Varying-coefficient stochastic differential equations with applications in ecology

TL;DR

This paper introduces a flexible, non-parametric approach to stochastic differential equations with time-varying parameters, enhancing modeling of non-stationary ecological data while maintaining interpretability.

Contribution

It develops a novel method combining SDEs with non-parametric functions for parameters, enabling detailed modeling of non-stationary processes in ecology.

Findings

The method effectively captures complex ecological dynamics.

Applications demonstrate improved modeling flexibility.

Computational efficiency allows practical use in ecological studies.

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 phenomeon 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 non-parametric functions of covariates, similar to generalized additive models. Combining the SDEs and non-parametric 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.