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Uncertainty, credal sets and second order probability
KTH, School of Architecture and the Built Environment (ABE), Philosophy and History of Technology, Philosophy.
2013 (English)In: Synthese, ISSN 0039-7857, E-ISSN 1573-0964, Vol. 190, no 3, 353-378 p.Article in journal (Refereed) Published
Abstract [en]

The last 20 years or so has seen an intense search carried out within Dempster–Shafer theory, with the aim of finding a generalization of the Shannon entropy for belief functions. In that time, there has also been much progress made in credal set theory—another generalization of the traditional Bayesian epistemic representation—albeit not in this particular area. In credal set theory, sets of probability functions are utilized to represent the epistemic state of rational agents instead of the single probability function of traditional Bayesian theory. The Shannon entropy has been shown to uniquely capture certain highly intuitive properties of uncertainty, and can thus be considered a measure of that quantity. This article presents two measures developed with the purpose of generalizing the Shannon entropy for (1) unordered convex credal sets and (2) possibly non-convex credal sets ordered by second order probability, thereby providing uncertainty measures for such epistemic representations. There is also a comparison with the results of the measure AU developed within Dempster–Shafer theory in a few instances where unordered convex credal set theory and Dempster–Shafer theory overlap.

Place, publisher, year, edition, pages
2013. Vol. 190, no 3, 353-378 p.
Keyword [en]
uncertainty, probability, information, credal set, entropy
National Category
Philosophy
Identifiers
URN: urn:nbn:se:kth:diva-72663DOI: 10.1007/s11229-011-0042-2ISI: 000313656400002Scopus ID: 2-s2.0-84872470316OAI: oai:DiVA.org:kth-72663DiVA: diva2:487929
Funder
Swedish Research Council
Note

QC 20130204

Available from: 2012-02-01 Created: 2012-02-01 Last updated: 2017-12-08Bibliographically approved
In thesis
1. Dealing with uncertainty
Open this publication in new window or tab >>Dealing with uncertainty
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Uncertainty is, it seems, more or less constantly present in our lives. Even so, grasping the concept philosophically is far from trivial. In this doctoral thesis, uncertainty and its conceptual companion information are studied. Axiomatic analyses are provided and numerical measures suggested. In addition to these basic conceptual analyses, the widespread practice of so-called safety factor use in societal regulation is analyzed along with the interplay between science and policy in European regulation of chemicals and construction.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. 25 p.
Series
Theses in philosophy from the Royal Institute of Technology, ISSN 1650-8831 ; 40
Keyword
safety factor, safety margin, uncertainty factor, uncertainty function, uncertainty, information, risk, risk assessment, risk management, epistemology, science, reasoning
National Category
Philosophy
Identifiers
urn:nbn:se:kth:diva-72680 (URN)978-91-7501-216-2 (ISBN)
Public defence
2012-02-17, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20120202Available from: 2012-02-02 Created: 2012-02-01 Last updated: 2012-02-02Bibliographically approved

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