Varying-coefficient stochastic differential equations with applications in ecology

Theo Michelot*, Richard Glennie, Catriona M Harris, Len Thomas

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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.
Original languageEnglish
Number of pages18
JournalJournal of Agricultural, Biological and Environmental Statistics
VolumeFirst Online
Early online date26 Mar 2021
Publication statusE-pub ahead of print - 26 Mar 2021


  • Continuous time
  • Diffusion process
  • Non-parametric
  • Smoothing splines
  • Generalized additive models
  • Animal movement


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