Notes to Robert et al.: Model criticism informs model choice and model comparison

TL;DR

This paper defends the use of Approximate Bayesian Computation with model uncertainty (ABCmu) for model criticism, clarifying its Bayesian validity and utility in comparing models when likelihoods are intractable.

Contribution

The authors clarify and defend the Bayesian foundations of ABCmu, demonstrating its effectiveness for model criticism and comparison in complex scenarios.

Findings

ABCmu is a valid Bayesian method for model criticism.

ABCmu effectively compares models without explicit likelihoods.

The utility of ABCmu in practical model assessment is highlighted.

Abstract

In their letter to PNAS and a comprehensive set of notes on arXiv [arXiv:0909.5673v2], Christian Robert, Kerrie Mengersen and Carla Chen (RMC) represent our approach to model criticism in situations when the likelihood cannot be computed as a way to "contrast several models with each other". In addition, RMC argue that model assessment with Approximate Bayesian Computation under model uncertainty (ABCmu) is unduly challenging and question its Bayesian foundations. We disagree, and clarify that ABCmu is a probabilistically sound and powerful too for criticizing a model against aspects of the observed data, and discuss further the utility of ABCmu.