A Bayesian Decision-Based Model for Aggregating Expert's Information

• Activity Number: 424
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): María Jesús Rufo*+ and Jacinto Martín and Carlos Javier Pérez
• Companies: University of Extremadura Escuela Politécnica and University of Extremadura and University of Extremadura
• Keywords: Bayesian decision model ; Kullback-Leibler divergence ; Opinion pooling

Abstract

This work provides a decision-based approach to assess the weights in a logarithmic pooling of prior distributions. Each expert provides prior information over the quantity of interest as a proper prior distribution. Then, the decision maker combines them through a logarithmic pooling. Next, the weights have to be assessed to obtain the full aggregated prior distribution. In order to do it, the problem is formulated as a decision one. Therefore, given the decision space and the states of nature, an appropriated loss function based on Kullback-Leibler divergence is defined. Two situations are considered depending on whether the decision maker assumes prior ignorance about the quantity of interest or not. These situations are distinguished through the choice of suitable prior distributions over the state of nature. Several methods are considered in order to obtain this prior distribution. Hence, the optimal weights are those that minimize the expected loss. Finally, the results obtained under the two considered frames are compared.