Artificial Intelligence
The uncertain reasoner's companion: a mathematical perspective
The uncertain reasoner's companion: a mathematical perspective
Algorithms for precise and imprecise conditional probability assessments
Mathematical models for handling partial knowledge in artificial intelligence
On the Linear Structure of Betting Criterion and the Checking of Coherence
Annals of Mathematics and Artificial Intelligence
Modeling uncertain and vague knowledge in possibility and evidence theories
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Belief revision and information fusion on optimum entropy: Research Articles
International Journal of Intelligent Systems - Uncertain Reasoning (Part 2)
Probabilistic logic under coherence: complexity and algorithms
Annals of Mathematics and Artificial Intelligence
Computing lower and upper expectations under epistemic independence
International Journal of Approximate Reasoning
Decision making under incomplete data using the imprecise Dirichlet model
International Journal of Approximate Reasoning
An introduction to the imprecise Dirichlet model for multinomial data
International Journal of Approximate Reasoning
Statistical matching of multiple sources: A look through coherence
International Journal of Approximate Reasoning
Generalizing inference rules in a coherence-based probabilistic default reasoning
International Journal of Approximate Reasoning
Imprecise probabilities for representing ignorance about a parameter
International Journal of Approximate Reasoning
Conditional random quantities and iterated conditioning in the setting of coherence
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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This paper considers the simple problem of abduction in the framework of Bayes theorem, when the prior probability of the hypothesis is not available, either because there are no statistical data to rely on, or simply because a human expert is reluctant to provide a subjective assessment of this prior probability. This abduction problem remains an open issue since a simple sensitivity analysis on the value of the unknown prior yields empty results. This paper tries to propose some criteria a solution to this problem should satisfy. It then surveys and comments on various existing or new solutions to this problem: the use of likelihood functions (as in classical statistics), the use of information principles like maximum entropy, Shapley value, maximum likelihood. Finally, we present a novel maximum likelihood solution by making use of conditional event theory. The formal setting includes de Finetti's coherence approach, which does not exclude conditioning on contingent events with zero probability.