New PDF release: Coping with Uncertainty: Robust Solutions

By Kurt Marti, Yuri Ermoliev, Marek Makowski

ISBN-10: 3642037348

ISBN-13: 9783642037344

Support for addressing the on-going worldwide adjustments wishes recommendations for brand new clinical difficulties which in flip require new ideas and instruments. A key factor matters an enormous number of irreducible uncertainties, together with severe occasions of excessive multidimensional outcomes, e.g., the weather swap. The drawback is anxious with huge, immense charges as opposed to large uncertainties of utmost affects. conventional medical techniques depend on genuine observations and experiments. but no enough observations exist for brand spanking new difficulties, and "pure" experiments, and studying via doing might be dear, risky, or very unlikely. additionally, the on hand historic observations are frequently infected by way of prior activities, and guidelines. therefore, instruments are provided for the categorical remedy of uncertainties utilizing "synthetic" info composed of obtainable "hard" information from ancient observations, the result of attainable experiments, and medical proof, in addition to "soft" info from specialists' critiques, and scenarios.

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Extra info for Coping with Uncertainty: Robust Solutions

Example text

This interpretation is based on the generalization of a similar interpretation of subjective probabilities introduced by de Finetti. According to Walley (see also [87]) the lower (or upper) probability of an event A can be interpreted by specifying acceptable betting rates for betting on (or against) A. A/. A/. ;/ D 0. P . / D PN . / D 1. AC /. A/ Ä 1. B/, for disjoint events A and B. B/, for all events A and B. A/. Moreover, possibility and necessity measures of the possibility theory and belief and plausibility measures of the Dempster–Shafer theory of evidence are lower and upper probabilities.

Oper. Res. 25, 345–356 (1986) 18. : Possibility Theory. Plenum, New York (1988) 19. : When upper probabilities are possibility measures. Fuzzy Sets Syst. 49, 65–74 (1992) 20. : Quantitative possibility theory and its probabilistic connections. A. ) Soft Methods in Probability, Statistics and Data Analysis, pp. 3–26. Physica, Heidelberg (2002) 21. : On possibility/probability transformations. , Roubens, M. ) Fuzzy Logic. State of the Art, pp. 103–112. Kluwer, Dordrecht (1993) 22. : Probability–possibility transformations, triangular fuzzy-sets and probabilistic inequalities.

23) i D1 Let ˛ be the probability of the type-I error (probability of an erroneous rejection of H0 ), and ˇ be the probability of the type-II error (probability of an erroneous acceptance of H1 ). 1 A 1 C 0 n . 24) ˛/. We reject H0 in favour of H1 if Sn Ä B 1 C 0 n . 1 ˇ/=˛. If neither of these inequality holds, we have to increase the sample size by one, and repeat the same procedure. In the sequential test described above we have assumed that the value of is known. In practice, we never know this value in advance, but when the amount of historical data is large enough we can estimate , and take this estimated value as the known one.

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Coping with Uncertainty: Robust Solutions by Kurt Marti, Yuri Ermoliev, Marek Makowski

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