# dynesty: A Dynamic Nested Sampling Package for Estimating Bayesian Posteriors and Evidences

## TL;DR

dynesty is an open-source Python package that efficiently estimates Bayesian posteriors and evidences using Dynamic Nested Sampling, adapting sample allocation to complex distributions for improved performance over traditional MCMC methods.

## Contribution

It introduces a novel implementation of Dynamic Nested Sampling in Python, enhancing sampling efficiency and accuracy in Bayesian inference for complex, multi-modal distributions.

## Key findings

- Substantial improvements in sampling efficiency over MCMC methods.
- Effective estimation of Bayesian evidences in complex problems.
- Successful application to astronomical data analysis.

## Abstract

We present dynesty, a public, open-source, Python package to estimate Bayesian posteriors and evidences (marginal likelihoods) using Dynamic Nested Sampling. By adaptively allocating samples based on posterior structure, Dynamic Nested Sampling has the benefits of Markov Chain Monte Carlo algorithms that focus exclusively on posterior estimation while retaining Nested Sampling's ability to estimate evidences and sample from complex, multi-modal distributions. We provide an overview of Nested Sampling, its extension to Dynamic Nested Sampling, the algorithmic challenges involved, and the various approaches taken to solve them. We then examine dynesty's performance on a variety of toy problems along with several astronomical applications. We find in particular problems dynesty can provide substantial improvements in sampling efficiency compared to popular MCMC approaches in the astronomical literature. More detailed statistical results related to Nested Sampling are also included in the Appendix.