Comparison of Step Samplers for Nested Sampling

TL;DR

This paper compares ten nested sampling algorithms based on slice sampling, hit-and-run, and differential evolution, evaluating their efficiency in high-dimensional Bayesian inference problems across various geometries.

Contribution

It provides a comprehensive numerical comparison of different step sampling algorithms for nested sampling, highlighting the effectiveness of differential vector proposals.

Findings

Differential vector proposals achieve the highest efficiency.

Slice sampling is outperformed by hit-and-run and whitened slice sampling.

Whitened hit-and-run is less effective than other methods.

Abstract

Bayesian inference with nested sampling requires a likelihood-restricted prior sampling method, which draws samples from the prior distribution that exceed a likelihood threshold. For high-dimensional problems, Markov Chain Monte Carlo derivatives have been proposed. We numerically study ten algorithms based on slice sampling, hit-and-run and differential evolution algorithms in ellipsoidal, non-ellipsoidal and non-convex problems from 2 to 100 dimensions. Mixing capabilities are evaluated with the nested sampling shrinkage test. This makes our results valid independent of how heavy-tailed the posteriors are. Given the same number of steps, slice sampling is outperformed by hit-and-run and whitened slice sampling, while whitened hit-and-run does not provide as good results. Proposing along differential vectors of live point pairs also leads to the highest efficiencies, and appears promising for multi-modal problems. The tested proposals are implemented in the UltraNest nested sampling package, enabling efficient low and high-dimensional inference of a large class of practical inference problems relevant to astronomy, cosmology, particle physics and astronomy.