Improving approximate Bayesian computation via quasi-Monte Carlo

TL;DR

This paper introduces quasi-Monte Carlo methods into approximate Bayesian computation, reducing variance and improving efficiency in likelihood-free inference through novel algorithms and adaptive techniques.

Contribution

It develops QMC-based ABC algorithms, including sequential variants, that outperform traditional Monte Carlo methods in variance reduction and efficiency.

Findings

QMC ABC estimates have lower variance than Monte Carlo counterparts.

QMC variants improve the efficiency of sequential ABC algorithms.

Numerical examples demonstrate the effectiveness of the proposed methods.

Abstract

ABC (approximate Bayesian computation) is a general approach for dealing with models with an intractable likelihood. In this work, we derive ABC algorithms based on QMC (quasi- Monte Carlo) sequences. We show that the resulting ABC estimates have a lower variance than their Monte Carlo counter-parts. We also develop QMC variants of sequential ABC algorithms, which progressively adapt the proposal distribution and the acceptance threshold. We illustrate our QMC approach through several examples taken from the ABC literature. Keywords: Approximate Bayesian computation, Likelihood-free inference, Quasi Monte Carlo, Randomized Quasi-Monte Carlo, Adaptive importance sampling