Enhancing evidence estimation through informed probability density approximation

TL;DR

This paper introduces MorphZ, a novel, efficient method for evidence estimation that uses posterior samples and improves accuracy and reliability across various complex statistical models and real-world gravitational-wave data.

Contribution

The paper presents MorphZ, a new posterior-based importance sampling method that enhances evidence estimation accuracy and reduces computational costs in high-dimensional Bayesian inference.

Findings

MorphZ achieves accurate evidence estimates across diverse benchmarks.

It reduces computational costs compared to standard methods.

It improves or resolves estimation failures in challenging scenarios.

Abstract

We introduce the Morph approximation, a class of product approximations of probability densities that selects low-order disjoint parameter blocks by maximizing the sum of their total correlations. We use the posterior approximation via Morph as the importance distribution in optimal bridge sampling. We denote this procedure by MorphZ, which serves as a post-processing estimator of the marginal likelihood. The MorphZ estimator requires only posterior samples, and is fully agnostic regarding the choice of sampler. We evaluate MorphZ's performance across statistical benchmarks, pulsar timing array (PTA) models, compact binary coalescence (CBC) gravitational-wave (GW) simulations and the GW150914 event. Across these applications, spanning low to high dimensionalities, MorphZ yields accurate evidence estimates at substantially reduced computational cost relative to standard approaches. We have found that when these approaches fail to provide accurate estimates, MorphZ has proven to either resolve the estimation failure or significantly improve the results. Its bridge sampling relative error diagnostic provides conservative uncertainty estimates. Because MorphZ operates directly on posterior draws, it complements exploration-oriented samplers by enabling fast and reliable evidence estimation, while it can be seamlessly integrated into existing inference workflows.