dc.contributor.author Giang, Phan H. dc.contributor.author Shenoy, Prakash P. dc.date.accessioned 2005-10-27T21:13:11Z dc.date.available 2005-10-27T21:13:11Z dc.date.issued 2005-07 dc.identifier.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 dc.identifier.issn 0004-3702 dc.identifier.uri http://hdl.handle.net/1808/758 dc.description.abstract 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. dc.format.extent 508024 bytes dc.format.mimetype application/pdf dc.language.iso en_US dc.publisher Elsevier Science Publishers B. V. dc.rights This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License dc.rights.uri https://creativecommons.org/licenses/by-nc-nd/4.0/ dc.subject Decision theory dc.subject Likelihood dc.subject Statistical inference dc.subject Ambiguity attitude dc.title Decision making on the sole basis of statistical likelihood dc.type Article dc.identifier.orcid https://orcid.org/0000-0002-8425-896X dc.rights.accessrights openAccess
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