Bayesian Ranks, Histograms, and Triple-Goal Estimates

• Activity Number: 281
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Thomas Louis*+
• Companies: U.S. Census Bureau/Johns Hopkins University
• Keywords: Ranking ; Histogram Estimation ; Bayesian Methods

Abstract

Prioritization of interventions in small areas, health services and educational effectiveness evaluations, environmental assessments, identifying gene and SNP associations all depend on unit-specific ranks. Ranking is challenging when estimation uncertainties vary, because Z-scores for units with relatively low variance tend to be extreme; MLEs for units with relatively high variance tend to be at the extremes. Effective ranking requires finding a middle ground, and loss function based Bayesian modeling is very effective. We outline the Bayesian approach, present simulation evaluations and data analysis based on Standardized Mortality Ratios from the United States Renal Data System. We present related work on histogram estimation for which a loss function based Bayesian estimate produces the right spread and shape. No set of estimates can simultaneously optimize ranking, histogram estimation and parameter estimation, but "triple-goal" estimates provide an excellent compromise.