floZ: Evidence estimation from posterior samples with normalizing flows
Rahul Srinivasan Marco Crisostomi Roberto Trotta Enrico Barausse Matteo Breschi
We propose a novel method (floZ), based on normalizing flows, for estimating
the Bayesian evidence (and its numerical uncertainty) from a set of samples
drawn from the unnormalized posterior distribution. We validate it on
distributions whose evidence is known analytically, up to 15 parameter space
dimensions, and compare with two state-of-the-art techniques for estimating the
evidence: nested sampling (which computes the evidence as its main target) and
a k-nearest-neighbors technique that produces evidence estimates from posterior
samples. Provided representative samples from the target posterior are
available, our method is more robust to posterior distributions with sharp
features, especially in higher dimensions. It has wide applicability, e.g., to
estimate the evidence from variational inference, Markov-chain Monte Carlo
samples, or any other method that delivers samples from the unnormalized
posterior density.