Parameter inference and model selection in deterministic and stochastic dynamical models via approximate Bayesian computation: modeling a wildlife epidemic

TL;DR

This paper introduces a hierarchical approximate Bayesian computation approach to compare deterministic and stochastic dynamical models, specifically applied to wildlife epidemic data, enabling model selection where likelihoods are complex or intractable.

Contribution

It presents a novel method for comparing ODE, CTMC, and SDE models within a hierarchical framework, addressing a gap in model selection techniques for complex dynamical systems.

Findings

Successfully distinguished between model types in epidemic data

Demonstrated the approach's applicability to ecological models

Provided insights into disease dynamics in mule deer

Abstract

We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on experience or subjective judgment. Due to the complex or intractable likelihood in most dynamical models, likelihood-based approaches for model selection are not suitable. We use approximate Bayesian computation for parameter estimation and model selection to gain further understanding of the dynamics of two epidemics of chronic wasting disease in mule deer. The main novel contribution of this work is that under a hierarchical model framework we compare three types of dynamical models: ordinary differential equation, continuous time Markov chain, and stochastic differential equation models. To our knowledge model selection between these types of models has not appeared previously. Since the practice of incorporating dynamical models into data models is becoming more common, the proposed approach may be very useful in a variety of applications.