Gaussian Markov random fields and structural additive regression : applications in freshwater fisheries management
Abstract
In this thesis structural additive regression (STAR) models are constructed for two
applications in freshwater fisheries management 1) large scale modelling of fish
abundance using electrofishing removal data and 2) assessing the effect on stream
temperature of tree felling. Both approaches take advantage of the central role
Gaussian Markov random fields (GMRFs) play in the construction of structured
additive regression components.
The R package mgcv can fit, in principle, any STAR model. In practice, however,
several extensions are required to allow a non-specialised user to access this functionality,
and a large part of this thesis is the developement of software to allow a
general user ready access to a wide range of GMRF models within the familiar mgcv
framework. All models are fitted making use of this extension where possible (and
practical).
The thesis is divided into three main chapters. Chapter 2 serves to provide background
and insight into penalised regression and STAR models and the role that GMRFs
play in smoothing. Also presented are the extensions required to fit GMRF models
in mgcv.
Chapter 3 presents a two stage model for fish density using electrofishing removal
data. The first stage of this model estimates fish capture probability and is not a
STAR model, but can utilise aspects of GMRFs through low rank approximations;
software to make this available is developed and presented. The second stage is a
Poisson STAR model and can therefore be fitted in the extended mgcv framework.
Finally, Chapter 4 presents a model for the impact of a clear felling event on stream
temperature. This model utilises cyclic smoothers applied to the functional principal
components of daily temperature curves. This allows for a detailed assessment of the
effects of felling on stream temperature that is not possible when modelling daily
summaries alone.
Type
Thesis, PhD Doctor of Philosophy
Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.