A comparison of inferential methods for highly non-linear state space models in ecology and epidemiology

TL;DR

This paper compares information reduction and state space methods for inference in highly non-linear, chaotic models in ecology and epidemiology, highlighting their strengths, limitations, and practical recommendations.

Contribution

It provides a comprehensive comparison of inference methods for chaotic models, guiding practitioners on method selection and practical implementation.

Findings

State space methods can face multimodality issues with low process noise.

Information reduction methods avoid multimodality but are less sharp with low noise.

Switching from information reduction to state space methods improves inference accuracy.

Abstract

Highly non-linear, chaotic or near chaotic, dynamic models are important in fields such as ecology and epidemiology: for example, pest species and diseases often display highly non-linear dynamics. However, such models are problematic from the point of view of statistical inference. The defining feature of chaotic and near chaotic systems is extreme sensitivity to small changes in system states and parameters, and this can interfere with inference. There are two main classes of methods for circumventing these difficulties: information reduction approaches, such as Approximate Bayesian Computation or Synthetic Likelihood and state space methods, such as Particle Markov chain Monte Carlo, Iterated Filtering or Parameter Cascading. The purpose of this article is to compare the methods, in order to reach conclusions about how to approach inference with such models in practice. We show that neither class of methods is universally superior to the other. We show that state space methods can suffer multimodality problems in settings with low process noise or model mis-specification, leading to bias toward stable dynamics and high process noise. Information reduction methods avoid this problem but, under the correct model and with sufficient process noise, state space methods lead to substantially sharper inference than information reduction methods. More practically, there are also differences in the tuning requirements of different methods. Our overall conclusion is that model development and checking should probably be performed using an information reduction method with low tuning requirements, while for final inference it is likely to be better to switch to a state space method, checking results against the information reduction approach.