Bayesian evidence estimation from posterior samples with normalizing flows
This method provides a more robust way to compute Bayesian evidence for researchers in fields like physics and statistics, though it is incremental as it builds on existing techniques like normalizing flows.
The authors tackled the problem of estimating Bayesian evidence from posterior samples by proposing a novel method called floZ based on normalizing flows, which demonstrated robustness to sharp features in up to 200 dimensions with 10^5 samples and showed good agreement with nested sampling in a gravitational wave application.
We propose a novel method ($floZ$), based on normalizing flows, to estimate the Bayesian evidence (and its numerical uncertainty) from a pre-existing 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. For a simple multivariate Gaussian, we demonstrate its accuracy for up to 200 dimensions with $10^5$ posterior samples. $floZ$ has wide applicability, e.g., to estimate evidence from variational inference, Markov Chain Monte Carlo samples, or any other method that delivers samples and their likelihood from the unnormalized posterior density. As a physical application, we use $floZ$ to compute the Bayes factor for the presence of the first overtone in the ringdown signal of the gravitational wave data of GW150914, finding good agreement with nested sampling.