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 $\mathsf{MorphZ}$, which serves as a postprocessing 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 models, compact binary coalescence gravitational wave (GW) simulations, and the GW150914 event. Across these applications, spanning low to high dimensionalities, $\mathsf{MorphZ}$ 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, $\mathsf{MorphZ}$ has proven to either resolve the estimation failure or significantly improve the results. Its bridge sampling relative error diagnostic provides conservative uncertainty estimates. Because $\mathsf{MorphZ}$ 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 work flows.

Close

PrevNext

View figure in article

• Gravitational wave detection
• Gravitational waves
• Neutron stars & pulsars
• Bayesian methods