Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems

TLDR

ABC methods estimate posterior distributions without explicit likelihood calculations. The study applies ABC SMC to estimate dynamical model parameters and to select the best model among alternatives. ABC SMC is implemented using sequential Monte Carlo and applied to several biological systems to infer parameters and credible intervals. ABC SMC yields insights into parameter inferability and model sensitivity, outperforming other ABC methods.

Abstract

Approximate Bayesian computation (ABC) methods can be used to evaluate posterior distributions without having to calculate likelihoods. In this paper, we discuss and apply an ABC method based on sequential Monte Carlo (SMC) to estimate parameters of dynamical models. We show that ABC SMC provides information about the inferability of parameters and model sensitivity to changes in parameters, and tends to perform better than other ABC approaches. The algorithm is applied to several well-known biological systems, for which parameters and their credible intervals are inferred. Moreover, we develop ABC SMC as a tool for model selection; given a range of different mathematical descriptions, ABC SMC is able to choose the best model using the standard Bayesian model selection apparatus.