On predictive inference for intractable models via approximate Bayesian computation

TL;DR

This paper explores the use of approximate Bayesian computation (ABC) for predictive inference in intractable models, focusing on methods to estimate future data distributions and introducing novel summary statistic choices.

Contribution

It introduces three ABC approaches for predictive inference, emphasizing minimal predictive sufficient statistics and latent variable representations, expanding ABC's applicability.

Findings

ABC can be effectively used for predictive inference in intractable models.

Minimal predictive sufficient statistics outperform traditional minimal sufficient statistics in ABC prediction.

ABC algorithms are adaptable for different intractable dynamic models.

Abstract

Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility of ABC as a generic approximate method for predictive inference, in particular, for computing the posterior predictive distribution of future observations or missing data of interest. We consider three complementary ABC approaches for this goal, each based on different assumptions regarding which predictive density of the intractable model can be sampled from. The case where only simulation from the joint density of the observed and future data given the model parameters can be used for inference is given particular attention and it is shown that the ideal summary statistic in this setting is minimal predictive sufficient instead of merely minimal sufficient (in the ordinary sense). An ABC prediction approach that takes advantage of a certain latent variable representation is also investigated. We additionally show how common ABC sampling algorithms can be used in the predictive settings considered. Our main results are first illustrated by using simple time-series models that facilitate analytical treatment, and later by using two common intractable dynamic models.