Abstract #300573

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JSM 2003 Abstract #300573
Activity Number: 115
Type: Topic Contributed
Date/Time: Monday, August 4, 2003 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Stat. Sciences
Abstract - #300573
Title: Covariate-Adjusted Spatio-Temporal Cumulative Distribution Functions with Application to Air Pollutant Data
Author(s): Margaret B. Short*+ and Bradley P. Carlin
Companies: University of Minnesota and University of Minnesota
Address: 2936 Orchard Ave. N., Golden Valley, MN, 55422-3005,
Keywords: spatial cumulative distribution function ; Bayesian kriging ; Markov chain Monte Carlo ; spatio-temporal models ; air pollution
Abstract:

We provide a fully hierarchical approach to the modeling of spatial cumulative distribution functions (SCDFs), using a Bayesian framework implemented via Markov chain Monte Carlo (MCMC) methods. The approach generalizes the SCDF to accommodate block-level variables, possibly utilizing a spatial change of support model within an MCMC algorithm. We then extend our approach to allow covariate weighting of the SCDF estimate. We further generalize the framework to the bivariate random process setting, which allows simultaneous modeling of both the responses and the weights. Once again MCMC methods (combined with a convenient Kronecker structure) enable straightforward estimates of weighted, bivariate, and conditional SCDFs. A temporal component is added to our model, again implemented with a Kronecker product covariance stucture, corresponding to separable correlations. We illustrate our methods with two air pollution data sets, one concerning ozone exposure and race in Atlanta, Georgia, and the other recording both NO and NO_2 ambient levels at 67 monitoring sites in central and southern California.

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