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
  • [31] A Markov chain Monte Carlo algorithm for Bayesian policy search
    Aghaei, Vahid Tavakol
    Onat, Ahmet
    Yildirim, Sinan
    [J]. SYSTEMS SCIENCE & CONTROL ENGINEERING, 2018, 6 (01): : 438 - 455
  • [32] Adaptive Markov Chain Monte Carlo for Bayesian Variable Selection
    Ji, Chunlin
    Schmidler, Scott C.
    [J]. JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS, 2013, 22 (03) : 708 - 728
  • [33] A Bayesian Markov chain Monte Carlo solution of the bilinear problem
    Ochs, AF
    Stoyanova, RS
    Brown, TR
    Rooney, WD
    Springer, CS
    [J]. BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING, 2001, 567 : 274 - 284
  • [34] Introduction: Bayesian models and Markov chain Monte Carlo methods
    Thomas, DC
    [J]. GENETIC EPIDEMIOLOGY, 2001, 21 : S660 - S661
  • [35] Application of Markov chain Monte carlo method in Bayesian statistics
    Zhao, Qi
    [J]. 2016 INTERNATIONAL CONFERENCE ON ELECTRONIC, INFORMATION AND COMPUTER ENGINEERING, 2016, 44
  • [36] Zero variance Markov chain Monte Carlo for Bayesian estimators
    Mira, Antonietta
    Solgi, Reza
    Imparato, Daniele
    [J]. STATISTICS AND COMPUTING, 2013, 23 (05) : 653 - 662
  • [37] Challenges in Markov Chain Monte Carlo for Bayesian Neural Networks
    Papamarkou, Theodore
    Hinkle, Jacob
    Young, M. Todd
    Womble, David
    [J]. STATISTICAL SCIENCE, 2022, 37 (03) : 425 - 442
  • [38] On the use of approximate Bayesian computation Markov chain Monte Carlo with inflated tolerance and post-correction
    Vihola, Matti
    Franks, Jordan
    [J]. BIOMETRIKA, 2020, 107 (02) : 381 - 395
  • [39] A comparison of strategies for Markov chain Monte Carlo computation in quantitative genetics
    Rasmus Waagepetersen
    Noelia Ibánẽz-Escriche
    Daniel Sorensen
    [J]. Genetics Selection Evolution, 40 (2)
  • [40] A comparison of strategies for Markov chain Monte!Carlo computation in quantitative genetics
    Waagepetersen, Rasmus
    Ibanez-Escriche, Noelia
    Sorensen, Daniel
    [J]. GENETICS SELECTION EVOLUTION, 2008, 40 (02) : 161 - 176
12345