Artificial Intelligence
Bayesian and non-Bayesian evidential updating
Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Decision Support Systems - Special issue on logic modeling
2U: an exact interval propagation algorithm for polytrees with binary variables
Artificial Intelligence
Irrelevance and Independence Axioms in Quasi-Bayesian Theory
ECSQARU '95 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Irrelevance and independence relations in Quasi-Bayesian networks
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Independence concepts for convex sets of probabilities
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Robustness analysis of Bayesian networks with local convex sets of distributions
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
Independence with lower and upper probabilities
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
Sequential decision making with partially ordered preferences
Artificial Intelligence
International Journal of Approximate Reasoning
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This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The adoption of a contraction condition leads to d-separation but still fails to guarantee a belief separation property. To overcome this unsatisfactory situation, a strong Markov condition is proposed, based on epistemic independence. The main result is that the strong Markov condition leads to strong independence and does enforce separation properties; this result implies that (1) separation properties of Bayesian networks do extend to epistemic independence and sets of probability measures, and (2) strong independence has a clear justification based on epistemic independence and the strong Markov condition.