient preventive measures. The literature has not applied statistical models able to account for complex spatio-temporal dependencies, despite their potential for explaining and preventing non-state terrorism at the sub-national level. In an effort to address this shortcoming, this thesis employs Bayesian hierarchical models, where the spatial random field is represented by a stochastic partial differential equation. The results show that lethal terrorist attacks perpetrated by non-state actors tend to be concentrated in areas located within failed states from which they may diffuse locally, towards neighbouring areas. At the sub-national level, the propensity of attacks to be lethal and the frequency of lethal attacks appear to be driven by antagonistic mechanisms. Attacks are more likely to be lethal far away from large cities, at higher altitudes, in less economically developed areas, and in locations with higher ethnic diversity. In contrast, the frequency of lethal attacks tends to be higher in more economically developed areas, close to large cities, and within democratic countries.Modelling complex dependencies inherent in spatial and spatio-temporal point pattern data
http://hdl.handle.net/10023/12009
Point processes are mechanisms that beget point patterns. Realisations of point processes are observed in many contexts, for example, locations of stars in the sky, or locations of trees in a forest. Inferring the mechanisms that drive point processes relies on the development of models that appropriately account for the dependencies inherent in the data. Fitting models that adequately capture the complex dependency structures in either space, time, or both is often problematic. This is commonly due to—but not restricted to—the intractability of the likelihood function, or computational burden of the required numerical operations.
This thesis primarily focuses on developing point process models with some hierarchical structure, and specifically where this is a latent structure that may be considered as one of the following: (i) some unobserved construct assumed to be generating the observed structure, or (ii) some stochastic process describing the structure of the point pattern. Model fitting procedures utilised in this thesis include either (i) approximate-likelihood techniques to circumvent intractable likelihoods, (ii) stochastic partial differential equations to model continuous spatial latent structures, or (iii) improving computational speed in numerical approximations by exploiting automatic differentiation.
Moreover, this thesis extends classic point process models by considering multivariate dependencies. This is achieved through considering a general class of joint point process model, which utilise shared stochastic structures. These structures account for the dependencies inherent in multivariate point process data. These models are applied to data originating from various scientific fields; in particular, applications are considered in ecology, medicine, and geology. In addition, point process models that account for the second order behaviour of these assumed stochastic structures are also considered.
Fri, 23 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/120092017-06-23T00:00:00ZJones-Todd, Charlotte MPoint processes are mechanisms that beget point patterns. Realisations of point processes are observed in many contexts, for example, locations of stars in the sky, or locations of trees in a forest. Inferring the mechanisms that drive point processes relies on the development of models that appropriately account for the dependencies inherent in the data. Fitting models that adequately capture the complex dependency structures in either space, time, or both is often problematic. This is commonly due to—but not restricted to—the intractability of the likelihood function, or computational burden of the required numerical operations.
This thesis primarily focuses on developing point process models with some hierarchical structure, and specifically where this is a latent structure that may be considered as one of the following: (i) some unobserved construct assumed to be generating the observed structure, or (ii) some stochastic process describing the structure of the point pattern. Model fitting procedures utilised in this thesis include either (i) approximate-likelihood techniques to circumvent intractable likelihoods, (ii) stochastic partial differential equations to model continuous spatial latent structures, or (iii) improving computational speed in numerical approximations by exploiting automatic differentiation.
Moreover, this thesis extends classic point process models by considering multivariate dependencies. This is achieved through considering a general class of joint point process model, which utilise shared stochastic structures. These structures account for the dependencies inherent in multivariate point process data. These models are applied to data originating from various scientific fields; in particular, applications are considered in ecology, medicine, and geology. In addition, point process models that account for the second order behaviour of these assumed stochastic structures are also considered.Title redacted
http://hdl.handle.net/10023/11739
Thu, 07 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/117392017-12-07T00:00:00ZSharifi Far, ServehBayesian multi-species modelling of non-negative continuous ecological data with a discrete mass at zero
http://hdl.handle.net/10023/9626
Severe declines in the number of some songbirds over the last 40 years
have caused heated debate amongst interested parties. Many factors
have been suggested as possible causes for these declines, including
an increase in the abundance and distribution of an avian predator,
the Eurasian sparrowhawk Accipiter nisus. To test for evidence for a
predator effect on the abundance of its prey, we analyse data on 10
species visiting garden bird feeding stations monitored by the British
Trust for Ornithology in relation to the abundance of sparrowhawks.
We apply Bayesian hierarchical models to data relating to averaged
maximum weekly counts from a garden bird monitoring survey. These
data are essentially continuous, bounded below by zero, but for many
species show a marked spike at zero that many standard distributions
would not be able to account for. We use the Tweedie distributions,
which for certain areas of parameter space relate to continuous nonnegative
distributions with a discrete probability mass at zero, and
are hence able to deal with the shape of the empirical distributions of
the data.
The methods developed in this thesis begin by modelling single prey
species independently with an avian predator as a covariate, using
MCMC methods to explore parameter and model spaces. This model
is then extended to a multiple-prey species model, testing for interactions
between species as well as synchrony in their response to environmental
factors and unobserved variation.
Finally we use a relatively new methodological framework, namely
the SPDE approach in the INLA framework, to fit a multi-species
spatio-temporal model to the ecological data.
The results from the analyses are consistent with the hypothesis that
sparrowhawks are suppressing the numbers of some species of birds
visiting garden feeding stations. Only the species most susceptible to
sparrowhawk predation seem to be affected.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/96262015-01-01T00:00:00ZSwallow, BenSevere declines in the number of some songbirds over the last 40 years
have caused heated debate amongst interested parties. Many factors
have been suggested as possible causes for these declines, including
an increase in the abundance and distribution of an avian predator,
the Eurasian sparrowhawk Accipiter nisus. To test for evidence for a
predator effect on the abundance of its prey, we analyse data on 10
species visiting garden bird feeding stations monitored by the British
Trust for Ornithology in relation to the abundance of sparrowhawks.
We apply Bayesian hierarchical models to data relating to averaged
maximum weekly counts from a garden bird monitoring survey. These
data are essentially continuous, bounded below by zero, but for many
species show a marked spike at zero that many standard distributions
would not be able to account for. We use the Tweedie distributions,
which for certain areas of parameter space relate to continuous nonnegative
distributions with a discrete probability mass at zero, and
are hence able to deal with the shape of the empirical distributions of
the data.
The methods developed in this thesis begin by modelling single prey
species independently with an avian predator as a covariate, using
MCMC methods to explore parameter and model spaces. This model
is then extended to a multiple-prey species model, testing for interactions
between species as well as synchrony in their response to environmental
factors and unobserved variation.
Finally we use a relatively new methodological framework, namely
the SPDE approach in the INLA framework, to fit a multi-species
spatio-temporal model to the ecological data.
The results from the analyses are consistent with the hypothesis that
sparrowhawks are suppressing the numbers of some species of birds
visiting garden feeding stations. Only the species most susceptible to
sparrowhawk predation seem to be affected.Random coeffcient models for complex longitudinal data
http://hdl.handle.net/10023/6386
Longitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data.
Biased inference can occur in linear mixed-effects modelling if subjects are drawn from a number of unknown sub-populations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a two-step approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially non-monotonic variance and correlation functions.
Spatially explicit capture-recapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multi-occasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radio-tagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animal-level covariates.
Fri, 27 Jun 2014 00:00:00 GMThttp://hdl.handle.net/10023/63862014-06-27T00:00:00ZKidney, DarrenLongitudinal data are common in biological research. However, real data sets vary considerably in terms of their structure and complexity and present many challenges for statistical modelling. This thesis proposes a series of methods using random coefficients for modelling two broad types of longitudinal response: normally distributed measurements and binary recapture data.
Biased inference can occur in linear mixed-effects modelling if subjects are drawn from a number of unknown sub-populations, or if the residual covariance is poorly specified. To address some of the shortcomings of previous approaches in terms of model selection and flexibility, this thesis presents methods for: (i) determining the presence of latent grouping structures using a two-step approach, involving regression splines for modelling functional random effects and mixture modelling of the fitted random effects; and (ii) flexible of modelling of the residual covariance matrix using regression splines to specify smooth and potentially non-monotonic variance and correlation functions.
Spatially explicit capture-recapture methods for estimating the density of animal populations have shown a rapid increase in popularity over recent years. However, further refinements to existing theory and fitting software are required to apply these methods in many situations. This thesis presents: (i) an analysis of recapture data from an acoustic survey of gibbons using supplementary data in the form of estimated angles to detections, (ii) the development of a multi-occasion likelihood including a model for stochastic availability using a partially observed random effect (interpreted in terms of calling behaviour in the case of gibbons), and (iii) an analysis of recapture data from a population of radio-tagged skates using a conditional likelihood that allows the density of animal activity centres to be modelled as functions of time, space and animal-level covariates.Novel methods for species distribution mapping including spatial models in complex regions
http://hdl.handle.net/10023/4514
Species Distribution Modelling (SDM) plays a key role in a number of biological applications: assessment of temporal trends in distribution, environmental impact assessment and spatial conservation planning. From a statistical perspective, this thesis develops two methods for increasing the accuracy and reliability of maps of density surfaces and provides a solution to the problem of how to collate multiple density maps of the same region, obtained from differing sources. From a biological perspective, these statistical methods are used to analyse two marine mammal datasets to produce accurate maps for use in spatial conservation planning and temporal trend assessment.
The first new method, Complex Region Spatial Smoother [CReSS; Scott-Hayward et al., 2013], improves smoothing in areas where the real distance an animal must travel (`as the animal swims') between two points may be greater than the straight line distance between them, a problem that occurs in complex domains with coastline or islands. CReSS uses estimates of the geodesic distance between points, model averaging and local radial smoothing. Simulation is used to compare its performance with other traditional and recently-developed smoothing techniques: Thin Plate Splines (TPS, Harder and Desmarais [1972]), Geodesic Low rank TPS (GLTPS; Wang and Ranalli [2007]) and the Soap lm smoother (SOAP; Wood et al. [2008]). GLTPS cannot be used in areas with islands and SOAP can be very hard to parametrise. CReSS outperforms all of the other methods on a range of simulations, based on their fit to the underlying function as measured by mean squared error, particularly for sparse data sets.
Smoothing functions need to be flexible when they are used to model density surfaces that are highly heterogeneous, in order to avoid biases due to under- or over-fitting. This issue was addressed using an adaptation of a Spatially Adaptive Local Smoothing Algorithm (SALSA, Walker et al. [2010]) in combination with the CReSS method (CReSS-SALSA2D). Unlike traditional methods, such as Generalised Additive Modelling, the adaptive knot selection approach used in SALSA2D naturally accommodates local changes in the smoothness of the density surface that is being modelled. At the time of writing, there are no other methods available to deal with this issue in topographically complex regions. Simulation results show that CReSS-SALSA2D performs better than CReSS (based on MSE scores), except at very high noise levels where there is an issue with over-fitting.
There is an increasing need for a facility to combine multiple density surface maps of individual species in order to make best use of meta-databases, to maintain existing maps, and to extend their geographical coverage. This thesis develops a framework and methods for combining species distribution maps as new information becomes available. The methods use Bayes Theorem to combine density surfaces, taking account of the levels of precision associated with the different sets of estimates, and kernel smoothing to alleviate artefacts that may be created where pairs of surfaces join. The methods were used as part of an algorithm (the Dynamic Cetacean Abundance Predictor) designed for BAE Systems to aid in risk mitigation for naval exercises.
Two case studies show the capabilities of CReSS and CReSS-SALSA2D when applied to real ecological data. In the first case study, CReSS was used in a Generalised Estimating Equation framework to identify a candidate Marine Protected Area for the Southern Resident Killer Whale population to the south of San Juan Island, off the Pacific coast of the United States. In the second case study, changes in the spatial and temporal distribution of harbour porpoise and minke whale in north-western European waters over a period of 17 years (1994-2010) were modelled. CReSS and CReSS-SALSA2D performed well in a large, topographically complex study area. Based on simulation results, maps produced using these methods are more accurate than if a traditional GAM-based method is used. The resulting maps identified particularly high densities of both harbour porpoise and minke whale in an area off the west coast of Scotland in 2010, that might be a candidate for inclusion into the
Scottish network of Nature Conservation Marine Protected Areas.
Tue, 05 Nov 2013 00:00:00 GMThttp://hdl.handle.net/10023/45142013-11-05T00:00:00ZScott-Hayward, Lindesay Alexandra SarahSpecies Distribution Modelling (SDM) plays a key role in a number of biological applications: assessment of temporal trends in distribution, environmental impact assessment and spatial conservation planning. From a statistical perspective, this thesis develops two methods for increasing the accuracy and reliability of maps of density surfaces and provides a solution to the problem of how to collate multiple density maps of the same region, obtained from differing sources. From a biological perspective, these statistical methods are used to analyse two marine mammal datasets to produce accurate maps for use in spatial conservation planning and temporal trend assessment.
The first new method, Complex Region Spatial Smoother [CReSS; Scott-Hayward et al., 2013], improves smoothing in areas where the real distance an animal must travel (`as the animal swims') between two points may be greater than the straight line distance between them, a problem that occurs in complex domains with coastline or islands. CReSS uses estimates of the geodesic distance between points, model averaging and local radial smoothing. Simulation is used to compare its performance with other traditional and recently-developed smoothing techniques: Thin Plate Splines (TPS, Harder and Desmarais [1972]), Geodesic Low rank TPS (GLTPS; Wang and Ranalli [2007]) and the Soap lm smoother (SOAP; Wood et al. [2008]). GLTPS cannot be used in areas with islands and SOAP can be very hard to parametrise. CReSS outperforms all of the other methods on a range of simulations, based on their fit to the underlying function as measured by mean squared error, particularly for sparse data sets.
Smoothing functions need to be flexible when they are used to model density surfaces that are highly heterogeneous, in order to avoid biases due to under- or over-fitting. This issue was addressed using an adaptation of a Spatially Adaptive Local Smoothing Algorithm (SALSA, Walker et al. [2010]) in combination with the CReSS method (CReSS-SALSA2D). Unlike traditional methods, such as Generalised Additive Modelling, the adaptive knot selection approach used in SALSA2D naturally accommodates local changes in the smoothness of the density surface that is being modelled. At the time of writing, there are no other methods available to deal with this issue in topographically complex regions. Simulation results show that CReSS-SALSA2D performs better than CReSS (based on MSE scores), except at very high noise levels where there is an issue with over-fitting.
There is an increasing need for a facility to combine multiple density surface maps of individual species in order to make best use of meta-databases, to maintain existing maps, and to extend their geographical coverage. This thesis develops a framework and methods for combining species distribution maps as new information becomes available. The methods use Bayes Theorem to combine density surfaces, taking account of the levels of precision associated with the different sets of estimates, and kernel smoothing to alleviate artefacts that may be created where pairs of surfaces join. The methods were used as part of an algorithm (the Dynamic Cetacean Abundance Predictor) designed for BAE Systems to aid in risk mitigation for naval exercises.
Two case studies show the capabilities of CReSS and CReSS-SALSA2D when applied to real ecological data. In the first case study, CReSS was used in a Generalised Estimating Equation framework to identify a candidate Marine Protected Area for the Southern Resident Killer Whale population to the south of San Juan Island, off the Pacific coast of the United States. In the second case study, changes in the spatial and temporal distribution of harbour porpoise and minke whale in north-western European waters over a period of 17 years (1994-2010) were modelled. CReSS and CReSS-SALSA2D performed well in a large, topographically complex study area. Based on simulation results, maps produced using these methods are more accurate than if a traditional GAM-based method is used. The resulting maps identified particularly high densities of both harbour porpoise and minke whale in an area off the west coast of Scotland in 2010, that might be a candidate for inclusion into the
Scottish network of Nature Conservation Marine Protected Areas.Modelling catch sampling uncertainty in fisheries stock assessment : the Atlantic-Iberian sardine case
http://hdl.handle.net/10023/4474
The statistical assessment of harvested fish populations, such as the Atlantic-Iberian sardine (AIS)
stock, needs to deal with uncertainties inherent in fisheries systems. Uncertainties arising from
sampling errors and stochasticity in stock dynamics must be incorporated in stock assessment
models so that management decisions are based on realistic evaluation of the uncertainty about
the status of the stock. The main goal of this study is to develop a stock assessment framework
that accounts for some of the uncertainties associated with the AIS stock that are currently not
integrated into stock assessment models. In particular, it focuses on accounting for the uncertainty
arising from the catch data sampling process.
The central innovation the thesis is the development of a Bayesian integrated stock assessment
(ISA) model, in which an observation model explicitly links stock dynamics parameters
with statistical models for the various types of data observed from catches of the AIS stock.
This allows for systematic and statistically consistent propagation of the uncertainty inherent in
the catch sampling process across the whole stock assessment model, through to estimates of
biomass and stock parameters. The method is tested by simulations and found to provide reliable
and accurate estimates of stock parameters and associated uncertainty, while also outperforming
existing designed-based and model-based estimation approaches.
The method is computationally very demanding and this is an obstacle to its adoption
by fisheries bodies. Once this obstacle is overcame, the ISA modelling framework developed
and presented in this thesis could provide an important contribution to the improvement in the
evaluation of uncertainty in fisheries stock assessments, not only of the AIS stock, but of any other
fish stock with similar data and dynamics structure. Furthermore, the models developed in this
study establish a solid conceptual platform to allow future development of more complex models
of fish population dynamics.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10023/44742013-01-01T00:00:00ZCaneco, BrunoThe statistical assessment of harvested fish populations, such as the Atlantic-Iberian sardine (AIS)
stock, needs to deal with uncertainties inherent in fisheries systems. Uncertainties arising from
sampling errors and stochasticity in stock dynamics must be incorporated in stock assessment
models so that management decisions are based on realistic evaluation of the uncertainty about
the status of the stock. The main goal of this study is to develop a stock assessment framework
that accounts for some of the uncertainties associated with the AIS stock that are currently not
integrated into stock assessment models. In particular, it focuses on accounting for the uncertainty
arising from the catch data sampling process.
The central innovation the thesis is the development of a Bayesian integrated stock assessment
(ISA) model, in which an observation model explicitly links stock dynamics parameters
with statistical models for the various types of data observed from catches of the AIS stock.
This allows for systematic and statistically consistent propagation of the uncertainty inherent in
the catch sampling process across the whole stock assessment model, through to estimates of
biomass and stock parameters. The method is tested by simulations and found to provide reliable
and accurate estimates of stock parameters and associated uncertainty, while also outperforming
existing designed-based and model-based estimation approaches.
The method is computationally very demanding and this is an obstacle to its adoption
by fisheries bodies. Once this obstacle is overcame, the ISA modelling framework developed
and presented in this thesis could provide an important contribution to the improvement in the
evaluation of uncertainty in fisheries stock assessments, not only of the AIS stock, but of any other
fish stock with similar data and dynamics structure. Furthermore, the models developed in this
study establish a solid conceptual platform to allow future development of more complex models
of fish population dynamics.Estimating wildlife distribution and abundance from line transect surveys conducted from platforms of opportunity
http://hdl.handle.net/10023/3727
Line transect data obtained from 'platforms of opportunity' are useful for the monitoring
of long term trends in dolphin populations which occur over vast areas, yet analyses of
such data axe problematic due to violation of fundamental assumptions of line transect
methodology. In this thesis we develop methods which allow estimates of dolphin relative
abundance to be obtained when certain assumptions of line transect sampling are violated.
Generalised additive models are used to model encounter rate and mean school size as
a function of spatially and temporally referenced covariates. The estimated relationship
between the response and the environmental and locational covariates is then used to
obtain a predicted surface for the response over the entire survey region. Given those
predicted surfaces, a density surface can then be obtained and an estimate of abundance
computed by numerically integrating over the entire survey region. This approach is
particularly useful when search effort is not random, in which case standard line transect
methods would yield biased estimates.
Estimates of f (0) (the inverse of the effective strip (half-)width), an essential component
of the line transect estimator, may also be biased due to heterogeneity in detection probabilities.
We developed a conditional likelihood approach in which covariate effects are
directly incorporated into the estimation procedure. Simulation results indicated that the
method performs well in the presence of size-bias. When multiple covariates are used, it
is important that covariate selection be carried out.
As an example we applied the methods described above to eastern tropical Pacific dolphin
stocks. However, uncertainty in stock identification has never been directly incorporated
into methods used to obtain estimates of relative or absolute abundance. Therefore we
illustrate an approach in which trends in dolphin relative abundance axe monitored by
small areas, rather than stocks.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10023/37272001-01-01T00:00:00ZMarques, Fernanda F. C.Line transect data obtained from 'platforms of opportunity' are useful for the monitoring
of long term trends in dolphin populations which occur over vast areas, yet analyses of
such data axe problematic due to violation of fundamental assumptions of line transect
methodology. In this thesis we develop methods which allow estimates of dolphin relative
abundance to be obtained when certain assumptions of line transect sampling are violated.
Generalised additive models are used to model encounter rate and mean school size as
a function of spatially and temporally referenced covariates. The estimated relationship
between the response and the environmental and locational covariates is then used to
obtain a predicted surface for the response over the entire survey region. Given those
predicted surfaces, a density surface can then be obtained and an estimate of abundance
computed by numerically integrating over the entire survey region. This approach is
particularly useful when search effort is not random, in which case standard line transect
methods would yield biased estimates.
Estimates of f (0) (the inverse of the effective strip (half-)width), an essential component
of the line transect estimator, may also be biased due to heterogeneity in detection probabilities.
We developed a conditional likelihood approach in which covariate effects are
directly incorporated into the estimation procedure. Simulation results indicated that the
method performs well in the presence of size-bias. When multiple covariates are used, it
is important that covariate selection be carried out.
As an example we applied the methods described above to eastern tropical Pacific dolphin
stocks. However, uncertainty in stock identification has never been directly incorporated
into methods used to obtain estimates of relative or absolute abundance. Therefore we
illustrate an approach in which trends in dolphin relative abundance axe monitored by
small areas, rather than stocks.Bayesian point process modelling of ecological communities
http://hdl.handle.net/10023/3710
The modelling of biological communities is important to further the understanding
of species coexistence and the mechanisms involved in maintaining
biodiversity. This involves considering not only interactions between individual
biological organisms, but also the incorporation of covariate information,
if available, in the modelling process. This thesis explores the use
of point processes to model interactions in bivariate point patterns within
a Bayesian framework, and, where applicable, in conjunction with covariate
data. Specifically, we distinguish between symmetric and asymmetric species
interactions and model these using appropriate point processes. In this thesis
we consider both pairwise and area interaction point processes to allow for
inhibitory interactions and both inhibitory and attractive interactions.
It is envisaged that the analyses and innovations presented in this thesis
will contribute to the parsimonious modelling of biological communities.
Fri, 28 Jun 2013 00:00:00 GMThttp://hdl.handle.net/10023/37102013-06-28T00:00:00ZNightingale, Glenna FaithThe modelling of biological communities is important to further the understanding
of species coexistence and the mechanisms involved in maintaining
biodiversity. This involves considering not only interactions between individual
biological organisms, but also the incorporation of covariate information,
if available, in the modelling process. This thesis explores the use
of point processes to model interactions in bivariate point patterns within
a Bayesian framework, and, where applicable, in conjunction with covariate
data. Specifically, we distinguish between symmetric and asymmetric species
interactions and model these using appropriate point processes. In this thesis
we consider both pairwise and area interaction point processes to allow for
inhibitory interactions and both inhibitory and attractive interactions.
It is envisaged that the analyses and innovations presented in this thesis
will contribute to the parsimonious modelling of biological communities.Animal population estimation using mark-recapture and plant-capture
http://hdl.handle.net/10023/3655
Mark-recapture is a method of population estimation that involves capturing a number
of animals from a population of unknown size on several occasions, and marking
those animals that are caught each time. By observing the number of marked
animals that are subsequently seen, estimates of the total population size can be
made. There are various subclasses of the mark-recapture method called the Otis-class
of models (Otis, Burnham, White & Anderson 1978). These relate to the
assumed behaviour of the individuals in the target population.
More recent work has generalised the theory of mark-recapture to the so-called
plant-capture, where a known number of animals are pre-inserted into the target
population. Sampling is then carried out as normal, but with additional information
coming from knowledge of the number of planted individuals.
The theory underpinning plant-capture is less well-developed than mark-recapture,
with the difference on population estimation of the former over the latter not often
tested. This thesis shows that, under fixed and random sample-size models, the
inclusion of plants can improve the mean point population estimation of various
estimators. The estimator of Pathak (1964) is generalised to allow for the inclusion
of plants into the target population. The results show that mean estimates from
most estimators, under most models, can be improved with the inclusion of plants,
and the sample standard deviations of the simulations can be reduced. This improvement
in mean point population estimation is particularly pronounced when
the number of animals captured is low.
Sample coverage, which is the proportion of distinct animals caught during sampling,
is also often sought by practitioners. Given here is a generalisation of the
inverse population estimator of Pathak (1964) to plant-capture and a proposed new
inverse population estimator, which can be used as estimates of the coverage of a
sample.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10023/36552012-01-01T00:00:00ZGormley, RichardMark-recapture is a method of population estimation that involves capturing a number
of animals from a population of unknown size on several occasions, and marking
those animals that are caught each time. By observing the number of marked
animals that are subsequently seen, estimates of the total population size can be
made. There are various subclasses of the mark-recapture method called the Otis-class
of models (Otis, Burnham, White & Anderson 1978). These relate to the
assumed behaviour of the individuals in the target population.
More recent work has generalised the theory of mark-recapture to the so-called
plant-capture, where a known number of animals are pre-inserted into the target
population. Sampling is then carried out as normal, but with additional information
coming from knowledge of the number of planted individuals.
The theory underpinning plant-capture is less well-developed than mark-recapture,
with the difference on population estimation of the former over the latter not often
tested. This thesis shows that, under fixed and random sample-size models, the
inclusion of plants can improve the mean point population estimation of various
estimators. The estimator of Pathak (1964) is generalised to allow for the inclusion
of plants into the target population. The results show that mean estimates from
most estimators, under most models, can be improved with the inclusion of plants,
and the sample standard deviations of the simulations can be reduced. This improvement
in mean point population estimation is particularly pronounced when
the number of animals captured is low.
Sample coverage, which is the proportion of distinct animals caught during sampling,
is also often sought by practitioners. Given here is a generalisation of the
inverse population estimator of Pathak (1964) to plant-capture and a proposed new
inverse population estimator, which can be used as estimates of the coverage of a
sample.Estimating anglerfish abundance from trawl surveys, and related problems
http://hdl.handle.net/10023/3652
The content of this thesis was motivated by the need to estimate anglerfish abundance
from stratified random trawl surveys of the anglerfish stock which occupies
the northern European shelf (Fernandes et al., 2007). The survey was conducted
annually from 2005 to 2010 in order to obtain age-structured estimates of absolute
abundance for this stock. An estimation method is considered to incorporate statistical models for herding, length-based net retention probability and missing age data and uncertainty from all of these sources in variance estimation.
A key component of abundance estimation is the estimation of capture probability.
Capture probability is estimated from the experimental survey data using various
logistic regression models with haul as a random effect. Conditional on the estimated
capture probability, a number of abundance estimators are developed and applied to
the anglerfish data. The abundance estimators differ in the way that the haul effect is incorporated. The performance of these estimators is investigated by simulation. An estimator with form similar to that conventionally used to estimate abundance from distance sampling surveys is found to perform best.
The estimators developed for the anglerfish survey data which incorporate random
effects in capture probability have wider application than trawl surveys. We examine
the analytic properties of these estimators when the capture/detection probability is
known. We apply these estimators to three different types of survey data in addition
to the anglerfish data, with different forms of random effects and investigate their
performance by simulation. We find that a generalization of the form of estimator
typically used on line transect surveys performs best overall. It has low bias, and
also the lowest bias and mean squared error among all the estimators we considered.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10023/36522012-01-01T00:00:00ZYuan, YuanThe content of this thesis was motivated by the need to estimate anglerfish abundance
from stratified random trawl surveys of the anglerfish stock which occupies
the northern European shelf (Fernandes et al., 2007). The survey was conducted
annually from 2005 to 2010 in order to obtain age-structured estimates of absolute
abundance for this stock. An estimation method is considered to incorporate statistical models for herding, length-based net retention probability and missing age data and uncertainty from all of these sources in variance estimation.
A key component of abundance estimation is the estimation of capture probability.
Capture probability is estimated from the experimental survey data using various
logistic regression models with haul as a random effect. Conditional on the estimated
capture probability, a number of abundance estimators are developed and applied to
the anglerfish data. The abundance estimators differ in the way that the haul effect is incorporated. The performance of these estimators is investigated by simulation. An estimator with form similar to that conventionally used to estimate abundance from distance sampling surveys is found to perform best.
The estimators developed for the anglerfish survey data which incorporate random
effects in capture probability have wider application than trawl surveys. We examine
the analytic properties of these estimators when the capture/detection probability is
known. We apply these estimators to three different types of survey data in addition
to the anglerfish data, with different forms of random effects and investigate their
performance by simulation. We find that a generalization of the form of estimator
typically used on line transect surveys performs best overall. It has low bias, and
also the lowest bias and mean squared error among all the estimators we considered.Mixed effect models in distance sampling
http://hdl.handle.net/10023/3618
Recently, much effort has been expended for improving conventional distance sampling methods, e.g. by replacing the design-based approach with a model-based approach where observed counts are related to environmental covariates (Hedley and Buckland, 2004) or by incorporating covariates in the detection function model (Marques and Buckland, 2003).
While these models have generally been limited to include fixed effects, we propose
four different methods for analysing distance sampling data using mixed effects models. These include an extension of the two-stage approach (Buckland et al., 2009),
where we include site random effects in the second-stage count model to account for
correlated counts at the same sites. We also present two integrated approaches which
include site random effects in the count model. These approaches combine the analysis stages for the detection and count models and allow simultaneous estimation of all
parameters. Furthermore, we develop a detection function model that incorporates
random effects. We also propose a novel Bayesian approach to analysing distance sampling data which uses a Metropolis-Hastings algorithm for updating model parameters and a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm for assessing model uncertainty. Lastly, we propose using hierarchical centering as a novel technique for improving model mixing and hence facilitating an RJMCMC algorithm for mixed models.
We analyse two case studies, both large-scale point transect surveys, where the interest lies in establishing the effects of conservation buffers on agricultural fields. For each case study, we compare the results from one integrated approach to those from
the extended two-stage approach. We find that these may differ in parameter estimates for covariates that were both in the detection and the count model and in model probabilities when model uncertainty was included in inference. The performance of the random effects based detection function is assessed via simulation and when heterogeneity in the data is present, one of the new estimators yields improved results compared to conventional distance sampling estimators.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10023/36182013-01-01T00:00:00ZOedekoven, Cornelia SabrinaRecently, much effort has been expended for improving conventional distance sampling methods, e.g. by replacing the design-based approach with a model-based approach where observed counts are related to environmental covariates (Hedley and Buckland, 2004) or by incorporating covariates in the detection function model (Marques and Buckland, 2003).
While these models have generally been limited to include fixed effects, we propose
four different methods for analysing distance sampling data using mixed effects models. These include an extension of the two-stage approach (Buckland et al., 2009),
where we include site random effects in the second-stage count model to account for
correlated counts at the same sites. We also present two integrated approaches which
include site random effects in the count model. These approaches combine the analysis stages for the detection and count models and allow simultaneous estimation of all
parameters. Furthermore, we develop a detection function model that incorporates
random effects. We also propose a novel Bayesian approach to analysing distance sampling data which uses a Metropolis-Hastings algorithm for updating model parameters and a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm for assessing model uncertainty. Lastly, we propose using hierarchical centering as a novel technique for improving model mixing and hence facilitating an RJMCMC algorithm for mixed models.
We analyse two case studies, both large-scale point transect surveys, where the interest lies in establishing the effects of conservation buffers on agricultural fields. For each case study, we compare the results from one integrated approach to those from
the extended two-stage approach. We find that these may differ in parameter estimates for covariates that were both in the detection and the count model and in model probabilities when model uncertainty was included in inference. The performance of the random effects based detection function is assessed via simulation and when heterogeneity in the data is present, one of the new estimators yields improved results compared to conventional distance sampling estimators.Quantifying biodiversity trends in time and space
http://hdl.handle.net/10023/3414
The global loss of biodiversity calls for robust large-scale diversity assessment. Biological diversity is a multi-faceted concept; defined as the “variety of life”, answering questions such as “How much is there?” or more precisely “Have we succeeded in reducing the rate of its decline?” is not straightforward. While various aspects of biodiversity give rise to numerous ways of quantification, we focus on temporal (and spatial) trends and their changes in species diversity.
Traditional diversity indices summarise information contained in the species abundance distribution, i.e. each species' proportional contribution to total abundance. Estimated from data, these indices can be biased if variation in detection probability is ignored. We discuss differences between diversity indices and demonstrate possible adjustments for detectability.
Additionally, most indices focus on the most abundant species in ecological communities. We introduce a new set of diversity measures, based on a family of goodness-of-fit statistics. A function of a free parameter, this family allows us to vary the sensitivity of these measures to dominance and rarity of species.
Their performance is studied by assessing temporal trends in diversity for five communities of British breeding birds based on 14 years of survey data, where they are applied alongside the current headline index, a geometric mean of relative abundances. Revealing the contributions of both rare and common species to biodiversity trends, these "goodness-of-fit" measures provide novel insights into how ecological communities change over time.
Biodiversity is not only subject to temporal changes, but it also varies across space. We take first steps towards estimating spatial diversity trends. Finally, processes maintaining biodiversity act locally, at specific spatial scales. Contrary to abundance-based summary statistics, spatial characteristics of ecological communities may distinguish these processes. We suggest a generalisation to a spatial summary, the cross-pair overlap distribution, to render it more flexible to spatial scale.
Fri, 30 Nov 2012 00:00:00 GMThttp://hdl.handle.net/10023/34142012-11-30T00:00:00ZStudeny, Angelika C.The global loss of biodiversity calls for robust large-scale diversity assessment. Biological diversity is a multi-faceted concept; defined as the “variety of life”, answering questions such as “How much is there?” or more precisely “Have we succeeded in reducing the rate of its decline?” is not straightforward. While various aspects of biodiversity give rise to numerous ways of quantification, we focus on temporal (and spatial) trends and their changes in species diversity.
Traditional diversity indices summarise information contained in the species abundance distribution, i.e. each species' proportional contribution to total abundance. Estimated from data, these indices can be biased if variation in detection probability is ignored. We discuss differences between diversity indices and demonstrate possible adjustments for detectability.
Additionally, most indices focus on the most abundant species in ecological communities. We introduce a new set of diversity measures, based on a family of goodness-of-fit statistics. A function of a free parameter, this family allows us to vary the sensitivity of these measures to dominance and rarity of species.
Their performance is studied by assessing temporal trends in diversity for five communities of British breeding birds based on 14 years of survey data, where they are applied alongside the current headline index, a geometric mean of relative abundances. Revealing the contributions of both rare and common species to biodiversity trends, these "goodness-of-fit" measures provide novel insights into how ecological communities change over time.
Biodiversity is not only subject to temporal changes, but it also varies across space. We take first steps towards estimating spatial diversity trends. Finally, processes maintaining biodiversity act locally, at specific spatial scales. Contrary to abundance-based summary statistics, spatial characteristics of ecological communities may distinguish these processes. We suggest a generalisation to a spatial summary, the cross-pair overlap distribution, to render it more flexible to spatial scale.Finite and infinite ergodic theory for linear and conformal dynamical systems
http://hdl.handle.net/10023/3220
The first main topic of this thesis is the thorough analysis of two families of piecewise linear
maps on the unit interval, the α-Lüroth and α-Farey maps. Here, α denotes a countably infinite
partition of the unit interval whose atoms only accumulate at the origin. The basic properties
of these maps will be developed, including that each α-Lüroth map (denoted Lα) gives rise to a
series expansion of real numbers in [0,1], a certain type of Generalised Lüroth Series. The first
example of such an expansion was given by Lüroth. The map Lα is the jump transformation
of the corresponding α-Farey map Fα. The maps Lα and Fα share the same relationship as the
classical Farey and Gauss maps which give rise to the continued fraction expansion of a real
number. We also consider the topological properties of Fα and some Diophantine-type sets of
numbers expressed in terms of the α-Lüroth expansion.
Next we investigate certain ergodic-theoretic properties of the maps Lα and Fα. It will turn
out that the Lebesgue measure λ is invariant for every map Lα and that there exists a unique
Lebesgue-absolutely continuous invariant measure for Fα. We will give a precise expression for
the density of this measure. Our main result is that both Lα and Fα are exact, and thus ergodic.
The interest in the invariant measure for Fα lies in the fact that under a particular condition on
the underlying partition α, the invariant measure associated to the map Fα is infinite.
Then we proceed to introduce and examine the sequence of α-sum-level sets arising from
the α-Lüroth map, for an arbitrary given partition α. These sets can be written dynamically in
terms of Fα. The main result concerning the α-sum-level sets is to establish weak and strong
renewal laws. Note that for the Farey map and the Gauss map, the analogue of this result has
been obtained by Kesseböhmer and Stratmann. There the results were derived by using advanced
infinite ergodic theory, rather than the strong renewal theorems employed here. This underlines
the fact that one of the main ingredients of infinite ergodic theory is provided by some delicate
estimates in renewal theory.
Our final main result concerning the α-Lüroth and α-Farey systems is to provide a fractal-geometric
description of the Lyapunov spectra associated with each of the maps Lα and Fα.
The Lyapunov spectra for the Farey map and the Gauss map have been investigated in detail by
Kesseböhmer and Stratmann. The Farey map and the Gauss map are non-linear, whereas the
systems we consider are always piecewise linear. However, since our analysis is based on a large
family of different partitions of U , the class of maps which we consider in this paper allows us
to detect a variety of interesting new phenomena, including that of phase transitions.
Finally, we come to the conformal systems of the title. These are the limit sets of discrete
subgroups of the group of isometries of the hyperbolic plane. For these so-called Fuchsian
groups, our first main result is to establish the Hausdorff dimension of some Diophantine-type
sets contained in the limit set that are similar to those considered for the maps Lα. These sets
are then used in our second main result to analyse the more geometrically defined strict-Jarník
limit set of a Fuchsian group. Finally, we obtain a “weak multifractal spectrum” for the Patterson
measure associated to the Fuchsian group.
Wed, 30 Nov 2011 00:00:00 GMThttp://hdl.handle.net/10023/32202011-11-30T00:00:00ZMunday, SaraThe first main topic of this thesis is the thorough analysis of two families of piecewise linear
maps on the unit interval, the α-Lüroth and α-Farey maps. Here, α denotes a countably infinite
partition of the unit interval whose atoms only accumulate at the origin. The basic properties
of these maps will be developed, including that each α-Lüroth map (denoted Lα) gives rise to a
series expansion of real numbers in [0,1], a certain type of Generalised Lüroth Series. The first
example of such an expansion was given by Lüroth. The map Lα is the jump transformation
of the corresponding α-Farey map Fα. The maps Lα and Fα share the same relationship as the
classical Farey and Gauss maps which give rise to the continued fraction expansion of a real
number. We also consider the topological properties of Fα and some Diophantine-type sets of
numbers expressed in terms of the α-Lüroth expansion.
Next we investigate certain ergodic-theoretic properties of the maps Lα and Fα. It will turn
out that the Lebesgue measure λ is invariant for every map Lα and that there exists a unique
Lebesgue-absolutely continuous invariant measure for Fα. We will give a precise expression for
the density of this measure. Our main result is that both Lα and Fα are exact, and thus ergodic.
The interest in the invariant measure for Fα lies in the fact that under a particular condition on
the underlying partition α, the invariant measure associated to the map Fα is infinite.
Then we proceed to introduce and examine the sequence of α-sum-level sets arising from
the α-Lüroth map, for an arbitrary given partition α. These sets can be written dynamically in
terms of Fα. The main result concerning the α-sum-level sets is to establish weak and strong
renewal laws. Note that for the Farey map and the Gauss map, the analogue of this result has
been obtained by Kesseböhmer and Stratmann. There the results were derived by using advanced
infinite ergodic theory, rather than the strong renewal theorems employed here. This underlines
the fact that one of the main ingredients of infinite ergodic theory is provided by some delicate
estimates in renewal theory.
Our final main result concerning the α-Lüroth and α-Farey systems is to provide a fractal-geometric
description of the Lyapunov spectra associated with each of the maps Lα and Fα.
The Lyapunov spectra for the Farey map and the Gauss map have been investigated in detail by
Kesseböhmer and Stratmann. The Farey map and the Gauss map are non-linear, whereas the
systems we consider are always piecewise linear. However, since our analysis is based on a large
family of different partitions of U , the class of maps which we consider in this paper allows us
to detect a variety of interesting new phenomena, including that of phase transitions.
Finally, we come to the conformal systems of the title. These are the limit sets of discrete
subgroups of the group of isometries of the hyperbolic plane. For these so-called Fuchsian
groups, our first main result is to establish the Hausdorff dimension of some Diophantine-type
sets contained in the limit set that are similar to those considered for the maps Lα. These sets
are then used in our second main result to analyse the more geometrically defined strict-Jarník
limit set of a Fuchsian group. Finally, we obtain a “weak multifractal spectrum” for the Patterson
measure associated to the Fuchsian group.Spatial patterns and species coexistence : using spatial statistics to identify underlying ecological processes in plant communities
http://hdl.handle.net/10023/3084
The use of spatial statistics to investigate ecological processes in plant communities is becoming increasingly widespread. In diverse communities such as tropical rainforests, analysis of spatial structure may help to unravel the various processes that act and interact to maintain high levels of diversity. In particular, a number of contrasting mechanisms have been suggested to explain species coexistence, and these differ greatly in their practical implications for the ecology and conservation of tropical forests. Traditional first-order measures of community structure have proved unable to distinguish these mechanisms in practice, but statistics that describe spatial structure may be able to do so. This is of great interest and relevance as spatially explicit data become available for a range of ecological communities and analysis methods for these data become more accessible.
This thesis investigates the potential for inference about underlying ecological processes in plant communities using spatial statistics. Current methodologies for spatial analysis are reviewed and extended, and are used to characterise the spatial signals of the principal theorised mechanisms of coexistence. The sensitivity of a range of spatial statistics to these signals is assessed, and the strength of such signals in natural communities is investigated.
The spatial signals of the processes considered here are found to be strong and robust to modelled stochastic variation. Several new and existing spatial statistics are found to be sensitive to these signals, and offer great promise for inference about underlying processes from empirical data. The relative strengths of particular processes are found to vary between natural communities, with any one theory being insufficient to explain observed patterns. This thesis extends both understanding of species coexistence in diverse plant communities and the methodology for assessing underlying process in particular cases. It demonstrates that the potential of spatial statistics in ecology is great and largely unexplored.
Thu, 01 Nov 2012 00:00:00 GMThttp://hdl.handle.net/10023/30842012-11-01T00:00:00ZBrown, CalumThe use of spatial statistics to investigate ecological processes in plant communities is becoming increasingly widespread. In diverse communities such as tropical rainforests, analysis of spatial structure may help to unravel the various processes that act and interact to maintain high levels of diversity. In particular, a number of contrasting mechanisms have been suggested to explain species coexistence, and these differ greatly in their practical implications for the ecology and conservation of tropical forests. Traditional first-order measures of community structure have proved unable to distinguish these mechanisms in practice, but statistics that describe spatial structure may be able to do so. This is of great interest and relevance as spatially explicit data become available for a range of ecological communities and analysis methods for these data become more accessible.
This thesis investigates the potential for inference about underlying ecological processes in plant communities using spatial statistics. Current methodologies for spatial analysis are reviewed and extended, and are used to characterise the spatial signals of the principal theorised mechanisms of coexistence. The sensitivity of a range of spatial statistics to these signals is assessed, and the strength of such signals in natural communities is investigated.
The spatial signals of the processes considered here are found to be strong and robust to modelled stochastic variation. Several new and existing spatial statistics are found to be sensitive to these signals, and offer great promise for inference about underlying processes from empirical data. The relative strengths of particular processes are found to vary between natural communities, with any one theory being insufficient to explain observed patterns. This thesis extends both understanding of species coexistence in diverse plant communities and the methodology for assessing underlying process in particular cases. It demonstrates that the potential of spatial statistics in ecology is great and largely unexplored.Estimating abundance of rare, small mammals: A case study of the Key Largo woodrat (Neotoma floridana smalli)
http://hdl.handle.net/10023/2068
Estimates of animal abundance or density are fundamental quantities in ecology and conservation, but for many species such as rare, small mammals, obtaining robust estimates is problematic. In this thesis, I combine elements of two standard abundance estimation methods, capture-recapture and distance sampling, to develop a method called trapping point transects (TPT). In TPT, a "detection function", g(r) (i.e. the probability of capturing an animal, given it is r m from a trap when the trap is set) is estimated using a subset of animals whose locations are known prior to traps being set. Generalised linear models are used to estimate the detection function, and the model can be extended to include random effects to allow for heterogeneity in capture probabilities. Standard point transect methods are modified to estimate abundance. Two abundance estimators are available. The first estimator is based on the reciprocal of the expected probability of detecting an animal, ^P, where the expectation is over r;
whereas the second estimator is the expectation of the reciprocal of ^P.
Performance of the TPT method under various sampling efforts and underlying true detection probabilities of individuals in the population was investigated in a simulation study. When underlying probability of detection was high (g(0) = 0:88) and between-individual variation was small, survey effort could be surprisingly low (c. 510 trap nights) to yield low bias (c. 4%) in the two estimators;
but under certain situations, the second estimator can be extremely biased. Uncertainty and relative bias in population estimates increased with decreasing detectability and increasing between-individual variation.
Abundance of the Key Largo woodrat (Neotoma floridana smalli), an endangered rodent with a restricted geographic range, was estimated using TPT. The TPT method compared well to other viable methods (capture-recapture and spatially-explicit capture-recapture), in terms of both field practicality and cost. The TPT method may generally be useful in estimating animal abundance in trapping studies and variants of the TPT method are presented.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10023/20682011-01-01T00:00:00ZPotts, Joanne M.Estimates of animal abundance or density are fundamental quantities in ecology and conservation, but for many species such as rare, small mammals, obtaining robust estimates is problematic. In this thesis, I combine elements of two standard abundance estimation methods, capture-recapture and distance sampling, to develop a method called trapping point transects (TPT). In TPT, a "detection function", g(r) (i.e. the probability of capturing an animal, given it is r m from a trap when the trap is set) is estimated using a subset of animals whose locations are known prior to traps being set. Generalised linear models are used to estimate the detection function, and the model can be extended to include random effects to allow for heterogeneity in capture probabilities. Standard point transect methods are modified to estimate abundance. Two abundance estimators are available. The first estimator is based on the reciprocal of the expected probability of detecting an animal, ^P, where the expectation is over r;
whereas the second estimator is the expectation of the reciprocal of ^P.
Performance of the TPT method under various sampling efforts and underlying true detection probabilities of individuals in the population was investigated in a simulation study. When underlying probability of detection was high (g(0) = 0:88) and between-individual variation was small, survey effort could be surprisingly low (c. 510 trap nights) to yield low bias (c. 4%) in the two estimators;
but under certain situations, the second estimator can be extremely biased. Uncertainty and relative bias in population estimates increased with decreasing detectability and increasing between-individual variation.
Abundance of the Key Largo woodrat (Neotoma floridana smalli), an endangered rodent with a restricted geographic range, was estimated using TPT. The TPT method compared well to other viable methods (capture-recapture and spatially-explicit capture-recapture), in terms of both field practicality and cost. The TPT method may generally be useful in estimating animal abundance in trapping studies and variants of the TPT method are presented.Bayesian modelling of integrated data and its application to seabird populations
http://hdl.handle.net/10023/1635
Integrated data analyses are becoming increasingly popular in studies of wild animal populations where two or more separate sources of data contain information about common parameters. Here we develop an integrated population model using abundance and demographic data from a study of common guillemots (Uria aalge) on the Isle of May, southeast Scotland. A state-space model for the count data is supplemented by three demographic time series (productivity and two mark-recapture-recovery (MRR)), enabling the estimation of prebreeder emigration rate - a parameter for which there is no direct observational data, and which is unidentifiable in the separate analysis of MRR data. A Bayesian approach using MCMC provides a flexible and powerful analysis framework.
This model is extended to provide predictions of future population trajectories. Adopting random effects models for the survival and productivity parameters, we implement the MCMC algorithm to obtain a posterior sample of the underlying process means and variances (and population sizes) within the study period. Given this sample, we predict future demographic parameters, which in turn allows us to predict future population sizes and obtain the corresponding posterior distribution. Under the assumption that recent, unfavourable conditions persist in the future, we obtain a posterior probability of 70% that there is a population decline of >25% over a 10-year period.
Lastly, using MRR data we test for spatial, temporal and age-related correlations in guillemot survival among three widely separated Scottish colonies that have varying overlap in nonbreeding distribution. We show that survival is highly correlated over time for colonies/age classes sharing wintering areas, and essentially uncorrelated for those with separate wintering areas. These results strongly suggest that one or more aspects of winter environment are responsible for spatiotemporal variation in survival of British guillemots, and provide insight into the factors driving multi-population dynamics of the species.
Tue, 30 Nov 2010 00:00:00 GMThttp://hdl.handle.net/10023/16352010-11-30T00:00:00ZReynolds, Toby J.Integrated data analyses are becoming increasingly popular in studies of wild animal populations where two or more separate sources of data contain information about common parameters. Here we develop an integrated population model using abundance and demographic data from a study of common guillemots (Uria aalge) on the Isle of May, southeast Scotland. A state-space model for the count data is supplemented by three demographic time series (productivity and two mark-recapture-recovery (MRR)), enabling the estimation of prebreeder emigration rate - a parameter for which there is no direct observational data, and which is unidentifiable in the separate analysis of MRR data. A Bayesian approach using MCMC provides a flexible and powerful analysis framework.
This model is extended to provide predictions of future population trajectories. Adopting random effects models for the survival and productivity parameters, we implement the MCMC algorithm to obtain a posterior sample of the underlying process means and variances (and population sizes) within the study period. Given this sample, we predict future demographic parameters, which in turn allows us to predict future population sizes and obtain the corresponding posterior distribution. Under the assumption that recent, unfavourable conditions persist in the future, we obtain a posterior probability of 70% that there is a population decline of >25% over a 10-year period.
Lastly, using MRR data we test for spatial, temporal and age-related correlations in guillemot survival among three widely separated Scottish colonies that have varying overlap in nonbreeding distribution. We show that survival is highly correlated over time for colonies/age classes sharing wintering areas, and essentially uncorrelated for those with separate wintering areas. These results strongly suggest that one or more aspects of winter environment are responsible for spatiotemporal variation in survival of British guillemots, and provide insight into the factors driving multi-population dynamics of the species.Statistical models for the long-term monitoring of songbird populations: a Bayesian analysis of constant effort sites and ring-recovery data
http://hdl.handle.net/10023/885
To underpin and improve advice given to government and other interested parties
on the state of Britain’s common songbird populations, new models for
analysing ecological data are developed in this thesis. These models use data
from the British Trust for Ornithology’s Constant Effort Sites (CES) scheme,
an annual bird-ringing programme in which catch effort is standardised. Data
from the CES scheme are routinely used to index abundance and productivity,
and to a lesser extent estimate adult survival rates. However, two features of
the CES data that complicate analysis were previously inadequately addressed,
namely the presence in the catch of “transient” birds not associated with the
local population, and the sporadic failure in the constancy of effort assumption
arising from the absence of within-year catch data. The current methodology
is extended, with efficient Bayesian models developed for each of these demographic
parameters that account for both of these data nuances, and from which
reliable and usefully precise estimates are obtained.
Of increasing interest is the relationship between abundance and the underlying
vital rates, an understanding of which facilitates effective conservation.
CES data are particularly amenable to an integrated approach to population
modelling, providing a combination of demographic information from a single
source. Such an integrated approach is developed here, employing Bayesian
methodology and a simple population model to unite abundance, productivity
and survival within a consistent framework. Independent data from ring-recoveries
provide additional information on adult and juvenile survival rates.
Specific advantages of this new integrated approach are identified, among which
is the ability to determine juvenile survival accurately, disentangle the probabilities
of survival and permanent emigration, and to obtain estimates of total
seasonal productivity.
The methodologies developed in this thesis are applied to CES data from Sedge
Warbler, Acrocephalus schoenobaenus, and Reed Warbler, A. scirpaceus.
Fri, 25 Jun 2010 00:00:00 GMThttp://hdl.handle.net/10023/8852010-06-25T00:00:00ZCave, Vanessa M.To underpin and improve advice given to government and other interested parties
on the state of Britain’s common songbird populations, new models for
analysing ecological data are developed in this thesis. These models use data
from the British Trust for Ornithology’s Constant Effort Sites (CES) scheme,
an annual bird-ringing programme in which catch effort is standardised. Data
from the CES scheme are routinely used to index abundance and productivity,
and to a lesser extent estimate adult survival rates. However, two features of
the CES data that complicate analysis were previously inadequately addressed,
namely the presence in the catch of “transient” birds not associated with the
local population, and the sporadic failure in the constancy of effort assumption
arising from the absence of within-year catch data. The current methodology
is extended, with efficient Bayesian models developed for each of these demographic
parameters that account for both of these data nuances, and from which
reliable and usefully precise estimates are obtained.
Of increasing interest is the relationship between abundance and the underlying
vital rates, an understanding of which facilitates effective conservation.
CES data are particularly amenable to an integrated approach to population
modelling, providing a combination of demographic information from a single
source. Such an integrated approach is developed here, employing Bayesian
methodology and a simple population model to unite abundance, productivity
and survival within a consistent framework. Independent data from ring-recoveries
provide additional information on adult and juvenile survival rates.
Specific advantages of this new integrated approach are identified, among which
is the ability to determine juvenile survival accurately, disentangle the probabilities
of survival and permanent emigration, and to obtain estimates of total
seasonal productivity.
The methodologies developed in this thesis are applied to CES data from Sedge
Warbler, Acrocephalus schoenobaenus, and Reed Warbler, A. scirpaceus.Topics in estimation of quantum channels
http://hdl.handle.net/10023/869
A quantum channel is a mapping which sends density matrices to density
matrices. The estimation of quantum channels is of great importance to the
field of quantum information. In this thesis two topics related to estimation
of quantum channels are investigated. The first of these is the upper
bound of Sarovar and Milburn (2006) on the Fisher information obtainable
by measuring the output of a channel. Two questions raised by Sarovar and
Milburn about their bound are answered. A Riemannian metric on the space
of quantum states is introduced, related to the construction of the Sarovar
and Milburn bound. Its properties are characterized.
The second topic investigated is the estimation of unitary channels. The
situation is considered in which an experimenter has several non-identical
unitary channels that have the same parameter. It is shown that it is possible
to improve estimation using the channels together, analogous to the case of
identical unitary channels. Also, a new method of phase estimation is given
based on a method sketched by Kitaev (1996). Unlike other phase estimation
procedures which perform similarly, this procedure requires only very basic
experimental resources.
Wed, 23 Jun 2010 00:00:00 GMThttp://hdl.handle.net/10023/8692010-06-23T00:00:00ZO'Loan, Caleb J.A quantum channel is a mapping which sends density matrices to density
matrices. The estimation of quantum channels is of great importance to the
field of quantum information. In this thesis two topics related to estimation
of quantum channels are investigated. The first of these is the upper
bound of Sarovar and Milburn (2006) on the Fisher information obtainable
by measuring the output of a channel. Two questions raised by Sarovar and
Milburn about their bound are answered. A Riemannian metric on the space
of quantum states is introduced, related to the construction of the Sarovar
and Milburn bound. Its properties are characterized.
The second topic investigated is the estimation of unitary channels. The
situation is considered in which an experimenter has several non-identical
unitary channels that have the same parameter. It is shown that it is possible
to improve estimation using the channels together, analogous to the case of
identical unitary channels. Also, a new method of phase estimation is given
based on a method sketched by Kitaev (1996). Unlike other phase estimation
procedures which perform similarly, this procedure requires only very basic
experimental resources.Multi-species state-space modelling of the hen harrier (Circus cyaneus) and red grouse (Lagopus lagopus scoticus) in Scotland
http://hdl.handle.net/10023/864
State-space modelling is a powerful tool to study ecological systems. The direct inclusion of uncertainty, unification of models and data, and ability to model unobserved, hidden states increases our knowledge about the environment and provides
new ecological insights. I extend the state-space framework to create multi-species
models, showing that the ability to model ecosystem interactions is limited only by data availability. State-space models are fit using both Bayesian and Frequentist methods, making them independent of a statistical school of thought. Bayesian approaches can have the advantage in their ability to account for missing data and fit hierarchical structures
and models with many parameters to limited data; often the case in ecological studies.
I have taken a Bayesian model fitting approach in this thesis.
The predator-prey interactions between the hen harrier (Circus cyaneus) and red grouse (Lagopus lagopus scoticus) are used to demonstrate state-space modelling’s
capabilities. The harrier data are believed to be known without error, while missing
data make the cyclic dynamics of the grouse harder to model. The grouse-harrier interactions are modelled in a multi-species state-space model, rather than including
one species as a covariate in the other’s model. Finally, models are included for the
harriers’ alternate prey.
The single- and multi-species state-space models for the predator-prey interactions
provide insight into the species’ management. The models investigate aspects of the species’ behaviour, from the mechanisms behind grouse cycles to what motivates harrier immigration. The inferences drawn from these models are applicable to management, suggesting actions to halt grouse cycles or mitigate the grouse-harrier conflict. Overall, the multi-species models suggest that two popular ideas for grouse-harrier management, diversionary feeding and habitat manipulation to reduce alternate prey densities, will not have the desired effect, and in the case of reducing prey densities, may even increase the harriers’ impact on grouse chicks.
Wed, 23 Jun 2010 00:00:00 GMThttp://hdl.handle.net/10023/8642010-06-23T00:00:00ZNew, Leslie FrancesState-space modelling is a powerful tool to study ecological systems. The direct inclusion of uncertainty, unification of models and data, and ability to model unobserved, hidden states increases our knowledge about the environment and provides
new ecological insights. I extend the state-space framework to create multi-species
models, showing that the ability to model ecosystem interactions is limited only by data availability. State-space models are fit using both Bayesian and Frequentist methods, making them independent of a statistical school of thought. Bayesian approaches can have the advantage in their ability to account for missing data and fit hierarchical structures
and models with many parameters to limited data; often the case in ecological studies.
I have taken a Bayesian model fitting approach in this thesis.
The predator-prey interactions between the hen harrier (Circus cyaneus) and red grouse (Lagopus lagopus scoticus) are used to demonstrate state-space modelling’s
capabilities. The harrier data are believed to be known without error, while missing
data make the cyclic dynamics of the grouse harder to model. The grouse-harrier interactions are modelled in a multi-species state-space model, rather than including
one species as a covariate in the other’s model. Finally, models are included for the
harriers’ alternate prey.
The single- and multi-species state-space models for the predator-prey interactions
provide insight into the species’ management. The models investigate aspects of the species’ behaviour, from the mechanisms behind grouse cycles to what motivates harrier immigration. The inferences drawn from these models are applicable to management, suggesting actions to halt grouse cycles or mitigate the grouse-harrier conflict. Overall, the multi-species models suggest that two popular ideas for grouse-harrier management, diversionary feeding and habitat manipulation to reduce alternate prey densities, will not have the desired effect, and in the case of reducing prey densities, may even increase the harriers’ impact on grouse chicks.Embedding population dynamics in mark-recapture models
http://hdl.handle.net/10023/718
Mark-recapture methods use repeated captures of individually identifiable animals to provide estimates of properties of populations. Different models allow estimates to be obtained for population size and rates of processes governing population dynamics. State-space models consist of two linked processes evolving simultaneously over time. The state process models the evolution of the true, but unknown, states of the population. The observation process relates observations on the population to these true states.
Mark-recapture models specified within a state-space framework allow population dynamics models to be embedded in inference ensuring that estimated changes in the population are consistent with assumptions regarding the biology of the modelled population. This overcomes a limitation of current mark-recapture methods.
Two alternative approaches are considered. The "conditional" approach conditions on known numbers of animals possessing capture history patterns including capture in the current time period. An animal's capture history determines its state; consequently, capture parameters appear in the state process rather than the observation process. There is no observation error in the model. Uncertainty occurs only through the numbers of animals not captured in the current time period.
An "unconditional" approach is considered in which the capture histories are regarded as observations. Consequently, capture histories do not influence an animal's state and capture probability parameters appear in the observation process. Capture histories are considered a random realization of the stochastic observation process. This is more consistent with traditional mark-recapture methods.
Development and implementation of particle filtering techniques for fitting these models under each approach are discussed. Simulation studies show reasonable performance for the unconditional approach and highlight problems with the conditional approach. Strengths and limitations of each approach are outlined, with reference to Soay sheep data analysis, and suggestions are presented for future analyses.
Wed, 24 Jun 2009 00:00:00 GMThttp://hdl.handle.net/10023/7182009-06-24T00:00:00ZBishop, Jonathan R. B.Mark-recapture methods use repeated captures of individually identifiable animals to provide estimates of properties of populations. Different models allow estimates to be obtained for population size and rates of processes governing population dynamics. State-space models consist of two linked processes evolving simultaneously over time. The state process models the evolution of the true, but unknown, states of the population. The observation process relates observations on the population to these true states.
Mark-recapture models specified within a state-space framework allow population dynamics models to be embedded in inference ensuring that estimated changes in the population are consistent with assumptions regarding the biology of the modelled population. This overcomes a limitation of current mark-recapture methods.
Two alternative approaches are considered. The "conditional" approach conditions on known numbers of animals possessing capture history patterns including capture in the current time period. An animal's capture history determines its state; consequently, capture parameters appear in the state process rather than the observation process. There is no observation error in the model. Uncertainty occurs only through the numbers of animals not captured in the current time period.
An "unconditional" approach is considered in which the capture histories are regarded as observations. Consequently, capture histories do not influence an animal's state and capture probability parameters appear in the observation process. Capture histories are considered a random realization of the stochastic observation process. This is more consistent with traditional mark-recapture methods.
Development and implementation of particle filtering techniques for fitting these models under each approach are discussed. Simulation studies show reasonable performance for the unconditional approach and highlight problems with the conditional approach. Strengths and limitations of each approach are outlined, with reference to Soay sheep data analysis, and suggestions are presented for future analyses.Using generalized estimating equations with regression splines to improve analysis of butterfly transect data
http://hdl.handle.net/10023/488
Surveying animal populations is an important aspect of wildlife
management. Distinguishing trend from random fluctuations and
quantifying trend are key goals in any analysis.
The aim of this thesis is to review analyses of Butterfly Monitoring
Survey (BMS) data and to develop new methods which address some
flaws in previous studies. The BMS was established in 1976 at Monks
Wood, Cambridgeshire and sites were added over time throughout
Britain in order to monitor butterfly population trends. Weekly
counts are made over the monitoring season and the main aims are to
produce annual indices and compare these indices over time for any
particular species.
Originally, weekly counts were summed to produce relative indices
and missing counts were estimated using linear interpolation. This
thesis discusses the weaknesses of this basic method
and suggests possible improvements.
In recent years, with advancements in statistical methods and
increased computer power, new methods can be applied to accommodate
the longitudinal and flexible nature of ecological data.
Mixed Models, Generalized Estimating Equations and Generalized
Additive Models are used and the relative merits of each modelling
approach discussed. These methods allow for correlation and
non-linearity in data.
Model selection is an important consideration when modelling and
different tests are introduced and compared.
Once a model is selected, site-level indices are estimated, which
can be collated to produce regional and national indices. Different
methods of estimating precision around indices are also contrasted.
Bootstrapping is found to be a convenient and dependable approach.
Abundance is difficult to disentangle from detectability when only
counts of species are carried out. Methods for dealing with this
problem are suggested.
Once reliable annual abundance estimates are found, they can be
compared over time using a variety of statistical techniques. The
chain-ratio method is applied to a subset of real data.
Sun, 01 Jun 2008 00:00:00 GMThttp://hdl.handle.net/10023/4882008-06-01T00:00:00ZBrewer, CiaraSurveying animal populations is an important aspect of wildlife
management. Distinguishing trend from random fluctuations and
quantifying trend are key goals in any analysis.
The aim of this thesis is to review analyses of Butterfly Monitoring
Survey (BMS) data and to develop new methods which address some
flaws in previous studies. The BMS was established in 1976 at Monks
Wood, Cambridgeshire and sites were added over time throughout
Britain in order to monitor butterfly population trends. Weekly
counts are made over the monitoring season and the main aims are to
produce annual indices and compare these indices over time for any
particular species.
Originally, weekly counts were summed to produce relative indices
and missing counts were estimated using linear interpolation. This
thesis discusses the weaknesses of this basic method
and suggests possible improvements.
In recent years, with advancements in statistical methods and
increased computer power, new methods can be applied to accommodate
the longitudinal and flexible nature of ecological data.
Mixed Models, Generalized Estimating Equations and Generalized
Additive Models are used and the relative merits of each modelling
approach discussed. These methods allow for correlation and
non-linearity in data.
Model selection is an important consideration when modelling and
different tests are introduced and compared.
Once a model is selected, site-level indices are estimated, which
can be collated to produce regional and national indices. Different
methods of estimating precision around indices are also contrasted.
Bootstrapping is found to be a convenient and dependable approach.
Abundance is difficult to disentangle from detectability when only
counts of species are carried out. Methods for dealing with this
problem are suggested.
Once reliable annual abundance estimates are found, they can be
compared over time using a variety of statistical techniques. The
chain-ratio method is applied to a subset of real data.Incorporating measurement error and density gradients in distance sampling surveys
http://hdl.handle.net/10023/391
Distance sampling is one of the most commonly used methods for estimating density
and abundance. Conventional methods are based on the distances of detected animals
from the center of point transects or the center line of line transects. These distances
are used to model a detection function: the probability of detecting an animal, given
its distance from the line or point. The probability of detecting an animal in the
covered area is given by the mean value of the detection function with respect to
the available distances to be detected. Given this probability, a Horvitz-Thompson-
like estimator of abundance for the covered area follows, hence using a model-based
framework. Inferences for the wider survey region are justified using the survey design.
Conventional distance sampling methods are based on a set of assumptions. In
this thesis I present results that extend distance sampling on two fronts.
Firstly, estimators are derived for situations in which there is measurement error in
the distances. These estimators use information about the measurement error in two
ways: (1) a biased estimator based on the contaminated distances is multiplied by an
appropriate correction factor, which is a function of the errors (PDF approach), and
(2) cast into a likelihood framework that allows parameter estimation in the presence
of measurement error (likelihood approach).
Secondly, methods are developed that relax the conventional assumption that the
distribution of animals is independent of distance from the lines or points (usually
guaranteed by appropriate survey design). In particular, the new methods deal with
the case where animal density gradients are caused by the use of non-random sampler
allocation, for example transects placed along linear features such as roads or streams.
This is dealt with separately for line and point transects, and at a later stage an
approach for combining the two is presented.
A considerable number of simulations and example analysis illustrate the performance of the proposed methods.
Thu, 01 Nov 2007 00:00:00 GMThttp://hdl.handle.net/10023/3912007-11-01T00:00:00ZMarques, Tiago Andre Lamas OliveiraDistance sampling is one of the most commonly used methods for estimating density
and abundance. Conventional methods are based on the distances of detected animals
from the center of point transects or the center line of line transects. These distances
are used to model a detection function: the probability of detecting an animal, given
its distance from the line or point. The probability of detecting an animal in the
covered area is given by the mean value of the detection function with respect to
the available distances to be detected. Given this probability, a Horvitz-Thompson-
like estimator of abundance for the covered area follows, hence using a model-based
framework. Inferences for the wider survey region are justified using the survey design.
Conventional distance sampling methods are based on a set of assumptions. In
this thesis I present results that extend distance sampling on two fronts.
Firstly, estimators are derived for situations in which there is measurement error in
the distances. These estimators use information about the measurement error in two
ways: (1) a biased estimator based on the contaminated distances is multiplied by an
appropriate correction factor, which is a function of the errors (PDF approach), and
(2) cast into a likelihood framework that allows parameter estimation in the presence
of measurement error (likelihood approach).
Secondly, methods are developed that relax the conventional assumption that the
distribution of animals is independent of distance from the lines or points (usually
guaranteed by appropriate survey design). In particular, the new methods deal with
the case where animal density gradients are caused by the use of non-random sampler
allocation, for example transects placed along linear features such as roads or streams.
This is dealt with separately for line and point transects, and at a later stage an
approach for combining the two is presented.
A considerable number of simulations and example analysis illustrate the performance of the proposed methods.A Bayesian approach to modelling field data on multi-species predator prey-interactions
http://hdl.handle.net/10023/174
Multi-species functional response models are required to model the predation of generalist preda-
tors, which consume more than one prey species. In chapter 2, a new model for the multi-species
functional response is presented. This model can describe generalist predators that exhibit func-
tional responses of Holling type II to some of their prey and of type III to other prey. In chapter
3, I review some of the theoretical distinctions between Bayesian and frequentist statistics and
show how Bayesian statistics are particularly well-suited for the fitting of functional response
models because uncertainty can be represented comprehensively. In chapters 4 and 5, the multi-
species functional response model is fitted to field data on two generalist predators: the hen
harrier Circus cyaneus and the harp seal Phoca groenlandica. I am not aware of any previous
Bayesian model of the multi-species functional response that has been fitted to field data.
The hen harrier's functional response fitted in chapter 4 is strongly sigmoidal to the densities
of red grouse Lagopus lagopus scoticus, but no type III shape was detected in the response to
the two main prey species, field vole Microtus agrestis and meadow pipit Anthus pratensis. The
impact of using Bayesian or frequentist models on the resulting functional response is discussed.
In chapter 5, no functional response could be fitted to the data on harp seal predation. Possible
reasons are discussed, including poor data quality or a lack of relevance of the available data for
informing a behavioural functional response model.
I conclude with a comparison of the role that functional responses play in behavioural, population
and community ecology and emphasise the need for further research into unifying these different
approaches to understanding predation with particular reference to predator movement.
In an appendix, I evaluate the possibility of using a functional response for inferring the abun-
dances of prey species from performance indicators of generalist predators feeding on these prey.
I argue that this approach may be futile in general, because a generalist predator's energy intake
does not depend on the density of any single of its prey, so that the possibly unknown densities
of all prey need to be taken into account.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10023/1742006-01-01T00:00:00ZAsseburg, ChristianMulti-species functional response models are required to model the predation of generalist preda-
tors, which consume more than one prey species. In chapter 2, a new model for the multi-species
functional response is presented. This model can describe generalist predators that exhibit func-
tional responses of Holling type II to some of their prey and of type III to other prey. In chapter
3, I review some of the theoretical distinctions between Bayesian and frequentist statistics and
show how Bayesian statistics are particularly well-suited for the fitting of functional response
models because uncertainty can be represented comprehensively. In chapters 4 and 5, the multi-
species functional response model is fitted to field data on two generalist predators: the hen
harrier Circus cyaneus and the harp seal Phoca groenlandica. I am not aware of any previous
Bayesian model of the multi-species functional response that has been fitted to field data.
The hen harrier's functional response fitted in chapter 4 is strongly sigmoidal to the densities
of red grouse Lagopus lagopus scoticus, but no type III shape was detected in the response to
the two main prey species, field vole Microtus agrestis and meadow pipit Anthus pratensis. The
impact of using Bayesian or frequentist models on the resulting functional response is discussed.
In chapter 5, no functional response could be fitted to the data on harp seal predation. Possible
reasons are discussed, including poor data quality or a lack of relevance of the available data for
informing a behavioural functional response model.
I conclude with a comparison of the role that functional responses play in behavioural, population
and community ecology and emphasise the need for further research into unifying these different
approaches to understanding predation with particular reference to predator movement.
In an appendix, I evaluate the possibility of using a functional response for inferring the abun-
dances of prey species from performance indicators of generalist predators feeding on these prey.
I argue that this approach may be futile in general, because a generalist predator's energy intake
does not depend on the density of any single of its prey, so that the possibly unknown densities
of all prey need to be taken into account.Reconstruction of foliations from directional information
http://hdl.handle.net/10023/158
In many areas of science, especially geophysics, geography and
meteorology, the data are often directions or axes rather than
scalars or unrestricted vectors. Directional statistics considers
data which are mainly unit vectors lying in two- or
three-dimensional space (R² or R³). One
way in which directional data arise is as normals to foliations. A
(codimension-1) foliation of {R}^{d} is a system
of non-intersecting (d-1)-dimensional surfaces filling out the
whole of {R}^{d}. At each point z of {R}^{d}, any given codimension-1 foliation determines a
unit vector v normal to the surface through z.
The problem considered here is that of reconstructing the foliation
from observations ({z}{i}, {v}{i}), i=1,...,n. One
way of doing this is rather similar to fitting smooth splines to
data. That is, the reconstructed foliation has to be as close to the
data as possible, while the foliation itself is not too rough. A
tradeoff parameter is introduced to control the balance between
smoothness and
closeness. The approach used in this thesis is to take the surfaces to be
surfaces of constant values of a suitable real-valued function h
on {R}^{d}. The problem of reconstructing a foliation is
translated into the language of Schwartz distributions and a deep
result in the theory of distributions is used to give the
appropriate general form of the fitted function h. The model
parameters are estimated by a simplified Newton method. Under appropriate distributional assumptions on v{1},...,v{n}, confidence regions for the true normals
are developed and estimates of concentration are given.
Fri, 01 Jun 2007 00:00:00 GMThttp://hdl.handle.net/10023/1582007-06-01T00:00:00ZYeh, Shu-YingIn many areas of science, especially geophysics, geography and
meteorology, the data are often directions or axes rather than
scalars or unrestricted vectors. Directional statistics considers
data which are mainly unit vectors lying in two- or
three-dimensional space (R² or R³). One
way in which directional data arise is as normals to foliations. A
(codimension-1) foliation of {R}^{d} is a system
of non-intersecting (d-1)-dimensional surfaces filling out the
whole of {R}^{d}. At each point z of {R}^{d}, any given codimension-1 foliation determines a
unit vector v normal to the surface through z.
The problem considered here is that of reconstructing the foliation
from observations ({z}{i}, {v}{i}), i=1,...,n. One
way of doing this is rather similar to fitting smooth splines to
data. That is, the reconstructed foliation has to be as close to the
data as possible, while the foliation itself is not too rough. A
tradeoff parameter is introduced to control the balance between
smoothness and
closeness. The approach used in this thesis is to take the surfaces to be
surfaces of constant values of a suitable real-valued function h
on {R}^{d}. The problem of reconstructing a foliation is
translated into the language of Schwartz distributions and a deep
result in the theory of distributions is used to give the
appropriate general form of the fitted function h. The model
parameters are estimated by a simplified Newton method. Under appropriate distributional assumptions on v{1},...,v{n}, confidence regions for the true normals
are developed and estimates of concentration are given.