Title page for ETD etd-0105104-195633

Document Type thesis

Author Name Erhardt, Erik Barry

URN etd-0105104-195633

Title Bayesian Simultaneous Intervals for Small Areas: An Application to Mapping Mortality Rates in U.S. Health Service Areas

Degree MS

Department Mathematical Sciences

Advisors
Prof. Balgobin Nandram, Advisor

Keywords
Poisson-Gamma Regression
MCMC
Bayesian
Small Area Estimation
Simultaneous Inference
Statistics

Date of Presentation/Defense 2003-11-24

Availability unrestricted

Abstract
It is customary when presenting a choropleth map of rates or counts to present only the estimates (mean or mode) of the parameters of interest. While this technique illustrates spatial variation, it ignores the variation inherent in the estimates. We describe an approach to present variability in choropleth maps by constructing 100(1-alpha)% simultaneous intervals. The result provides three maps (estimate with two bands).

We propose two methods to construct simultaneous intervals from the optimal individual highest posterior density (HPD) intervals to ensure joint simultaneous coverage of 100(1-alpha)%.

Both methods exhibit the main feature of multiplying the lower bound and dividing the upper bound of the individual HPD intervals by parameters 0
For illustrative purposes we apply our methods to chronic obstructive pulmonary disease (COPD) mortality rates from 1988--92, subset White Males age group 65 and older, for the continental United States consisting of 798 Health Service Areas (HSA).

Files
eerhardt.pdf

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Document Type	thesis
Author Name	Erhardt, Erik Barry
URN	etd-0105104-195633
Title	Bayesian Simultaneous Intervals for Small Areas: An Application to Mapping Mortality Rates in U.S. Health Service Areas
Degree	MS
Department	Mathematical Sciences
Advisors	Prof. Balgobin Nandram, Advisor
Keywords	Poisson-Gamma Regression MCMC Bayesian Small Area Estimation Simultaneous Inference Statistics
Date of Presentation/Defense	2003-11-24
Availability	unrestricted
Abstract It is customary when presenting a choropleth map of rates or counts to present only the estimates (mean or mode) of the parameters of interest. While this technique illustrates spatial variation, it ignores the variation inherent in the estimates. We describe an approach to present variability in choropleth maps by constructing 100(1-alpha)% simultaneous intervals. The result provides three maps (estimate with two bands). We propose two methods to construct simultaneous intervals from the optimal individual highest posterior density (HPD) intervals to ensure joint simultaneous coverage of 100(1-alpha)%. Both methods exhibit the main feature of multiplying the lower bound and dividing the upper bound of the individual HPD intervals by parameters 0 For illustrative purposes we apply our methods to chronic obstructive pulmonary disease (COPD) mortality rates from 1988--92, subset White Males age group 65 and older, for the continental United States consisting of 798 Health Service Areas (HSA).
Files	eerhardt.pdf