A Brief Introduction to Nested Sampling - IPAM at UCLA

Explore a comprehensive introduction to Nested Sampling in this 38-minute lecture by Joshua Speagle from the University of Toronto. Delve into the fundamentals of this Bayesian framework, designed to estimate marginal likelihoods and posterior distributions. Discover the advantages and limitations of Nested Sampling compared to Markov Chain Monte Carlo approaches. Learn about recent extensions like Dynamic Nested Sampling and their applications in scientific analysis, particularly in astronomy. Gain insights into sampling strategies, bounding techniques, and practical implementations through illustrative examples. Understand the importance of quantifying model uncertainty and performing model selection in gravitational wave astronomy and beyond.

Intro
Background
Motivation: Sampling the Posterior
Motivation: Integrating the Posterior
Stopping Criteria
Nested Sampling In Practice
Naïve Approach: Sampling from the Prior
Examples of Bounding Strategies
Examples of Sampling Strategies
Advantages and Disadvantages
Dynamic Nested Sampling
Illustrative Example
Summary