Estimation via Markov chain Monte Carlo

2003/03/26 by James C. Spall · 3 citations
Computer Science · Mathematics · #Algorithm #Artificial intelligence #Bayesian Methods and Mixture Models #Bayesian probability #Computer science #Gibbs sampling #Hybrid Monte Carlo #Machine learning #Markov Chains and Monte Carlo Methods #Markov chain #Markov chain Monte Carlo #Mathematics #Metropolis–Hastings algorithm #Monte Carlo method #Rejection sampling #Statistical Methods and Bayesian Inference #Statistics

paper · doi:10.1109/mcs.2003.1188770

openalex publication_date 2003/03/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/04/11

Abstract

Markov chain Monte Carlo (MCMC) is a powerful means for generating random samples that can be used in computing statistical estimates and marginal and conditional probabilities. MCMC methods rely on dependent (Markov) sequences having a limiting distribution corresponding to a distribution of interest. This article is a survey of popular implementations of MCMC, focusing particularly on the two most popular specific implementations of MCMC: Metropolis-Hastings (M-H) and Gibbs sampling. Our aim is to provide the reader with some of the central motivation and the rudiments needed for a straightforward application.

Citations

• Equation of State Calculations by Fast Computing Machines
• Novel approach to nonlinear/non-Gaussian Bayesian state estimation
• Understanding the Metropolis-Hastings Algorithm
• On Gibbs sampling for state space models
• Monte Carlo sampling methods using Markov chains and their applications
• Sampling-Based Approaches to Calculating Marginal Densities

Cited by

• Stationarity and Convergence of the Metropolis-Hastings Algorithm: Insights into Theoretical Aspects
• Probabilistic Optimal Estimation and Filtering under Uncertainty
• Monte Carlo method [wikipedia]