Marginal extension in the theory of coherent lower previsions
We generalise Walley's Marginal Extension Theorem to the case of any finite number of conditional lower previsions. Unlike the procedure of natural extension, our marginal extension always provides the smallest (most conservative) coherent extensions. We show that they can also be calculated as lower envelopes of marginal extensions of conditional linear (precise) previsions. Finally, we use our version of the theorem to study the so-called forward irrelevant product and forward irrelevant natural extension of a number of marginal lower previsions. (C) 2007 Elsevier Inc. All rights reserved.
marginal extension coherence lower previsions natural extension forward irrelevance forward irrelevant product forward irrelevant natural extension imprecise probabilities epistemic irrelevance