A Comparison of Kernels for ABC-SMC

TL;DR

This paper reviews various Markov kernels used in ABC-SMC algorithms, introduces new options, and empirically compares them to recommend the most effective kernel for likelihood-free inference.

Contribution

The paper provides a comprehensive review of kernels for ABC-SMC, proposes novel kernel options, and offers empirical evidence to guide default kernel selection.

Findings

One-hit kernel with mixture proposal performs best

Less known kernels can be competitive or superior

Empirical comparison guides kernel choice in ABC-SMC

Abstract

A popular method for likelihood-free inference is approximate Bayesian computation sequential Monte Carlo (ABC-SMC) algorithms. These approximate the posterior using a population of particles, which are updated using Markov kernels. Several such kernels have been proposed. In this paper we review these, highlighting some less well known choices, and proposing some novel options. Further, we conduct an extensive empirical comparison of kernel choices. Our results suggest using a one-hit kernel with a mixture proposal as a default choice.