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Bayesian analysis of cross-classifie...

Li, Xiaolei.

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Bayesian analysis of cross-classified spatial data with autocorrelation.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Bayesian analysis of cross-classified spatial data with autocorrelation./
作者:	Li, Xiaolei.
面頁冊數:	124 p.
附註:	Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5172.
Contained By:	Dissertation Abstracts International67-09B.
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3234659
ISBN:	9780542886232

Bayesian analysis of cross-classified spatial data with autocorrelation.
Li, Xiaolei.

Bayesian analysis of cross-classified spatial data with autocorrelation. - 124 p.

Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5172.

Thesis (Ph.D.)--The University of Wisconsin - Madison, 2006.

The work is focused on the development and application of statistical methodologies to the analyses of categorical data collected over space. In many settings such as epidemiology, plant pathology, medical imaging, GIS, etc., such data are often encountered. From site to site, data may be spatially autocorrelated. When several attributes are considered simultaneously, their mutual associations are hard to characterize. The standard chi-squared analysis becomes invalid and can lead to wrong conclusions because of the spatial autocorrelation within each attribute. Our methods focus on identifying the mutual independence between two multi-categorical spatial processes over a finite lattice. An auto-logistic multinomial Markov model is first constructed for a single multi-categorical spatial process. Then, two or more multi-categorical spatial processes are modeled, where the mutual dependence between any two processes is parameterized through corresponding coefficients. For model inferences, Bayesian methods are adopted. First, the likelihood is estimated by a Monte Carlo method via auxiliary fields generated with Gibbs sampler. Then, posteriors are obtained using a component-wise Metropolis algorithm, which is a modified version of the classic Metropolis algorithm for high-dimensional parameter spaces. In particular, the validity of the Bayesian estimating procedure is related to the existence of maximum likelihood estimates (MLE), maximum pseudo-likelihood estimates (MPLE) and Monte Carlo maximum likelihood estimates (MCMLE). A sufficient condition for the existence of estimates is constructed as an integral part of the work.

ISBN: 9780542886232Subjects--Topical Terms:

517247
Statistics.

Bayesian analysis of cross-classified spatial data with autocorrelation.
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520 $a The work is focused on the development and application of statistical methodologies to the analyses of categorical data collected over space. In many settings such as epidemiology, plant pathology, medical imaging, GIS, etc., such data are often encountered. From site to site, data may be spatially autocorrelated. When several attributes are considered simultaneously, their mutual associations are hard to characterize. The standard chi-squared analysis becomes invalid and can lead to wrong conclusions because of the spatial autocorrelation within each attribute. Our methods focus on identifying the mutual independence between two multi-categorical spatial processes over a finite lattice. An auto-logistic multinomial Markov model is first constructed for a single multi-categorical spatial process. Then, two or more multi-categorical spatial processes are modeled, where the mutual dependence between any two processes is parameterized through corresponding coefficients. For model inferences, Bayesian methods are adopted. First, the likelihood is estimated by a Monte Carlo method via auxiliary fields generated with Gibbs sampler. Then, posteriors are obtained using a component-wise Metropolis algorithm, which is a modified version of the classic Metropolis algorithm for high-dimensional parameter spaces. In particular, the validity of the Bayesian estimating procedure is related to the existence of maximum likelihood estimates (MLE), maximum pseudo-likelihood estimates (MPLE) and Monte Carlo maximum likelihood estimates (MCMLE). A sufficient condition for the existence of estimates is constructed as an integral part of the work.
520 $a Our methods address issues including uncertainty incurred in estimation and irregular lattices, which often arise in practice. Models and the Bayesian procedure are evaluated with simulated data. Examples of applications include Lansing Woods data and Illinois lung cancer incidence vs. asbestos-related mortality.
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