Varying-coefficient stochastic differential equations with applications in ecology
Abstract
Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomenon of interest, and their parameters often have a clear interpretation. These advantages come at the cost of requiring a relatively simple model specification. We propose a flexible model for SDEs with time-varying dynamics where the parameters of the process are nonparametric functions of covariates, similar to generalized additive models. Combining the SDE and nonparametric approaches allows for the SDE to capture more detailed, non-stationary, features of the data-generating process. We present a computationally efficient method of approximate inference, where the SDE parameters can vary according to fixed covariate effects, random effects, or basis-penalty smoothing splines. We demonstrate the versatility and utility of this approach with three applications in ecology, where there is often a modelling trade-off between interpretability and flexibility.
Citation
Michelot , T , Glennie , R , Harris , C M & Thomas , L 2021 , ' Varying-coefficient stochastic differential equations with applications in ecology ' , Journal of Agricultural, Biological and Environmental Statistics , vol. First Online . https://doi.org/10.1007/s13253-021-00450-6
Publication
Journal of Agricultural, Biological and Environmental Statistics
Status
Peer reviewed
ISSN
1085-7117Type
Journal article
Rights
Copyright © 2021 The Author(s). Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Description
This work was funded by the US office of Naval Research, Grant N000141812807.Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.