Updating beliefs with incomplete observations
Artificial Intelligence
A survey of the theory of coherent lower previsions
International Journal of Approximate Reasoning
Imprecise probability trees: Bridging two theories of imprecise probability
Artificial Intelligence
Artificial Intelligence
Representation insensitivity in immediate prediction under exchangeability
International Journal of Approximate Reasoning
Conservative inference rule for uncertain reasoning under incompleteness
Journal of Artificial Intelligence Research
Imprecise markov chains and their limit behavior
Probability in the Engineering and Informational Sciences
Epistemic irrelevance in credal nets: The case of imprecise Markov trees
International Journal of Approximate Reasoning
Artificial Intelligence
The use of Markov operators to constructing generalised probabilities
International Journal of Approximate Reasoning
Generalizing inference rules in a coherence-based probabilistic default reasoning
International Journal of Approximate Reasoning
Conglomerable natural extension
International Journal of Approximate Reasoning
Irrelevant and independent natural extension for sets of desirable gambles
Journal of Artificial Intelligence Research
Artificial Intelligence
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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.