A thermodynamic approach to Approximate Bayesian Computation with multiple summary statistics
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911589954748416 |
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| author | Albert, Carlo Ulzega, Simone Dirmeier, Simon Scheidegger, Andreas Bassi, Alberto Mira, Antonietta |
| author_facet | Albert, Carlo Ulzega, Simone Dirmeier, Simon Scheidegger, Andreas Bassi, Alberto Mira, Antonietta |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A thermodynamic approach to Approximate Bayesian Computation with multiple summary statistics Albert, Carlo Ulzega, Simone Dirmeier, Simon Scheidegger, Andreas Bassi, Alberto Mira, Antonietta Computation 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. |
| title | A thermodynamic approach to Approximate Bayesian Computation with multiple summary statistics |
| topic | Computation |
| url | https://arxiv.org/abs/2505.23261 |