Document Detail

Neighborhood dependence in Bayesian spatial models.
MedLine Citation:
PMID:  19827056     Owner:  NLM     Status:  MEDLINE    
The conditional autoregressive model and the intrinsic autoregressive model are widely used as prior distribution for random spatial effects in Bayesian models. Several authors have pointed out impractical or counterintuitive consequences on the prior covariance matrix or the posterior covariance matrix of the spatial random effects. This article clarifies many of these puzzling results. We show that the neighborhood graph structure, synthesized in eigenvalues and eigenvectors structure of a matrix associated with the adjacency matrix, determines most of the apparently anomalous behavior. We illustrate our conclusions with regular and irregular lattices including lines, grids, and lattices based on real maps.
Renato Assun????o; Elias Krainski
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Publication Detail:
Type:  Journal Article; Research Support, Non-U.S. Gov't    
Journal Detail:
Title:  Biometrical journal. Biometrische Zeitschrift     Volume:  51     ISSN:  1521-4036     ISO Abbreviation:  Biom J     Publication Date:  2009 Oct 
Date Detail:
Created Date:  2009-10-26     Completed Date:  2010-01-06     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  7708048     Medline TA:  Biom J     Country:  Germany    
Other Details:
Languages:  eng     Pagination:  851-69     Citation Subset:  IM    
Departamento de Estat??stica, Universidade Federal de Minas Gerais, 31270-901 Belo Horizonte, Minas Gerais, Brazil.
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MeSH Terms
Analysis of Variance
Bayes Theorem*
Biometry / methods*
Geography / statistics & numerical data
Linear Models
Markov Chains
Models, Statistical
Regression Analysis
United States

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