The Use of a Single Pseudo-Sample in Approximate Bayesian Computation

TL;DR

This paper demonstrates that using a single pseudo-sample in approximate Bayesian computation (ABC), including ABC-MCMC, is as efficient as using multiple samples, simplifying implementation without sacrificing performance.

Contribution

The paper proves that increasing pseudo-samples in ABC-MCMC does not improve efficiency, contrasting with particle MCMC methods, and suggests no need to tune pseudo-sample size.

Findings

Single pseudo-sample suffices for efficient ABC-MCMC

Multiple pseudo-samples do not significantly improve efficiency in ABC

Contrast with particle MCMC where more particles help

Abstract

We analyze the computational efficiency of approximate Bayesian computation (ABC), which approximates a likelihood function by drawing pseudo-samples from the associated model. For the rejection sampling version of ABC, it is known that multiple pseudo-samples cannot substantially increase (and can substantially decrease) the efficiency of the algorithm as compared to employing a high-variance estimate based on a single pseudo-sample. We show that this conclusion also holds for a Markov chain Monte Carlo version of ABC, implying that it is unnecessary to tune the number of pseudo-samples used in ABC-MCMC. This conclusion is in contrast to particle MCMC methods, for which increasing the number of particles can provide large gains in computational efficiency.