Marginal extension in the theory of coherent lower previsions. (English) Zbl 1148.68045
Summary: 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.
MSC:
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
Keywords:
imprecise probabilities; lower previsions; coherence; natural extension; marginal extension; epistemic irrelevance; forward irrelevance; forward irrelevant natural extension; forward irrelevant productReferences:
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