TY - JOUR
T1 - Varying-coefficient stochastic differential equations with applications in ecology
AU - Michelot, Theo
AU - Glennie, Richard
AU - Harris, Catriona M
AU - Thomas, Len
N1 - This work was funded by the US office of Naval Research, Grant N000141812807.
PY - 2021/3/26
Y1 - 2021/3/26
N2 - 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.
AB - 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.
KW - Continuous time
KW - Diffusion process
KW - Non-parametric
KW - Smoothing splines
KW - Generalized additive models
KW - Animal movement
UR - https://link.springer.com/article/10.1007/s13253-021-00450-6#Sec14
U2 - 10.1007/s13253-021-00450-6
DO - 10.1007/s13253-021-00450-6
M3 - Article
SN - 1085-7117
VL - First Online
JO - Journal of Agricultural, Biological and Environmental Statistics
JF - Journal of Agricultural, Biological and Environmental Statistics
ER -