Empirical Bayes in Large Scale Inference

Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction

Author: Bradley Efron, Stanford University, California
http://statweb.stanford.edu/~ckirby/brad/LSI/monograph_CUP.pdf

Recursive update of hypergeometric distribution

Recursively update dhyper(x,a,N-a,b):
dhyper(x,a+1,N-a-1,b)=dhyper(x,a,N-a,b) * ((a+1)/(a+1-x)) * ((N-a-b+x) /(N-a))
dhyper(x,a,N-a,b)=dhyper(x,a-1,N-a+1,b) * (a/(a-x)) * ((N-a+1-b+x) /(N-a+1))
dhyper(x+1,a,N-a,b)=dhyper(x,a,N-a,b) * ((a-x)/(x+1)) * ((b-x) /(N-a-b+x+1))
dhyper(x,a,N-a,b)=dhyper(x-1,a,N-a,b) * ((a-x+1)/x) * ((b-x+1) /(N-a-b+x))
dhyper(x+1,a+1,N-a-1,b)=dhyper(x,a,N-a,b) *  ((a+1)/(x+1)) * ((b-x)/(N-a))

Reference: see dhyper in R package.