Abstract This Primer examines Skilling's nested sampling algorithm for Bayesian inference
and, more broadly, multidimensional integration. The principles of nested sampling are …

ABSTRACT Statisticians often use Monte Carlo methods to approximate probability
distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential …

We introduce dynamic nested sampling: a generalisation of the nested sampling algorithm
in which the number of “live points” varies to allocate samples more efficiently. In empirical …

Nested sampling (NS) computes parameter posterior distributions and makes Bayesian
model comparison computationally feasible. Its strengths are the unsupervised navigation of …

Regularized Zero-Variance Control Variates Page 1 Bayesian Analysis (2023) 18, Number 3,
pp. 865–888 Regularized Zero-Variance Control Variates ∗ LF South †,‡ , CJ Oates § , A. Mira …

We present an improved version of the nested sampling algorithm nessai in which the core
algorithm is modified to use importance weights. In the modified algorithm, samples are …

Abstract Sequential Monte Carlo (SMC) samplers are an alternative to MCMC for Bayesian
computation. However, their performance depends strongly on the Markov kernels used to …

A standard way to move particles in a sequential Monte Carlo (SMC) sampler is to apply
several steps of a Markov chain Monte Carlo (MCMC) kernel. Unfortunately, it is not clear …

Nested sampling (NS) is a stochastic method for computing the log-evidence of a Bayesian
problem. It relies on stochastic estimates of prior volumes enclosed by likelihood contours …

Posterior distributions often feature intractable normalizing constants, called marginal
likelihoods or evidence, that are useful for model comparison via Bayes factors. This has …