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Shifted Dirichlet Distributions as Second-Order Probability Distributions that Factors into Marginals
Univ Gavle, Gavle, Sweden..
KTH.
Univ Stockholm, S-10691 Stockholm, Sweden..
2009 (English)In: ISIPTA '09: PROCEEDINGS OF THE SIXTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS / [ed] Augustin, T Coolen, FPA Moral, S Troffaes, MCM, SOC IMPRECISE PROBABILITY THEORY & APPLICATIONS-SIPTA , 2009, p. 405-+Conference paper, Published paper (Refereed)
Abstract [en]

In classic decision theory it is assumed that a decision-maker can assign precise numerical values corresponding to the true value of each consequence, as well as precise numerical probabilities for their occurrences. In attempting to address real-life problems, where uncertainty in the input data prevails, some kind of representation of imprecise information is important. Second-order distributions, probability distributions over probabilities, is one way to achieve such a representation. However, it is hard to intuitively understand statements in a multi-dimensional space and user statements must be provided more locally. But the information-theoretic interplay between joint and marginal distributions may give rise to unwanted effects on the global level. We consider this problem in a setting of second-order probability distributions and find a family of distributions that normalised over the probability simplex equals its own product of marginals. For such distributions, there is no flow of information between the joint distributions and the marginal distributions other than the trivial fact that the variables belong to the probability simplex.

Place, publisher, year, edition, pages
SOC IMPRECISE PROBABILITY THEORY & APPLICATIONS-SIPTA , 2009. p. 405-+
Keywords [en]
Second-order probability distribution, Dirichlet distribution, Beta distribution, Kullback-Leibler divergence, relative entropy, product of marginal distributions
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:kth:diva-242875ISI: 000280248700042Scopus ID: 2-s2.0-84867584079OAI: oai:DiVA.org:kth-242875DiVA, id: diva2:1289209
Conference
6th International Symposium on Imprecise Probability: Theories and Applications, ISIPTA 2009; Durham; United Kingdom
Note

QC 20190215

Available from: 2019-02-15 Created: 2019-02-15 Last updated: 2019-02-15Bibliographically approved

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  • apa
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