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Discrete Second-order Probability Distributions that Factor into MarginalsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2011 (English)In: Proceedings of the Seventh International Symposium on Imprecise Probabilities: Theories and Applications / [ed] Frank Coolen, Gert de Cooman, Thomas Fetz, Michael Oberguggenberger, SIPTA , 2011, p. 335-342Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

SIPTA , 2011. p. 335-342
##### Keywords [en]

Discrete probability, second-order probability, imprecise probability, multivariate Pólya distribution, conjugate prior, compound hypergeometric likelihood.
##### National Category

Probability Theory and Statistics
##### Identifiers

URN: urn:nbn:se:hig:diva-9807ISI: 000323983600036Scopus ID: 2-s2.0-84883215401ISBN: 978-3-902652-40-9 (print)OAI: oai:DiVA.org:hig-9807DiVA, id: diva2:432108
##### Conference

7th International Symposium on Imprecise Probabilities: Theories and Applications (ISIPTA), July 25-28, 2011, Innsbruck, Austria
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt756",{id:"formSmash:j_idt756",widgetVar:"widget_formSmash_j_idt756",multiple:true}); Available from: 2011-09-01 Created: 2011-07-30 Last updated: 2018-03-13Bibliographically approved

In realistic decision problems there is more often than not uncertainty in the background information. As for representation of uncertain or imprecise probability values, second-order probability, i.e. probability distributions over probabilities, offers an option. With a subjective view of probability second-order probability would seem to be impractical since it is hard for a person to construct a second-order distributions that reflects his or her beliefs. From the perspective of probability as relative frequency the task of constructing or updating a second-order probability distribution from data is somewhat easier. Here a very simple model for updating lower bounds of probabilities is employed. But the difficulties in choosing second-order distributions may be further alleviated if structural properties are considered. Either some of the probability values are dependent in some way, e.g. that they are known to be almost equal, or they are not dependent in any other way than what follows from that the values sum to one. In this work we present the unique family of discrete second-order probability distributions that correspond to the case where dependence is limited. These distributions are shown to have the property that the joint distributions are equal to normalised products of marginal distributions. The distribution family introduced here is a generalisation of a special case of the multivariate Pólya distribution and is shown to be conjugate prior to a compound hypergeometric distribution.

isbn
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