BibTeX

@article{2505.23261v3,
Author        = {Carlo Albert and Simone Ulzega and Simon Dirmeier and Andreas Scheidegger and Alberto Bassi and Antonietta Mira},
Title         = {A thermodynamic approach to Approximate Bayesian Computation with multiple summary statistics},
Eprint        = {2505.23261v3},
ArchivePrefix = {arXiv},
PrimaryClass  = {stat.CO},
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.},
Year          = {2025},
Month         = {May},
Url           = {http://arxiv.org/abs/2505.23261v3},
File          = {2505.23261v3.pdf}
}