Combining marginal probability distributions via minimization of weighted sum of Kullback-Leibler divergences
This paper deals with the problem of combining marginal probability distributions as a means for aggregating pieces of expert information. A novel approach, which takes the combining problem as an analogy of statistical estimation, is proposed and discussed. The combined distribution is then searched as a minimizer of a weighted sum of Kullback-Leibler divergences of the given marginal distributions and corresponding marginals of the searched one. Necessary and sufficient conditions for a distribution to be a minimizer are stated. For discrete random variables an iterative algorithm for approximate solution of the minimization problem is proposed and its convergence is proved. (C) 2011 Elsevier Inc. All rights reserved.
kullback-leibler divergence combining probabilities maximum likelihood expert opinions linear opinion pool