Diffusive Nested Sampling

TL;DR

Diffusive Nested Sampling is a new Monte Carlo technique that improves the efficiency and accuracy of sampling complex distributions and estimating normalizing constants, outperforming traditional MCMC-based methods.

Contribution

It introduces a novel Monte Carlo method based on Nested Sampling that enhances sampling efficiency and accuracy, integrating Markov Chain Monte Carlo exploration.

Findings

Achieves four times the accuracy of classic MCMC-based Nested Sampling.

Provides a fourfold speedup for the same computational effort.

Enables more samples and better evidence estimates by extending runs.

Abstract

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested probability distributions, each successive distribution occupying ~e^-1 times the enclosed prior mass of the previous distribution. While NS technically requires independent generation of particles, Markov Chain Monte Carlo (MCMC) exploration fits naturally into this technique. We illustrate the new method on a test problem and find that it can achieve four times the accuracy of classic MCMC-based Nested Sampling, for the same computational effort; equivalent to a factor of 16 speedup. An additional benefit is that more samples and a more accurate evidence value can be obtained simply by continuing the run for longer, as in standard MCMC.