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

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 judgement. 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.