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Journal Article

Combining Marginal Probability Distributions via Minimization of Weighted Sum of Kullback-Leibler Divergences

Kracík Jan

: International Journal of Approximate Reasoning vol.52, 6 (2011), p. 659-671

: CEZ:AV0Z10750506

: GA102/08/0567, GA ČR

: combining probabilities, Kullback-Leibler divergence, maximum likelihood, expert opinions, linear opinion pool

: 10.1016/j.ijar.2011.01.002

: http://library.utia.cas.cz/separaty/2011/AS/kracik-0359399.pdf

(eng): The paper deals with the problem of combining marginal probability distributions as a means for aggregating pieces of expert information. The combined distribution is 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.

: BB