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

摘要

We consider the problem of selecting deterministic or stochastic models for abiological, ecological, or environmental dynamical process. In most cases, oneprefers either deterministic or stochastic models as candidate models based onexperience or subjective judgment. Due to the complex or intractable likelihoodin most dynamical models, likelihood-based approaches for model selection arenot suitable. We use approximate Bayesian computation for parameter estimationand model selection to gain further understanding of the dynamics of twoepidemics of chronic wasting disease in mule deer. The main novel contributionof this work is that under a hierarchical model framework we compare threetypes of dynamical models: ordinary differential equation, continuous timeMarkov chain, and stochastic differential equation models. To our knowledgemodel selection between these types of models has not appeared previously.Since the practice of incorporating dynamical models into data models isbecoming more common, the proposed approach may be very useful in a variety ofapplications.