# Asymptotics of ABC

## TL;DR

This paper reviews recent theoretical insights into the asymptotic behavior of Approximate Bayesian Computation (ABC), highlighting its strengths in point estimation and challenges in uncertainty quantification, with practical implementation guidance.

## Contribution

It provides an informal review of recent asymptotic results for ABC, emphasizing the impact of different implementations on uncertainty estimation.

## Key findings

- ABC performs well in point estimation with more data.
- Standard ABC overestimates parameter uncertainty.
- Regression correction improves uncertainty quantification.

## Abstract

We present an informal review of recent work on the asymptotics of Approximate Bayesian Computation (ABC). In particular we focus on how does the ABC posterior, or point estimates obtained by ABC, behave in the limit as we have more data? The results we review show that ABC can perform well in terms of point estimation, but standard implementations will over-estimate the uncertainty about the parameters. If we use the regression correction of Beaumont et al. then ABC can also accurately quantify this uncertainty. The theoretical results also have practical implications for how to implement ABC.