Considerate Approaches to Achieving Sufficiency for ABC model selection

TL;DR

This paper introduces an information-theoretic method to construct approximately sufficient statistics for ABC model selection, improving the accuracy of inference when likelihood evaluation is infeasible.

Contribution

It proposes a novel framework for building sufficient statistics in ABC by minimizing information loss, applicable to both parameter estimation and model selection.

Findings

Constructed approximately sufficient statistics for various problems

Reduced information loss in ABC model selection

Enhanced accuracy in model inference

Abstract

For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations from a model, but cannot evaluate the likelihood directly. When summary statistics of real and simulated data are compared --- rather than the data directly --- information is lost, unless the summary statistics are sufficient. Here we employ an information-theoretical framework that can be used to construct (approximately) sufficient statistics by combining different statistics until the loss of information is minimized. Such sufficient sets of statistics are constructed for both parameter estimation and model selection problems. We apply our approach to a range of illustrative and real-world model selection problems.