PLACE: 319 Snedecor

SPEAKER:
Richard Evans
Department of Veterinary Diagnostic and Production Animal Medicine
Iowa State University

TITLE:
Methods for Uncertain Pooling
 

ABSTRACT:
Hierarchical models for L studies, domains or experiments often assume that the study means have a common normal population distribution.  However, modeling normal sampling distributions with a normal population distribution may overstate the level of exchangeability of the studies.  Using heavy tailed population distributions, in particular t distributions, provide some protection from combining dissimilar studies, domains or experiments Gelman, Carlin, Stern, and Rubin, 1995, O'Hagan, 1988).  We also use t population distributions, but use an analytic method to provide posterior inference for study means when the sampling variance is unknown.  In the case that the prior parameters are unknown the analytic method may be modified to provide a parametric empirical Bayes method for inference about the study means. The analytic method circumvents Markov chain Monte Carlo convergence problems and permits a more direct model sensitivity analysis.  Using examples and analytic results we demonstrate the characteristic of posterior means and variances under t distribution priors, and suggest that for applied data analysis problems the Cauchy prior is a reasonable population distribution.  The examples also suggest that the prior variance should be estimated from the data rather than assigned an arbitrary constant. Finally we demonstrate the method using real data in a small area estimation example.

COFFEE: 3:45 p.m., 104 Snedecor Hall