On Model Selection with Summary Statistics

TL;DR

This paper investigates the limitations of ABC model choice with sufficient statistics and proposes a method to recover the posterior normalizing constant without likelihood, applicable even with approximate summaries.

Contribution

It introduces a novel approach to recover the posterior normalizing constant in ABC, addressing issues with sufficient statistics in model selection.

Findings

Using sufficient statistics can lead to unreliable ABC model choice results.

The method can recover the posterior normalizing constant without likelihood.

Approximate methods extend applicability to realistic scenarios.

Abstract

Recently, many authors have cast doubts on the validity of ABC model choice. It has been shown that the use of sufficient statistic in ABC model selection leads, apart from few exceptional cases in which the sufficient statistic is also cross-model sufficient, to unreliable results. In a single model context and given a sufficient summary statistic, we show that it is possible to fully recover the posterior normalising constant, without using the likelihood function. The idea can be applied, in an approximate way, to more realistic scenarios in which the sufficient statistic is not unavailable but a "good" summary statistic for estimation is available.