Bayesian multivariate spatial models and their applications
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Univariate hierarchical Bayes models are being vigorously researched for use in disease mapping, engineering, geology, and ecology. This dissertation shows how the models can also be used to build modelbased risk maps for areabased roadway traﬃc crashes. Countylevel vehicle crash records and roadway data from Texas are used to illustrate the method. A potential extension that uses univariate hierarchical models to develop networkbased risk maps is also discussed. Several Bayesian multivariate spatial models for estimating the traﬃc crash rates from diﬀerent types of crashes simultaneously are then developed. The speciﬁc class of spatial models considered is conditional autoregressive (CAR) model. The univariate CAR model is generalized for several multivariate cases. A general theorem for each case is provided to ensure that the posterior distribution is proper under improper and ﬂat prior. The performance of various multivariate spatial models is compared using a Bayesian information criterion. The Markov chain Monte Carlo (MCMC) computational techniques are used for the model parameter estimation and statistical inference. These models are illustrated and compared again with the Texas crash data. There are many directions in which this study can be extended. This dissertation concludes with a short summary of this research and recommends several promising extensions.
SubjectHierarchical Bayesian Model
Markov Chain Monte Carlo
Song, Joon Jin (2004). Bayesian multivariate spatial models and their applications. Doctoral dissertation, Texas A&M University. Texas A&M University. Available electronically from