Approximate Bayesian Computation via Population Monte Carlo and Classification

TL;DR

This paper introduces Classification-PMC, a novel likelihood-free inference method that combines population Monte Carlo with classification to efficiently sample from complex posterior distributions, reducing subjectivity and improving performance.

Contribution

The paper proposes a new classification-based approach called Classification-PMC that integrates adaptive proposals with classification for likelihood-free Bayesian inference.

Findings

Classification-PMC outperforms existing methods in simulation studies.

It efficiently produces posterior samples without subjective choices.

The method is particularly effective when likelihood simulations are computationally expensive.

Abstract

Approximate Bayesian computation (ABC) methods can be used to sample from posterior distributions when the likelihood function is unavailable or intractable, as is often the case in biological systems. ABC methods suffer from inefficient particle proposals in high dimensions, and subjectivity in the choice of summary statistics, discrepancy measure, and error tolerance. Sequential Monte Carlo (SMC) methods have been combined with ABC to improve the efficiency of particle proposals, but suffer from subjectivity and require many simulations from the likelihood function. Likelihood-Free Inference by Ratio Estimation (LFIRE) leverages classification to estimate the posterior density directly but does not explore the parameter space efficiently. This work proposes a classification approach that approximates population Monte Carlo (PMC), where model class probabilities from classification are used to update particle weights. This approach, called Classification-PMC, blends adaptive proposals and classification, efficiently producing samples from the posterior without subjectivity. We show through a simulation study that Classification-PMC outperforms two state-of-the-art methods: ratio estimation and SMC ABC when it is computationally difficult to simulate from the likelihood.