Geodesic
Bayes sharpening of imprecise information
International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 3, pp. 393-404.

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A complete algorithm is presented for the sharpening of imprecise information, based on the methodology of kernel estimators and the Bayes decision rule, including conditioning factors. The use of the Bayes rule with a nonsymmetrical loss function enables the inclusion of different results of an under- and overestimation of a sharp value (real number), as well as minimizing potential losses. A conditional approach allows to obtain a more precise result thanks to using information entered as the assumed (e.g. current) values of conditioning factors of continuous and/or binary types. The nonparametric methodology of statistical kernel estimators freed the investigated procedure from arbitrary assumptions concerning the forms of distributions characterizing both imprecise information and conditioning random variables. The concept presented here is universal and can be applied in a wide range of tasks in contemporary engineering, economics, and medicine.
Keywords: imprecise information, sharpening, conditioning factors, kernel estimators, Bayes decision rule, nonsymmetrical loss function, numerical calculations
Mots-clés : informacja niepewna, współczynnik kondycji, estymator jądrowy, funkcja strat, obliczenia numerycze 
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Kulczycki, B.; Charytanowicz, M. Bayes sharpening of imprecise information. International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 3, pp. 393-404. http://geodesic.mathdoc.fr/item/IJAMCS_2005_15_3_a7/

[1] Billingsley P. (1989): Probability and Measure. — New York: Wiley.

[2] Brandt S. (1999): Statistical and Computational Methods in Data Analysis. —New York: Springer.

[3] Charytanowicz M. (2005): Bayesian sharpening of imprecise information in medical applications. — Ph.D. thesis, Systems Research Institute, Polish Academy of Sciences,Warsaw, (in Polish).

[4] Dahlquist G. and Bjorck A. (1983): Numerical Methods. — Englewood Cliffs: Prentice-Hall.

[5] Kacprzyk J. (1986): Fuzzy Sets in Systems Analysis.—Warsaw: PWN, (in Polish).

[6] Kiełbasiński A. and Schwetlick H. (1994): Numerical Linear Algebra. —Warsaw: WNT, (in Polish).

[7] Kulczycki P. (2000): Fuzzy controller for mechanical systems. — IEEE Trans. Fuzzy Syst., Vol. 8, No. 5, pp. 645–652.

[8] Kulczycki P. (2001): An algorithm for Bayes parameter identification. — J. Dynam. Syst. Meas. Contr., Vol. 123, No. 4, pp. 611–614.

[9] Kulczycki P. (2002a): Statistical inference for fault detection: A complete algorithm based on kernel estimators. — Kybernetika, Vol. 38, No. 2, pp. 141–168.

[10] Kulczycki P. (2002b): A test for comparing distribution functions with strongly unbalanced samples. — Statistica, Vol. LXII, No. 1, pp. 39–49.

[11] Kulczycki P. (2005): Kernel Estimators in Systems Analysis. — Warsaw: WNT in press, (in Polish).

[12] Kulczycki P. and Wiśniewski R. (2002): Fuzzy controller for a system with uncertain load. — Fuzzy Sets Syst., Vol. 131, No. 2, pp. 185–195.

[13] Silverman B.W. (1986): Density Estimation for Statistics and Data Analysis. —London: Chapman and Hall.

[14] Stoer J. and Bulirsch R. (1987): Introduction to Numerical Analysis. —New York: Springer.

[15] Wand M.P. and Jones M.C. (1995): Kernel Smoothing. — London: Chapman and Hall.