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.

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