Choosing Bayes Priors for Estimating Values Near Zero: A Case Study with the Beta-Binomial and the Gamma-Poisson Distributions

• Activity Number: 536
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Marcela Alfaro *+
• Companies: Universidad de Costa Rica
• Keywords: Priors ; Bayesian ; Beta-Binomial ; Gamma-Poisson ; Estimation

Abstract

The present study has as a goal to describe the effect of the chosen prior distribution for Bayes Estimators when the parameter to estimate is near zero with both the Beta-Binomial and the Gamma-Poisson distributions. It is from our interest to study two case scenarios: when we have prior knowledge about the parameter and when we do not. For that purpose data set with few success values in it for each distribution, and for each case scenario was taken and analyzed to describe the different effects from a different set of prior distributions. The effects were measured by comparisons within posterior distributions for each prior distribution and data set. A simulation study was performed to see effects in cases where we do not have prior information. Bayes Predictive Checks also were executed to establish if there exist any signifficant differences between the distributions.