PolyStan: PolyChord nested sampling and Bayesian evidences for Stan models

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.