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
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).
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