Approximating likelihoods for large spatial data sets

• 成果类型: Article
• 署名作者: Stein, ML; Chi, ZY; Welty, LJ
• 署名单位: University of Chicago
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1046/j.1369-7412.2003.05512.x
• 发表日期: 2004
• 页码: 275-296
• 关键词: covariance parameters; variogram; soil; inference

摘要

Likelihood methods are often difficult to use with large, irregularly sited spatial data sets, owing to the computational burden. Even for Gaussian models, exact calculations of the likelihood for n observations require O(n(3)) operations. Since any joint density can be written as a product of conditional densities based on some ordering of the observations, one way to lessen the computations is to condition on only some of the 'past' observations when computing the conditional densities. We show how this approach can be adapted to approximate the restricted likelihood and we demonstrate how an estimating equations approach allows us to judge the efficacy of the resulting approximation. Previous work has suggested conditioning on those past observations that are closest to the observation whose conditional density we are approximating. Through theoretical, numerical and practical examples, we show that there can often be considerable benefit in conditioning on some distant observations as well.