Normalizing Constant Estimation with Gaussianized Bridge Sampling
This addresses the challenge of accurate and efficient normalizing constant estimation for Bayesian practitioners, representing a strong specific gain rather than a foundational advancement.
The paper tackled the problem of estimating normalizing constants in Bayesian inference, which is often expensive and inaccurate, by developing Gaussianized Bridge Sampling (GBS), a method that uses normalizing flows and optimal bridge sampling on MCMC samples. The result showed that GBS is significantly faster and substantially more accurate than existing methods like Nested Sampling and Annealed Importance Sampling, with reliable error estimation.
Normalizing constant (also called partition function, Bayesian evidence, or marginal likelihood) is one of the central goals of Bayesian inference, yet most of the existing methods are both expensive and inaccurate. Here we develop a new approach, starting from posterior samples obtained with a standard Markov Chain Monte Carlo (MCMC). We apply a novel Normalizing Flow (NF) approach to obtain an analytic density estimator from these samples, followed by Optimal Bridge Sampling (OBS) to obtain the normalizing constant. We compare our method which we call Gaussianized Bridge Sampling (GBS) to existing methods such as Nested Sampling (NS) and Annealed Importance Sampling (AIS) on several examples, showing our method is both significantly faster and substantially more accurate than these methods, and comes with a reliable error estimation.