Decision making on the sole basis of statistical likelihood

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Issue Date
2005-07Author
Giang, Phan H.
Shenoy, Prakash P.
Publisher
Elsevier Science Publishers B. V.
Format
508024 bytes
Type
Article
Rights
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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Show full item recordAbstract
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.
ISSN
0004-3702Collections
Citation
Giang, P. H. and Shenoy, P. P., "Decision making on the sole basis of statistical likelihood," Artificial Intelligence, Vol. 165, No. 2, 2005, pp. 137--163
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