Approximating hidden Gaussian Markov random fields

• 成果类型: Article
• 署名作者: Rue, H; Steinsland, I; Erland, S
• 署名单位: Norwegian University of Science & Technology (NTNU)
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2004.B5590.x
• 发表日期: 2004
• 页码: 877-892
• 关键词: chain monte-carlo; likelihood-estimation; maximum-likelihood; time; disease; models

摘要

Gaussian Markov random-field (GMRF) models are frequently used in a wide variety of applications. In most cases parts of the GMRF are observed through mutually independent data; hence the full conditional of the GMRF, a hidden GMRF (HGMRF), is of interest. We are concerned with the case where the likelihood is non-Gaussian, leading to non-Gaussian HGMRF models. Several researchers have constructed block sampling Markov chain Monte Carlo schemes based on approximations of the HGMRF by a GMRF, using a second-order expansion of the log-density at or near the mode. This is possible as the GMRF approximation can be sampled exactly with a known normalizing constant. The Markov property of the GMRF approximation yields computational efficiency.The main contribution in the paper is to go beyond the GMRF approximation and to construct a class of non-Gaussian approximations which adapt automatically to the particular HGMRF that is under study. The accuracy can be tuned by intuitive parameters to nearly any precision. These non-Gaussian approximations share the same computational complexity as those which are based on GMRFs and can be sampled exactly with computable normalizing constants. We apply our approximations in spatial disease mapping and model-based geostatistical models with different likelihoods, obtain procedures for block updating and construct Metropolized independence samplers.