Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Artificial Intelligence
Graphoid properties of epistemic irrelevance and independence
Annals of Mathematics and Artificial Intelligence
Epistemic irrelevance on sets of desirable gambles
Annals of Mathematics and Artificial Intelligence
Computing lower and upper expectations under epistemic independence
International Journal of Approximate Reasoning
Notes on conditional previsions
International Journal of Approximate Reasoning
Marginal extension in the theory of coherent lower previsions
International Journal of Approximate Reasoning
A survey of the theory of coherent lower previsions
International Journal of Approximate Reasoning
Probabilistic logic with independence
International Journal of Approximate Reasoning
Artificial Intelligence
Updating coherent previsions on finite spaces
Fuzzy Sets and Systems
The inferential complexity of Bayesian and credal networks
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
Epistemic irrelevance in credal nets: The case of imprecise Markov trees
International Journal of Approximate Reasoning
New complexity results for MAP in Bayesian networks
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three
The use of Markov operators to constructing generalised probabilities
International Journal of Approximate Reasoning
On the connection between probability boxes and possibility measures
Information Sciences: an International Journal
Irrelevant and independent natural extension for sets of desirable gambles
Journal of Artificial Intelligence Research
International Journal of Approximate Reasoning
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There is no unique extension of the standard notion of probabilistic independence to the case where probabilities are indeterminate or imprecisely specified. Epistemic independence is an extension that formalises the intuitive idea of mutual irrelevance between different sources of information. This gives epistemic independence very wide scope as well as appeal: this interpretation of independence is often taken as natural also in precise-probabilistic contexts. Nevertheless, epistemic independence has received little attention so far. This paper develops the foundations of this notion for variables assuming values in finite spaces. We define (epistemically) independent products of marginals (or possibly conditionals) and show that there always is a unique least-committal such independent product, which we call the independent natural extension. We supply an explicit formula for it, and study some of its properties, such as associativity, marginalisation and external additivity, which are basic tools to work with the independent natural extension. Additionally, we consider a number of ways in which the standard factorisation formula for independence can be generalised to an imprecise-probabilistic context. We show, under some mild conditions, that when the focus is on least-committal models, using the independent natural extension is equivalent to imposing a so-called strong factorisation property. This is an important outcome for applications as it gives a simple tool to make sure that inferences are consistent with epistemic independence judgements. We discuss the potential of our results for applications in Artificial Intelligence by recalling recent work by some of us, where the independent natural extension was applied to graphical models. It has allowed, for the first time, the development of an exact linear-time algorithm for the imprecise probability updating of credal trees.