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Some second order effects on interval based probabilities
University of Gävle.
Dept. of Computer and Systems Sciences, Stockholm University, KTH.
Dept. of Computer and Systems Sciences, Stockholm University, KTH.
2006 (English)In: FLAIRS 2006 - Proceedings of the Nineteenth International Florida Artificial Intelligence Research Society Conference, 2006, 848-853 p.Conference paper, Published paper (Refereed)
Abstract [en]

In real-life decision analysis, the probabilities and values of consequences are in general vague and imprecise. One way to model imprecise probabilities is to represent a probability with the interval between the lowest possible and the highest possible probability, respectively. However, there are disadvantages with this approach, one being that when an event has several possible out-comes, the distributions of belief in the different probabilities are heavily concentrated to their centers of mass, meaning that much of the information of the original intervals are lost. Representing an imprecise probability with the distribution's center of mass therefore in practice gives much the same result as using an interval, but a single number instead of an interval is computationally easier and avoids problems such as overlapping intervals. Using this, we demonstrate why second-order calculations can add information when handling imprecise representations, as is the case of decision trees or probabilistic networks. We suggest a measure of belief density for such intervals. We also demonstrate important properties when operating on general distributions. The results herein apply also to approaches which do not explicitly deal with second-order distributions, instead using only first-order concepts such as upper and lower bounds

Place, publisher, year, edition, pages
2006. 848-853 p.
Keyword [en]
Computational methods; Distributed parameter control systems; Information analysis; Probability; Problem solving; Real time systems
National Category
Information Science
Identifiers
URN: urn:nbn:se:kth:diva-7340Scopus ID: 2-s2.0-33746052058OAI: oai:DiVA.org:kth-7340DiVA: diva2:12325
Conference
FLAIRS 2006 - 19th International Florida Artificial Intelligence Research Society Conference; Melbourne Beach, FL; 11 May 2006 through 13 May 2006
Note
QC 20101117Available from: 2007-06-18 Created: 2007-06-18 Last updated: 2010-11-17Bibliographically approved
In thesis
1. Distribution of expected utility in second-order decision analysis
Open this publication in new window or tab >>Distribution of expected utility in second-order decision analysis
2007 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [la]

In explicatione consiliorum, maxima facere communis utilitas saepe trita ratio deligendi meliorem optionem est. Verum si probabilitates et utilitates incertae vel dubiae sint, communis utilitas perturbationes affert. Studium secundi ordinis effectuum in explicatione consiliorum explanat momentum structurae quaestionium consilii, insidias aliquas ad consilium capiendum indicat et facilem ad efficiendum et intellegendum rationem comparandi varia consilia suadet. Haec thesis tractat de secundi ordinis effectibus explicationis consilii, praesertim de commune utilitate et de probabilitatibus coniunctis intervallo. Voces apertae distributionum ordinis secundi in probabilitatibus intervallo conjunctis insitarum omnino et item distributionum utilitatis expectatae in parvis quaestionibus consiliorum eduntur. His distributionibus cognitis studetur res inflexionis, aliter dictu intentio fidei.

Abstract [en]

In decision analysis maximising the expected utility is an often used approach in choosing the optimal alternative. But when probabilities and utilities are vague or imprecise expected utility is fraught with complications. Studying second-order effects on decision analysis casts light on the importance of the structure of decision problems, pointing out some pitfalls in decision making and suggesting an easy to implement and easy to understand method of comparing decision alternatives. The topic of this thesis is such second-order effects of decision analysis, particularly with regards to expected utility and interval-bound probabilities. Explicit expressions for the second-order distributions inherent in interval-bound probabilities in general and likewise for distributions of expected utility for small decision problems are produced. By investigating these distributions the phenomenon of warping, that is concentration of belief, is studied.

Place, publisher, year, edition, pages
Stockholm: KTH, 2007. vi, 20 p.
Series
Report series / DSV, ISSN 1101-8526 ; 07-006
National Category
Information Science
Identifiers
urn:nbn:se:kth:diva-4442 (URN)
Presentation
2007-06-05, Sal C, KTH-Forum, entréplanet, trapphus C, Isafjordsgatan 39, Kista, 13:00
Opponent
Supervisors
Note
QC 20101118Available from: 2007-06-18 Created: 2007-06-18 Last updated: 2010-11-18Bibliographically approved

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  • apa
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