Objective Bayesian analysis for autoregressive models with nugget effects

JOURNAL OF MULTIVARIATE ANALYSIS

卷:124

Article

Ren, Cuirong¹  Sun, Dongchu² 

[1] USPS, Stat Programs, Washington, DC 20260 USA

[2] Univ Missouri, Dept Stat, Columbia, MO 65211 USA

关键词: Autoregressive models;    CAR model;    SAR model;    Jeffreys prior;    Reference prior;    Integrated likelihood;    Propriety of posterior;   

DOI  :  10.1016/j.jmva.2013.11.003

来源: Elsevier

【 摘 要 】

The conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models both have been used extensively for the analysis of spatial structure underlying lattice data in many areas, such as epidemiology, demographics, economics, and geography. Default Bayesian analyses have been conducted recently, but the Bayesian approach has not used or explored these two models with nugget effects. In this paper, we consider general autoregressive models including both CAR and SAR models. The Jeffreys-rule, independence Jeffreys, commonly used reference and exact reference priors are derived. The propriety of the marginal priors and joint posteriors is studied for a large class of objective priors. Various Jeffreys and reference priors are shown to yield improper posteriors and only the Jeffreys-rule and the exact reference priors yield proper posteriors. We make comparisons for these two objective priors using the frequentist coverage probabilities of the credible intervals. An illustration is given using a real spatial data-set. Published by Elsevier Inc.

【 授权许可】

Free