gistfile1.txt

Modeling a binomial process with the beta binomial

Case 1: You have no information

This requires using a non-informative prior for the beta distribution. Normally this is done
with a uniform prior for all values of p, which corresponds to alpha = beta = 1.

Case 2: You have some prior information in terms of the mean and variance of p

You calculate alpha and beta, like in this post: http://stats.stackexchange.com/questions/12232/calculating-the-parameters-of-a-beta-distribution-using-the-mean-and-variance
That gives you a beta prior which reflects your prior information.

Case 3: You have information from previous binomial events, in the form ok k successes out of n trials:

Given that the beta is conjugate to the binomial, the posterior takes the form of the previous beta like this:

Beta(alpha, beta) => Beta(alpha + k, beta + n - k)

Thus, if you started with a uniform prior and have info on binomial events, you get this prior:

Beta(alpha, beta) => Beta(1 + k, 1 + n - k)

The process is, prior + evidence = posterior, which becomes the new prior for your new distribution.