Robust Bayesian analysis in partially ordered plausibility calculi
2016 (English)In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 78, 1-14 p.Article in journal (Refereed) Published
In Robust Bayesian analysis one attempts to avoid the 'Dogma of Precision' in Bayesian analysis by entertaining a set of probability distributions instead of exactly one. The algebraic approach to plausibility calculi is inspired by Cox's and Jaynes' analyses of plausibility assessment as a logic of uncertainty. In the algebraic approach one is not so much interested in different ways to prove that precise Bayesian probability is inevitable but rather in how different sets of assumptions are reflected in the resulting plausibility calculus. It has repeatedly been pointed out that a partially ordered plausibility domain is more appropriate than a totally ordered one, but it has not yet been completely resolved exactly what such domains can look like. One such domain is the natural robust Bayesian representation, an indexed family of probabilities. We show that every plausibility calculus embeddable in a partially ordered ring is equivalent to a subring of a product of ordered fields, i.e., the robust Bayesian representation is universal under our assumptions, if extended rather than standard probability is used. We also show that this representation has at least the same expressiveness as coherent sets of desirable gambles with real valued payoffs, for a finite universe.
Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 78, 1-14 p.
Robust Bayesian analysis, Imprecise probabilities, Algebraic plausibility calculi
IdentifiersURN: urn:nbn:se:kth:diva-193970DOI: 10.1016/j.ijar.2016.06.006ISI: 000383935200001ScopusID: 2-s2.0-84976551409OAI: oai:DiVA.org:kth-193970DiVA: diva2:1037684
QC 201610172016-10-172016-10-142016-10-17Bibliographically approved