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  • 1.
    Sundgren, David
    et al.
    University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik.
    Danielson, Mats
    Deptartment of Computer and Systems Sciences, Stockholm University and TH, Kista, Sweden.
    Ekenberg, Love
    Deptartment of Computer and Systems Sciences, Stockholm University and TH, Kista, Sweden.
    Warp effects on calculating interval probabilities2009In: International Journal of Approximate Reasoning, ISSN 0888-613X, E-ISSN 1873-4731, Vol. 50, no 9, p. 1360-1368Article in journal (Refereed)
    Abstract [en]

    In real-life decision analysis, the probabilities and utilities 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 outcomes, the distributions of belief in the different probabilities are heavily concentrated toward their centres of mass, meaning that much of the information of the original intervals are lost. Representing an imprecise probability with the distribution’s centre 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. We demonstrate why second-order calculations 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 discuss properties applicable to 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.

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