Convergence of Regression Adjusted Approximate Bayesian Computation

TL;DR

This paper provides asymptotic analysis of regression-adjusted approximate Bayesian computation, showing that with proper bandwidth selection, it accurately quantifies uncertainty and enables efficient sampling as data size grows.

Contribution

It demonstrates that regression adjustment in ABC yields correct uncertainty quantification asymptotically with optimal bandwidth, improving sampling efficiency.

Findings

Regression adjustment leads to correct uncertainty quantification asymptotically.

Proper bandwidth choice results in acceptance probability approaching one.

Standard ABC requires smaller bandwidths, reducing efficiency.

Abstract

We present asymptotic results for the regression-adjusted version of approximate Bayesian computation introduced by Beaumont(2002). We show that for an appropriate choice of the bandwidth, regression adjustment will lead to a posterior that, asymptotically, correctly quantifies uncertainty. Furthermore, for such a choice of bandwidth we can implement an importance sampling algorithm to sample from the posterior whose acceptance probability tends to unity as the data sample size increases. This compares favourably to results for standard approximate Bayesian computation, where the only way to obtain a posterior that correctly quantifies uncertainty is to choose a much smaller bandwidth; one for which the acceptance probability tends to zero and hence for which Monte Carlo error will dominate.