Bayesian Model Selection Methods and Their Application to Biological ODE Systems

Abstract

In this chapter, we focus on Bayesian model selection for biological dynamical systems. We do not present an overview over existing methods, but showcase their comparison and the application to ordinary differential equation (ODE) systems, as well as the inference of the parameters in the ODE system. For this, our method of choice is the Bayes factor, computed by Thermodynamic Integration. We first present several model selection methods, both alternatives to the Bayes factor as well as several methods for calculating the Bayes factor, foremost among them said Thermodynamic Integration. As a simple example for the selection problem, we resort to a choice between normal distributions, which is analytically tractable. We apply our chosen method to a medium sized ODE model selection problem from radiation science and demonstrate how predictions can be drawn from the model selection results.