Bayesian Analysis

Log-Linear Pool to Combine Prior Distributions: A Suggestion for a Calibration-Based Approach

M. J. Rufo, J. Martín, and C. J. Pérez

Full-text: Open access

Abstract

An important issue involved in group decision making is the suitable aggregation of experts’ beliefs about a parameter of interest. Two widely used combination methods are linear and log-linear pools. Yet, a problem arises when the weights have to be selected. This paper provides a general decision-based procedure to obtain the weights in a log-linear pooled prior distribution. The process is based on Kullback-Leibler divergence, which is used as a calibration tool. No information about the parameter of interest is considered before dealing with the experts’ beliefs. Then, a pooled prior distribution is achieved, for which the expected calibration is the best one in the Kullback-Leibler sense. In the absence of other information available to the decision-maker prior to getting experimental data, the methodology generally leads to selection of the most diffuse pooled prior. In most cases, a problem arises from the marginal distribution related to the noninformative prior distribution since it is improper. In these cases, an alternative procedure is proposed. Finally, two applications show how the proposed techniques can be easily applied in practice.

Article information

Source
Bayesian Anal., Volume 7, Number 2 (2012), 411-438.

Dates
First available in Project Euclid: 16 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1339878894

Digital Object Identifier
doi:10.1214/12-BA714

Mathematical Reviews number (MathSciNet)
MR2934957

Zentralblatt MATH identifier
1330.62057

Keywords
Bayesian analysis Kullback-Leibler divergence Pooled distribution

Citation

Rufo, M. J.; Martín, J.; Pérez, C. J. Log-Linear Pool to Combine Prior Distributions: A Suggestion for a Calibration-Based Approach. Bayesian Anal. 7 (2012), no. 2, 411--438. doi:10.1214/12-BA714. https://projecteuclid.org/euclid.ba/1339878894


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