Generalized Posteriors in Approximate Bayesian Computation

Abstract

Complex simulators have become a ubiquitous tool in many scientific disciplines, providing high-fidelity, implicit probabilistic models of natural and social phenomena. Unfortunately, they typically lack the tractability required for conventional statistical analysis. Approximate Bayesian computation (ABC) has emerged as a key method in simulation-based inference, wherein the true model likelihood and posterior are approximated using samples from the simulator. In this paper, we draw connections between ABC and generalized Bayesian inference (GBI). First, we re-interpret the accept/reject step in ABC as an implicitly defined error model. We then argue that these implicit error models will invariably be misspecified. While ABC posteriors are often treated as a necessary evil for approximating the standard Bayesian posterior, this allows us to re-interpret ABC as a potential robustification strategy. This leads us to suggest the use of GBI within ABC, a use case we explore empirically.

Accepted at Advances in Approximate Bayesian Inference, AABI 2020

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• Approximating Bayes in the 21st Century
• Computing Bayes: From Then 'Til Now'
• Approximate Bayesian Computation via Classification
• Approximate Bayesian Computation with Path Signatures
• Discrepancy-based Inference for Intractable Generative Models using Quasi-Monte Carlo
• Approximate Bayesian inference from noisy likelihoods with Gaussian process emulated MCMC