Likelihood-free MCMC with Amortized Approximate Ratio Estimators

TL;DR

This paper introduces a novel likelihood-free MCMC method that uses an amortized ratio estimator to efficiently sample from intractable posteriors, demonstrating improved accuracy and stability on benchmarks and physics applications.

Contribution

It proposes a new approach combining amortized ratio estimation with MCMC to handle intractable likelihoods in Bayesian inference.

Findings

Accurately approximates likelihood ratios in complex models.

Improves numerical stability in likelihood-free MCMC.

Demonstrates effectiveness on benchmarks and physics problems.

Abstract

Posterior inference with an intractable likelihood is becoming an increasingly common task in scientific domains which rely on sophisticated computer simulations. Typically, these forward models do not admit tractable densities forcing practitioners to make use of approximations. This work introduces a novel approach to address the intractability of the likelihood and the marginal model. We achieve this by learning a flexible amortized estimator which approximates the likelihood-to-evidence ratio. We demonstrate that the learned ratio estimator can be embedded in MCMC samplers to approximate likelihood-ratios between consecutive states in the Markov chain, allowing us to draw samples from the intractable posterior. Techniques are presented to improve the numerical stability and to measure the quality of an approximation. The accuracy of our approach is demonstrated on a variety of benchmarks against well-established techniques. Scientific applications in physics show its applicability.