A thermodynamic approach to Approximate Bayesian Computation with multiple summary statistics

TL;DR

This paper introduces a thermodynamic-inspired variant of ABC algorithms that optimizes the use of multiple summary statistics, improving inference efficiency and accuracy.

Contribution

It develops a novel annealing schedule based on non-equilibrium thermodynamics and minimal-entropy-production principles for ABC with multiple summary statistics.

Findings

The method is highly competitive with state-of-the-art ABC algorithms.

It effectively handles high-dimensional summary statistics.

Validated on benchmark and real-world inference problems.

Abstract

Bayesian inference with stochastic models is often difficult because their likelihood functions involve high-dimensional integrals. Approximate Bayesian Computation (ABC) avoids evaluating the likelihood function and instead infers model parameters by comparing model simulations with observations using a few carefully chosen summary statistics and a tolerance that can be decreased over time. Here, we present a new variant of simulated-annealing ABC algorithms, drawing intuition from non-equilibrium thermodynamics. We associate each summary statistic with a state variable (energy) quantifying its distance from the observed value, as well as a temperature that controls the extent to which the statistic contributes to the posterior. We derive an optimal annealing schedule on a Riemannian manifold of state variables based on a minimal-entropy-production principle. We validate our approach on standard benchmark tasks from the simulation-based inference literature as well as on challenging real-world inference problems, and show that it is highly competitive with the state of the art.