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On Numerical Calculation of Probabilities According to Dirichlet Distribution

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Abstract:
Dirichlet distribution is a continuous multivariate probability distribution having all beta one dimensional marginal distributions. Although it may have many interesting applications in statistics, inventory control, PERT modeling and stochastic programming, the numerical calculation of probability values according to this distribution became possible only in the last decade. In my talk I will give algorithms for the numerical calculation of the cumulative distribution function (c.d.f.) values of Dirichlet distribution. These algorithms use the so called Lauricella hypergeometric functions in low dimension and in higher dimensions they utilize the so called hyper-multitree bounds introduced by Jozsef Bukszar and variance reduction simulation procedures based on these bounds. There will be given formulae for the calculation of the first and second order partial derivatives, too. The common property of these formulae is that they involve only lower dimensional Dirichlet c. d. f. calculations. Some other multivariate distributions deriving from the Dirichlet distribution will also be mentioned. In the second part of my talk I will show how the Sequential Conditional Sampling (SCS) procedure works in the case of the Dirichlet distribution. On the base of this sampling technique one can apply importance sampling algorithms called Sequential conditional Importance Sampling (SCIS) for the estimation of extremely small c.d.f. values of the Dirichlet distribution. All results of this talk were achieved jointly with my earlier Egyptian PhD student Ashraf Gouda.

http://www.math.bme.hu/diffe/szantaia.htm
Type of Seminar:
Optimization and Applications Seminar
Speaker:
Prof. Tamas Szantai
Budapest University of Technology and Economics
Date/Time:
May 03, 2010   16:30
Location:

HG G 19.1, Rämistrasse 101
Contact Person:

Prof. J. Lygeros
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Biographical Sketch: