Stochastic dominance and expected utility: survey and analysis
Management Science
An axiomatic treatment of three qualitative decision criteria
Journal of the ACM (JACM)
On the possibilistic decision model: from decision under uncertainty to case-based decision
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - A special issue on fuzzy measures
A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Reasoning about Uncertainty
A decision theory for non-probabilistic uncertainty and its applications
A decision theory for non-probabilistic uncertainty and its applications
Possibility theory as a basis for qualitative decision theory
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
Statistical decisions using likelihood information without prior probabilities
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Three approaches to probability model selection
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
A decision theory for partially consonant belief functions
International Journal of Approximate Reasoning
| Hi-index | 0.00 |
This paper presents a new axiomatic decision theory for choice under uncertainty. Unlike Bayesian decision theory where uncertainty is represented by a probability function, in our theory, uncertainty is given in the form of a likelihood function extracted from statistical evidence. The likelihood principle in statistics stipulates that likelihood functions encode all relevant information obtainable from experimental data. In particular, we do not assume any knowledge of prior probabilities. Consequently, a Bayesian conversion of likelihoods to posterior probabilities is not possible in our setting. We make an assumption that defines the likelihood of a set of hypotheses as the maximum likelihood over the elements of the set. We justify an axiomatic system similar to that used by von Neumann and Morgenstern for choice under risk. Our main result is a representation theorem using the new concept of binary utility. We also discuss how ambiguity attitudes are handled. Applied to the statistical inference problem, our theory suggests a novel solution. The results in this paper could be useful for probabilistic model selection.