Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series A, Pt. 3, 763--819

A BAYESIAN PEEK INTO FELLER VOLUME i

By

PERSI DIACONIS, Stanford University, USA and SUSAN HOLMES, Stanford University, USA and INRA, France

SUMMARY. We develop Bayesian versions of three classic probability problems: the birthday problem, the coupon collector's problem and the matching problem. In each case, the Bayesian component involves a prior on the underlying probability mechanism. Sometimes this appreciably changes the answer, sometimes not.

*AMS (1991) subject classification}. *60A99, 60-02, 60E0.

*Key words and phrases. *Birthday Problem, coupon collector's problem, matching problem, Dirichlet prior, Stein's Method, Bose-Einstein distribution.