Nested sampling for physical scientists

TL;DR

This paper reviews nested sampling, a Bayesian inference algorithm, discussing its principles, recent developments, practical implementation in high dimensions, and applications across cosmology, gravitational-wave astronomy, and materials science.

Contribution

It provides a comprehensive overview of nested sampling, including recent methodological advances, best practices, and its diverse scientific applications.

Findings

Effective high-dimensional sampling methods discussed

Applications demonstrated in cosmology, gravitational waves, materials science

Guidelines for best practices and limitations provided

Abstract

We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice in high-dimensions, including methods for sampling from the so-called constrained prior. We outline the ways in which NS may be applied and describe the application of NS in three scientific fields in which the algorithm has proved to be useful: cosmology, gravitational-wave astronomy, and materials science. We close by making recommendations for best practice when using NS and by summarizing potential limitations and optimizations of NS.