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5/8/2011 12:29:42 PM
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abstract
Employment functional analysis to derive Bayesian approximation to select the smallest category (cell) in multinomial population, with linear loss function and prior Dirichlet distribution.
Introduction
A ranking and selection problem usually results from questions like : "which brand of cigarettes is least likely to cause cancer ?" ; "which type of seat belt reduces car accident injuries the most ?";"which type of atomic power plant increases radiation levels the best?"; or" which type of catalyst increases a certain chemical process yield the most ?". Thus, we have several alternatives[KIM,S.H and NELSON,2003]
The general formulation which we use below is as follows. We have sources of observation (each such source is called a population denoted by From source we may obtain independent and identically distributed observation whose distribution involves an unknown parameter ; except for the value of the distribution is assumed not to differ from population to population . our goal is to select that population which has the largest parameter .we are to perform the selection in such a way that the probability of selecting the correct population is at least (where is a specified number between 1/k and 1)[SEONG,KIM and L.NELSON,2004]. Whenever the largest and next largest of are "sufficiently far" apart (it being usually impossible to satisfy for all ,since the ?s could then be arbitrarily close together); the demand that any proposed procedure satisfy this criterion is called the probability requirement. more general formulations can be considered ( and will be noted in this paper) , but this one (with minor variations such as a goal of selecting that population which has the smallest parameter accounts for more than 75 percent of the work in this area to date .[6,5]
Bayesian Multinomial Selection Problem[S.A.MADHI and K.F.HAMZA,2007]
Let denote the ordered values of the and let has the multinomial distribution with probability mass function, such that the probability of an observation in the cell i , where .
In the Bayesian procedure we depended prior and posterior distribution. Prior distribution of is conjugate to the multinomial distribution

وصف الــ Tags لهذا الموضوع
 Approximation, Bayesian, selecting, multinomial population by functional analysis
