Characterization and Empirical Evaluation of Bayesian and Credal Combination Operators

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1 December 2011
Alexander Karlsson, Ronnie Johansson, Sten F. Andler

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We address the problem of combining independent evidences from multiple sources by utilizing the Bayesian and credal combi-nation operators. We present measures for degree of conflict and imprecision, which we use in order to characterize the behavior of the operators through a number of examples. We introduce dis-counting operators that can be used whenever information about the reliability of sources is available. The credal discounting operator discounts a credal set with respect to an interval of reliability weights, hence, we allow for expressing reliability of sources im-precisely. We prove that the credal discounting operator can be computed by using the extreme points of its operands. We also per-form two experiments containing different levels of risk where we compare the performance of the Bayesian and credal combination operators by using a simple score function that measures the informativeness of a reported decision set. We show that the Bayesian combination operator performed on centroids of operand credal sets outperforms the credal combination operator when no risk is involved in the decision problem. We also show that if a risk component is present in the decision problem, a simple cautious decision policy for the Bayesian combination operator can be constructed that outperforms the corresponding credal decision policy.