Nested Sampling: A Critical and Comprehensive Theoretical Guide

arXiv:2606.17916 · stat.CO, astro-ph.CO, astro-ph.IM, stat.ML · Submitted 2026-06-16 · Read on arXiv

stat.CO, astro-ph.CO, astro-ph.IM, stat.ML

Submitted: 2026-06-16

Updated: 2026-10-21

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Nested Sampling — 48× in this paper
• Bayesian Inference — 3× in this paper · explained in 6 episodes
• Hamiltonian Monte Carlo — 2× in this paper
• Absorb — 1× in this paper · explained in 1 episode
• Bayesian Framework — 1× in this paper · explained in 3 episodes
• Computational Biology — 1× in this paper · explained in 2 episodes
• Degeneracies — 1× in this paper · explained in 2 episodes
• Diagnostic Tools — 1× in this paper · explained in 2 episodes
• Effective Sample Size (ESS) — 1× in this paper · explained in 2 episodes
• Normalizing Flow — 1× in this paper · explained in 4 episodes
• Normalizing Flows — 1× in this paper · explained in 4 episodes

Sources

• Vertical-likelihood Monte Carlo

Related papers

• A fast non-reversible sampler for Bayesian mixture models
• A Computable Measure of Suboptimality for Entropy-Regularised Variational Objectives
• BKP: An R Package for Beta Kernel Process Modeling
• Edgewise Envelopes Between Balanced Forman and Ollivier-Ricci Curvature
• Amortized quadrature for posterior expectations in inverse problems
• A Non-asymptotic Analysis for Learning and Applying a Preconditioner in MCMC