Alexander Karlsson, David Sundgren

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Second-Order Credal Combination of Evidence

Abstract

We utilize second-order probability distributions for modeling second-order information over imprecise evidence in the form of credal sets. We generalize the Dirichlet distribution to a shifted version, denoted the S-Dirichlet, which allows one to restrict the support of the distribution by lower bounds. Based on the S-Dirichlet distribution, we present a simple combination schema denoted as second-order credal combination (SOCC), which takes second-order probability into account. The combination schema is based on a set of particles, sampled from the operands, and a set of weights that are obtained through the S-Dirichlet distribution. We show by examples that the second-order probability distribution over the imprecise joint evidence can be remarkably concentrated and hence that the credal combination operator can significantly overestimate the imprecision.

Keywords

Second-order credal combination, Imprecise probability, Credal sets, Second-order probability, Combination, Evidence

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E-mail addresses

Alexander Karlsson		alexander.karlsson@his.se
David Sundgren		dsn@dsv.su.se