In article <[EMAIL PROTECTED]>, Duncan Smith <[EMAIL PROTECTED]> wrote:
>"wuzzy" <[EMAIL PROTECTED]> wrote in message >news:[EMAIL PROTECTED] >> I asked this elswhere, this group may be more appropriate, appologies >> for simple question? >> Can someone describe an algorithm in MS Excel to find the posterior >> distribution given a likelihood function (=BINOMDIST) and a prior >> distribution (=NORMDIST mu=0, sigma=0.05)? >> I know that it is proportional to L*P (likelihood times prior). >> [anyone know how to calculate the denominator in excel?] >> But what is an exact algorithm?! >> For instance I was considering sampling 10 random parameters in ten >> columns >> of BINOMDIST()*NORMDIST(from 1..10) for each case. But what does this >> product tell me? how do I actually plot the distribution? >> Thanks >Does it make sense to have a Normal prior (particularly with mu=0) with a >Binomial likelihood? If a Beta prior makes at least as much sense it makes >the maths much easier. >Duncan I see two common errors here. In principle, the prior, or the operational loss-prior combination, should come from the user, with no consideration of computational ease. It MAY be that a conjugate prior provides a reasonable approximation, or it may not. My prior distribution for baseball players' batting averages is definitely not well approximated by a Beta distribution. The other error is that, while the logistic is a model for probabilities, the parameters of the logistic are not the direct calculation of the probabilities. In fact, I have seen the logistic model as a conditional normal model. Computationally, one can give priors easier to work with, but they will be logistic type priors. Numerical integration is an art, especially if it is in more than one dimension. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
