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Paper No. 15-08

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Leonelli M, Riccomagno E, Smith JQ

The algebra of integrated partial belief systems

Abstract: Current decision support systems address domains that are heterogeneous in nature and becoming larger. Such systems often require the input of expert judgement about a variety of dierent elds and an intensive computational power to produce scores to rank the available policies. The technology of integrating decision support systems has been recently extended to enable a formal distributed multi-agent decision analysis. Inference in these system is designed to be distributed so that for the sole purpose of decision support each panel needs to deliver only certain summaries of the variables under its jurisdiction. By using an algebraic approach, we are able to identify the required summaries and to demonstrate that coherence, in a sense we formalize here, is still guaranteed when panels only share a partial specication of their model with other panel members. We illustrate such algorithms for a variety of frameworks, including a specic class of Bayesian networks. For this class we derive closed form formulae for the computations of the joint moments of variables that determine the score of dierent policies.

Keywords: Bayesian networks, Integrating decision support systems, Polynomial algebra, Structural equation models.