PolyStan: PolyChord nested sampling and Bayesian evidences for Stan models

TL;DR

PolyStan integrates PolyChord nested sampling with Stan, enabling robust sampling from complex distributions and accurate marginal likelihood estimation, thus broadening Stan's capabilities for challenging Bayesian inference problems.

Contribution

It introduces PolyStan, a novel interface combining PolyChord nested sampling with Stan, providing a black-box solution for complex distribution sampling and evidence computation.

Findings

Robust nested sampling performance on degenerate problems

Effective comparison with bridge sampling and HMC

Enhanced Bayesian inference capabilities in Stan

Abstract

Sampling from multi-modal distributions and estimating marginal likelihoods, also known as evidences and normalizing constants, are well-known challenges in statistical computation. They can be overcome by nested sampling, which evolves a set of live points through a sequence of distributions upwards in likelihood. We introduce PolyStan -- a nested sampling inference engine for Stan. PolyStan provides a Stan interface to the PolyChord nested sampling algorithm using bridgestan. PolyStan introduces a new user-base to nested sampling algorithms and provides a black-box method for sampling from challenging distributions and computing marginal likelihoods. We demonstrate the robustness of nested sampling on several degenerate and multi-modal problems, comparing it to bridge sampling and Hamiltonian Monte Carlo.