JSM 2004 - Toronto

Abstract #301176

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Activity Number: 272
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract - #301176
Title: Normal Observables with CAR Priors Having Two Types of Neighbor Relations
Author(s): Brian J. Reich*+ and James S. Hodges and Brad Carlin
Companies: University of Minnesota and University of Minnesota and University of Minnesota
Address: A460 Mayo Building, Minneapolis, MN, 55455,
Keywords: Bayesian ; spatial ; conditional ; autoregressive ; prior
Abstract:

Bayesian analyses of areal data often use a conditionally autoregressive (CAR) prior distribution which allows fitted values to be smoothed toward values of neighboring regions. Sometimes it is desirable to have more than one type of neighbor relation in the spatial structure, so the different types of neighbor relations can induce different degrees of smoothing. For example, in the periodontal datasets, the degree of smoothing of neighbor pairs bridging the gap between teeth may be different from the smoothing of pairs that do not bridge such gaps. We develop a two neighbor relation CAR (2NRCAR) model to handle this situation, and present associated theory to help explain the sometimes unusual posterior behavior of the parameters that control the different types of smoothing in this model. We also illustrate use of this model by applying it to an analysis of some periodontal data on attachment loss.

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