A Bayesian approach to aggregate experts’ initial information

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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.

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