Comparing Methods of Inference on the Basis of Imprecise Posterior Distributions

• Activity Number: 470 - Bayes Theory and Foundations
• Type: Contributed
• Date/Time: Wednesday, August 2, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Reyhaneh Hosseini* and David R. Bickel
• Companies: University of Ottawa and University of Ottawa
• Keywords: Bayesian inference ; Imprecise distribution ; Decision theory ; Maximum-entropy ; Linear combination ; E-admissibility with caution

Abstract

The prior selection has always been an issue in Bayesian inference. In this article, in order to estimate the parameter of interest which is the mean of a normal distribution, we consider two most extreme normal priors. Then, we apply various decision making criteria on a convex set constructed by all linear combinations of two corresponding posterior distributions. The performance of these criteria is compared by different measurements such as the MSE, the mean worst case error (MWCE) and the mean deviability (Mdevi). While the Gamma-minimax is the best method by the MWCE measurement, the simulation results indicate that the linear combination with equal weights and the E-admissibility with caution k=0.5 are the second best methods. Also, the results show that by the Mdevi measurement, the extreme distributions are the second best methods after the maximumentropy method.