Approximate reference priors for Gaussian random fields

被引:0
作者
De Oliveira, Victor [1 ]
Han, Zifei [2 ]
机构
[1] Univ Texas San Antonio, Dept Management Sci & Stat, San Antonio, TX USA
[2] Univ Int Business & Econ, Sch Stat, Beijing, Peoples R China
基金
美国国家科学基金会;
关键词
Bayesian analysis; default prior; geostatistics; spectral representation; OBJECTIVE BAYESIAN-ANALYSIS; SPATIAL DATA; MODELS; INFERENCE;
D O I
10.1111/sjos.12577
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Reference priors are theoretically attractive for the analysis of geostatistical data since they enable automatic Bayesian analysis and have desirable Bayesian and frequentist properties. But their use is hindered by computational hurdles that make their application in practice challenging. In this work, we derive a new class of default priors that approximate reference priors for the parameters of some Gaussian random fields. It is based on an approximation to the integrated likelihood of the covariance parameters derived from the spectral approximation of stationary random fields. This prior depends on the structure of the mean function and the spectral density of the model evaluated at a set of spectral points associated with an auxiliary regular grid. In addition to preserving the desirable Bayesian and frequentist properties, these approximate reference priors are more stable, and their computations are much less onerous than those of exact reference priors. Unlike exact reference priors, the marginal approximate reference prior of correlation parameter is always proper, regardless of the mean function or the smoothness of the correlation function. This property has important consequences for covariance model selection. An illustration comparing default Bayesian analyses is provided with a dataset of lead pollution in Galicia, Spain.
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页码:296 / 326
页数:31
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