Journal
BIOMETRICAL JOURNAL
Volume 51, Issue 5, Pages 851-869Publisher
WILEY
DOI: 10.1002/bimj.200900056
Keywords
CAR model; Lattice data; Spatial autoregression, Spatial interaction
Funding
- CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico) of the Ministry for Science and Technology of Brazil [PQ 309708/2007-9]
- FAPEMIG [CEX APQ 4096-5.01/07]
- CAPES
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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 kind irregular lattices including lines, grids. and lattices based on real maps.
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