Combining marginal probability distributions via minimization of weighted sum of Kullback-Leibler divergences |
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Authors: | Jan Krací k |
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Affiliation: | Department of Adaptive Systems, Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague, Czech Republic |
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Abstract: | 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. |
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Keywords: | Combining probabilities Kullback-Leibler divergence Maximum likelihood Expert opinions Linear opinion pool |
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