# On extensions of marginals for decision-making

## Abstract

An *extension of a set of marginals* (small-dimensional distributions) is a joint probability distribution that is a ”good” representative of the knowledge (about the problem area) contained in the marginals. ”Good” means with respect to the subsequent decision-making for which the extension is needed. In the context of probabilistic expert systems, constructing the extension from the marginals may be referred to as the *knowledge integration* [4], *reconstructability analysis* [9] or *marginal problem*. The paper surveys different types of known extensions and on the basis of underlying principles and considerations, new types of extensions — the *EEV-centroid* and the *weighted centroid* are suggested.

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