Likelihood-free MCMC with Amortized Approximate Ratio Estimators
This addresses a common challenge in scientific domains relying on computer simulations, offering a novel method for likelihood-free inference, though it appears incremental as it builds on existing MCMC and ratio estimation techniques.
The paper tackles the problem of posterior inference with intractable likelihoods in scientific simulations by introducing an amortized estimator for the likelihood-to-evidence ratio, which is embedded in MCMC samplers to draw samples from the posterior, demonstrating accuracy on benchmarks and applicability in physics.
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.