Bayesian Computation Via Markov Chain Monte Carlo

被引：43
|
作者：
Craiu, Radu V. [1 ]
Rosenthal, Jeffrey S. [1 ]
机构：
[1] Univ Toronto, Dept Stat, Toronto, ON M5S SG3, Canada
来源：
ANNUAL REVIEW OF STATISTICS AND ITS APPLICATION, VOL 1 | 2014年 / 1卷
关键词：
Markov chain Monte Carlo; adaptive MCMC; parallel tempering; Gibbs sampler; Metropolis sampler; DATA AUGMENTATION; GIBBS SAMPLER; POSTERIOR DISTRIBUTIONS; METROPOLIS ALGORITHMS; STOCHASTIC RELAXATION; COVARIANCE STRUCTURE; ADAPTIVE MCMC; CONVERGENCE; HASTINGS; RATES;
D O I：
10.1146/annurev-statistics-022513-115540
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Markov chain Monte Carlo (MCMC) algorithms are an indispensable tool for performing Bayesian inference. This review discusses widely used sampling algorithms and illustrates their implementation on a probit regression model for lupus data. The examples considered highlight the importance of tuning the simulation parameters and underscore the important contributions of modern developments such as adaptive MCMC. We then use the theory underlying MCMC to explain the validity of the algorithms considered and to assess the variance of the resulting Monte Carlo estimators.
引用
收藏
页码：179 / 201
页数：23
相关论文
共 50 条
  • [1] Computation in Bayesian econometrics: An introduction to Markov chain Monte Carlo
    Albert, J
    Chib, S
    [J]. ADVANCES IN ECONOMETRICS, 1996, 11 : 3 - 24
  • [2] BAYESIAN COMPUTATION VIA THE GIBBS SAMPLER AND RELATED MARKOV-CHAIN MONTE-CARLO METHODS
    SMITH, AFM
    ROBERTS, GO
    [J]. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-METHODOLOGICAL, 1993, 55 (01): : 3 - 23
  • [3] Markov Chain Monte Carlo Algorithms for Bayesian Computation, a Survey and Some Generalisation
    Wu Changye
    Robert, Christian P.
    [J]. CASE STUDIES IN APPLIED BAYESIAN DATA SCIENCE: CIRM JEAN-MORLET CHAIR, FALL 2018, 2020, 2259 : 89 - 119
  • [4] Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
    Green, PJ
    [J]. BIOMETRIKA, 1995, 82 (04) : 711 - 732
  • [5] Comparing variational Bayes with Markov chain Monte Carlo for Bayesian computation in neuroimaging
    Nathoo, F. S.
    Lesperance, M. L.
    Lawson, A. B.
    Dean, C. B.
    [J]. STATISTICAL METHODS IN MEDICAL RESEARCH, 2013, 22 (04) : 398 - 423
  • [6] Bayesian phylogenetic inference via Markov chain Monte Carlo methods
    Mau, B
    Newton, MA
    Larget, B
    [J]. BIOMETRICS, 1999, 55 (01) : 1 - 12
  • [7] Bayesian Mixture Modelling in Geochronology via Markov Chain Monte Carlo
    Ajay Jasra
    David A. Stephens
    Kerry Gallagher
    Christopher C. Holmes
    [J]. Mathematical Geology, 2006, 38 : 269 - 300
  • [8] Bayesian Trend Filtering via Proximal Markov Chain Monte Carlo
    Heng, Qiang
    Zhou, Hua
    Chi, Eric C.
    [J]. JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, 2023, 32 (03) : 938 - 949
  • [9] Bayesian system identification via Markov chain Monte Carlo techniques
    Ninness, Brett
    Henriksen, Soren
    [J]. AUTOMATICA, 2010, 46 (01) : 40 - 51
  • [10] Bayesian mixture modelling in geochronology via Markov chain Monte Carlo
    Jasra, Ajay
    Stephens, David A.
    Gallagher, Kerry
    Holmes, Christopher C.
    [J]. MATHEMATICAL GEOLOGY, 2006, 38 (03): : 269 - 300
12345