hig.sePublications
Change search

Cite
Citation style
• apa
• harvard-cite-them-right
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• sv-SE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• de-DE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
Discrete Second-order Probability Distributions that Factor into Marginals
University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics. (Matematik)
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]

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.

##### Place, publisher, year, edition, pages
SIPTA , 2011. p. 335-342
##### Keyword [en]
Discrete probability, second-order probability, imprecise probability, multivariate Pólya distribution, conjugate prior, compound hypergeometric likelihood.
##### National Category
Probability Theory and Statistics
##### Identifiers
ISI: 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
Available from: 2011-09-01 Created: 2011-07-30 Last updated: 2018-03-13Bibliographically approved

#### Open Access in DiVA

##### File information
File name FULLTEXT01.pdfFile size 303 kBChecksum SHA-512
fd30644757c2b7f9c94fff18a9c2ed5a0f0c36f35e1eb672f1bdff04b8bf860352c36f1a14d17c9078c7491dd16f6f291ece63fbd5d4a72db9872f9ca06febcb
Type fulltextMimetype application/pdf

Scopushttp://www.sipta.org/isipta11/index.php?id=paper&paper=038.html

Sundgren, David

#### Search in DiVA

Sundgren, David
Mathematics
##### On the subject
Probability Theory and Statistics

#### Search outside of DiVA

The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available
isbn
urn-nbn

#### Altmetric score

isbn
urn-nbn
Total: 124 hits

Cite
Citation style
• apa
• harvard-cite-them-right
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• sv-SE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• de-DE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf