BAYESIAN COMPUTATION AND STOCHASTIC-SYSTEMS
BAYESIAN COMPUTATION AND STOCHASTIC-SYSTEMS
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DOI：
10.1214/ss/1177010123
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发表时间：
1995-02-01
影响因子：
5.7
通讯作者：
MENGERSEN, K
中科院分区：
文献类型：
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作者：
BESAG, J;GREEN, P;MENGERSEN, K
马尔可夫链蒙特卡罗 (MCMC) 方法在过去 40 年中广泛应用于统计物理学，在过去 20 年中广泛应用于空间统计，在过去十年中广泛应用于贝叶斯图像分析。在过去五年中，MCMC 已被引入显着性检验、一般贝叶斯推理和最大似然估计。本文介绍了MCMC的基本方法，强调了贝叶斯范式、条件概率以及与空间统计中马尔可夫随机场的密切关系。讨论了 Hastings 算法，包括 Gibbs、Metropolis 和其他一些变体。描述了成对差异先验，并随后在三个贝叶斯应用中使用，每个应用中的建模都有明显的空间或时间方面。这些例子涉及在存在未观察到的协变量和序数因素的情况下进行逻辑回归；农业田间试验分析，并调整肥力梯度；以及处理由伽玛相机获得的低分辨率医学图像。这些申请和附录中都出现了其他方法学问题。该论文特别强调后验概率的计算，并同意其他人的观点，即 MCMC 促进了应用贝叶斯建模的根本性突破。
Markov chain Monte Carlo (MCMC) methods have been used extensively in statistical physics over the last 40 years, in spatial statistics for the past 20 and in Bayesian image analysis over the last decade. In the last five years, MCMC has been introduced into significance testing, general Bayesian inference and maximum likelihood estimation. This paper presents basic methodology of MCMC, emphasizing the Bayesian paradigm, conditional probability and the intimate relationship with Markov random fields in spatial statistics. Hastings algorithms are discussed, including Gibbs, Metropolis and some other variations. Pairwise difference priors are described and are used subsequently in three Bayesian applications, in each of which there is a pronounced spatial or temporal aspect to the modeling. The examples involve logistic regression in the presence of unobserved covariates and ordinal factors; the analysis of agricultural field experiments, with adjustment for fertility gradients; and processing of low-resolution medical images obtained by a gamma camera. Additional methodological issues arise in each of these applications and in the Appendices. The paper lays particular emphasis on the calculation of posterior probabilities and concurs with others in its view that MCMC facilitates a fundamental breakthrough in applied Bayesian modeling.