Model Comparison in Approximate Bayesian Computation

TL;DR

This paper introduces an efficient method for Bayesian model comparison in Approximate Bayesian Computation, using a mixture-density network to estimate model posterior probabilities, demonstrated on biological models.

Contribution

The paper presents a novel, computationally efficient approach to Bayesian model comparison in ABC using posterior density estimation with neural networks.

Findings

Accurately predicts posterior model probabilities on a tractable problem.

Reliably identifies the true model in a neuroscience application.

Provides a scalable method independent of model complexity.

Abstract

A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for the data. However, this framework relies on the calculation of likelihood functions which are intractable for most models used in practice. Previous approaches in the field of Approximate Bayesian Computation (ABC) circumvent the evaluation of the likelihood and estimate the model evidence based on rejection sampling, but they are typically computationally intense. Here, I propose a new efficient method to perform Bayesian model comparison in ABC. Based on recent advances in posterior density estimation, the method approximates the posterior over models in parametric form. In particular, I train a mixture-density network to map features of the observed data to the posterior probability of the models. The performance is assessed with two examples. On a tractable model comparison problem, the underlying exact posterior probabilities are predicted accurately. In a use-case scenario from computational neuroscience -- the comparison between two ion channel models -- the underlying ground-truth model is reliably assigned a high posterior probability. Overall, the method provides a new efficient way to perform Bayesian model comparison on complex biophysical models independent of the model architecture.