  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.
