Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models
Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models
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DOI：
10.1002/1097-0258(20000915/30)19:17/18
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发表时间：
2000-09-15
影响因子：
2
通讯作者：
Carlin, BP
中科院分区：
文献类型：
--
作者：
Eberly, LE;Carlin, BP
在过去的十年中，贝叶斯方法在统计实践中的流行程度显着增加，这在很大程度上归功于马尔可夫链蒙特卡罗（MCMC）方法的同时发展，用于评估所需的后验分布。然而，沿着计算能力的提高，拟合模型的诱惑已经超过了数据所能支持的范围，这意味着某些参数的后验分布的适当性通常取决于相关先验分布的适当性。一个重要的例子出现在空间建模，其中单独的随机效应捕捉非结构化异质性和空间聚类的实质性利益，即使只有他们的总和是很好地确定的数据。增加相关先验分布的信息内容提供了一个明显的补救措施，但妨碍参数的可解释性，也可能显着减缓MCMC算法的收敛。针对一类常见的空间模型，研究了可辨识性、贝叶斯学习和MCMC收敛速度之间的关系，以期为模型的选择和算法的调整提供指导。我们能够用相对简单的例子阐明关键问题，并说明协变量，离群值和算法初始值对所得算法和后验分布的不同影响。版权所有（C）2000约翰威利父子有限公司
The marked increase in popularity of Bayesian methods in statistical practice over the last decade owes much to the simultaneous development of Markov chain Monte Carlo (MCMC) methods for the evaluation of requisite posterior distributions. However, along with this increase in computing power has come the temptation to fit models larger than the data can readily support, meaning that often the propriety of the posterior distributions for certain parameters depends on the propriety of the associated prior distributions. An important example arises in spatial modelling, wherein separate random effects for capturing unstructured heterogeneity and spatial clustering are of substantive interest, even though only their sum is well identified by the data. Increasing the informative content of the associated prior distributions offers an obvious remedy, but one that hampers parameter interpretability and may also significantly slow the convergence of the MCMC algorithm. In this paper we investigate the relationship among identifiability, Bayesian learning and MCMC convergence rates for a common class of spatial models, in order to provide guidance for piror selection and algorithm tuning. We are able to elucidate the key issues with relatively simple examples, and also illustrate the varying impacts of covariates, outliers and algorithm starting values on the resulting algorithms and posterior distributions. Copyright (C) 2000 John Wiley & Sons, Ltd.