State‐space models for ecological time‐series data: Practical model‐fitting

Abstract

Abstract State‐space models are an increasingly common and important tool in the quantitative ecologists’ armoury, particularly for the analysis of time‐series data. This is due to both their flexibility and intuitive structure, describing the different individual processes of a complex system, thus simplifying the model specification step. State‐space models are composed of two processes (a) the system (or state) process that describes the dynamics of the true underlying state of the system over time; and (b) the observation process that links the observed data with the current true state of the system at that time. Specification of the general model structure consists of considering each distinct ecological process within the system and observation processes, which are then automatically combined within the state‐space structure. There is typically a trade‐off between the complexity of the model and the associated model‐fitting process. Simpler model specifications permit the application of simpler model‐fitting tools; whereas more complex model specifications, with nonlinear dynamics and/or non‐Gaussian stochasticity often require more sophisticated model‐fitting algorithms to be applied. We provide a brief overview of general state‐space models before focusing on the different model‐fitting tools available. In particular for different general state‐space model structures we discuss established model‐fitting tools that are available. We also offer practical guidance for choosing a specific fitting procedure.

Keywords

• hidden Markov model
• Kalman filter
• Laplace approximation
• likelihood‐free methods
• Markov chain Monte Carlo
• sampling‐based methods