Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Assumptions, beliefs and probabilities
Artificial Intelligence
Perspectives on the theory and practice of belief functions
International Journal of Approximate Reasoning
Resolving misunderstandings about belief functions
International Journal of Approximate Reasoning - Special issue: The belief functions revisited: questions and answers
What is Dempster-Shafer's model?
Advances in the Dempster-Shafer theory of evidence
Axioms for probability and belief-function proagation
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Information Algebras: Generic Structures for Inference
Information Algebras: Generic Structures for Inference
Logical Compilation of Bayesian Networks with Discrete Variables
ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Belief functions on real numbers
International Journal of Approximate Reasoning
Extending stochastic ordering to belief functions on the real line
Information Sciences: an International Journal
A belief function classifier based on information provided by noisy and dependent features
International Journal of Approximate Reasoning
Particle filtering in the Dempster--Shafer theory
International Journal of Approximate Reasoning
Inference about constrained parameters using the elastic belief method
International Journal of Approximate Reasoning
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Statistical problems were at the origin of the mathematical theory of evidence, or Dempster-Shafer theory. It was also one of the major concerns of Philippe Smets, starting with his PhD dissertation. This subject is reconsidered here, starting with functional models, describing how data is generated in statistical experiments. Inference is based on these models, using probabilistic assumption-based reasoning. It results in posterior belief functions on the unknown parameters. Formally, the information used in the process of inference can be represented by hints. Basic operations on hints are combination, corresponding to Dempster's rule, and focussing. This leads to an algebra of hints. Applied to functional models, this introduces an algebraic flavor into statistical inference. It emphasizes the view that in statistical inference different pieces of information have to be combined and then focussed onto the question of interest. This theory covers Bayesian and Fisher type inference as two extreme cases of a more general theory of inference.