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

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.

Considerate approaches to constructing summary statistics for ABC model selection

“…It is, of course, in principle possible to use the KL divergence with respect to the distribution obtained with the full data as an overall benchmark, but in cases where this is indeed possible, it may be best to use the full data (see e.g. Toni et al (2009)) for inference rather than risk the information reduction inherent to most summary statistics.…”

A tutorial introduction to Bayesian inference for stochastic epidemic models using Approximate Bayesian Computation

“…In this paper we concentrate on the widely used algorithm of Toni et al (2009), Algorithm 4. This effectively performs repeated importance sampling, also known as population Monte Carlo (Cappé et al, 2004).…”

“…The key difference to the ABC-PMC algorithm of Toni et al (2009) is that we have to take account of the weight for the set of ϕ values in the coupled simulation which will result in a simulation being accepted. For the household epidemic moments of λ G can easily be estimated from {(A (i) , w (i) T )} with a consistent estimate of E[h(λ G )|x * ] provided by…”

“…We again consider the ABC algorithm but instead of using the computationally intensive coupled ABC algorithm of Neal (2012) we introduce a partially coupled version of the algorithm, which offers substantive gains over the ABC algorithm for very little additional complexity in coding and implementation over the ABC algorithm. We apply the algorithms along with ABC-PMC versions (Toni et al, 2009) to a range of data sets demonstrating the significant improvements that both ABC-PMC and the coupled ABC algorithm offer over the vanilla ABC.…”

A Subordinated Stochastic Process Model

“…We illustrate this approach with a naive example. We apply the ABC method to the real bacterial data of 2 to estimate the parameters of the time change function and the intensity rate (see [5]) . The simplest rejection-ABC algorithm was implemented, assuming informative prior distributions for the Gompertz parameters.…”