On Dependence in Second-Order Probability
2012 (English)In: Scalable Uncertainty Management: 6th International Conference, SUM 2012, Proceedings / [ed] Eyke Hüllermeier, Sebastian Link, Thomas Fober and Bernhard Seeger, Berlin/Heidelberg: Springer Berlin/Heidelberg, 2012, 379-391 p.Conference paper (Refereed)
We present a notion, relative independence, that models independence in relation to a predicate. The intuition is to capture the notion of a minimum of dependencies among variables with respect to the predicate. We prove that relative independence coincides with conditional independence only in a trivial case. For use in second-order probability, we let the predicate express first-order probability, i.e. that the probability variables must sum to one in order to restrict dependency to the necessary relation between probabilities of exhaustive and mutually exclusive events. We then show examples of Dirichlet distributions that do and do not have the property of relative independence. These distributions are compared with respect to the impact of further dependencies, apart from those imposed by the predicate.
Place, publisher, year, edition, pages
Berlin/Heidelberg: Springer Berlin/Heidelberg, 2012. 379-391 p.
, Lecture Notes in Artificial Intelligence, ISSN 0302-9743 ; 7520
Imprecise probability, second-order probability, dependency
Research subject Computer and Systems Sciences
IdentifiersURN: urn:nbn:se:su:diva-80469DOI: 10.1007/978-3-642-33362-0ISBN: 978-3-642-33361-3OAI: oai:DiVA.org:su-80469DiVA: diva2:555502
Sixth International Conference on Scalable Uncertainty Management, Marburg, Germany, September 17-19, 2012