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347 – Computationally Intensive Bayesian Methodology
Order-Restricted Bayesian Estimation of Multinomial Counts for Small Areas
Xinyu Chen
Worcester Polytechnic Institute
Balgobin Nandram
Worcester Polytechnic Institute
We consider making inference about several small areas with data obtained in the form of multino- mial counts. The cell probabilities have the same unimodal order restriction across areas, and these cell probabilities share a common effect. Therefore, a hierarchical multinomial-Dirichlet model, used to model the cell probabilities and the cell counts, allows a borrowing of strength across areas. We used the Gibbs sampler to make inference about the order-restricted multinomial parameters. We show how to perform the computations because there are difficulties poised by the order re- strictions. An application on body mass index showed that the order restriction is necessary and it provides increased precision over the scenario without the restriction.