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Approximation Bayesian for selecting functional analysis

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 كوثر فوزي حمزة الحسن
5/8/2011 12:29:42 PM
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Employment functional analysis to derive Bayesian approximation to select the smallest category (cell) in multinomial population, with linear loss function and prior Dirichlet distribution.
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