Electronic Journal of Statistics

A Bayesian approach to aggregate experts’ initial information

María Jesús Rufo, Carlos J. Pérez, and Jacinto Martín

Full-text: Open access

Abstract

This paper provides a Bayesian procedure to aggregate experts’ information in a group decision making context. The belief of each expert is elicited as a multivariate prior distribution. Then, linear and logarithmic combination methods are used to represent a consensus distribution. Anyway, the choice of the appropriate strategy will depend on the decision maker’s judgements. A significant task when using opinion pooling is to find the optimal weights. In order to carry it out, a criterion based on Kullback-Leibler divergence is proposed. Furthermore, based on the previous idea, an alternative procedure is presented when a solution cannot be found. The theoretical foundations are discussed in detail for each aggregation scheme. In particular, it is shown that a general unified method is achieved when they are applied to multivariate natural exponential families. Finally, two illustrative examples show that the proposed techniques can be easily applied in practice and their usefulness for decision making under the described situations.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 2362-2382.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1356098615

Digital Object Identifier
doi:10.1214/12-EJS752

Mathematical Reviews number (MathSciNet)
MR3020268

Zentralblatt MATH identifier
1295.62095

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62H99: None of the above, but in this section

Keywords
Bayesian analysis group decision Kullback-Leibler divergence multivariate exponential families opinion pooling

Citation

Rufo, María Jesús; Pérez, Carlos J.; Martín, Jacinto. A Bayesian approach to aggregate experts’ initial information. Electron. J. Statist. 6 (2012), 2362--2382. doi:10.1214/12-EJS752. https://projecteuclid.org/euclid.ejs/1356098615


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