Parameter Inference and Model Selection in Deterministic and Stochastic Dynamical Models via Approximate Bayesian Computation

• Activity Number: 398
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Libo Sun*+ and Chihoon Lee and Jennifer A. Hoeting
• Companies: Colorado State University and Colorado State University and Colorado State University
• Keywords: Approximate Bayesian computation ; Chronic wasting disease ; Parameter inference ; Model selection ; Ordinary and Stochastic differential equation ; Continuous time Markov chain

Abstract

We consider the problem of selecting deterministic or stochastic models for 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 of dynamical models, likelihood based approaches for model selecting are not suitable. We illustrate a model selection example on a real world dataset, two epidemics of chronic wasting disease in mule deer, via an approximate Bayesian computation method. 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 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.