Bayesian Simultaneous Intervals for Small Areas: an Application to Variation in Maps

• Activity Number: 417
• Type: Contributed
• Date/Time: Wednesday, August 9, 2006 : 10:30 AM to 12:20 PM
• Sponsor: Section on Health Policy Statistics
• Author(s): Erik B. Erhardt*+ and Balgobin Nandram and Jai Choi
• Companies: University of New Mexico and Worcester Polytechnic Institute and National Center for Health Statistics
• Keywords: hierarchical Bayesian model ; highest posterior density ; Metropolis-Hastings algorithm ; Nelder-Mead algorithm ; Rao-Blackwellized estimator ; simultaneous inference

Abstract

Simultaneous intervals for parameters for small area inference are needed because these parameters are correlated. Our method finds simultaneous credible intervals for a large number of parameters, each for a single area. Our method uses a hierarchical Bayesian model, starting with either the 100(1-alpha)% credible interval or highest posterior density (HPD) interval for each area. Our method solves two simultaneous equations, one accounting for the probability content, 100(1-alpha)% of all the intervals combined, and one containing an optimality condition like the "equal ordinates" condition in the HPD interval. We compare our method with one based on a nonparametric method, which as expected under a parametric model, does not perform as well as ours, but is a good competitor. We illustrate our method using an example on disease mapping using a standard Poisson regression model.