# zbMATH — the first resource for mathematics

A characterization of the Dirichlet process. (English) Zbl 0736.62007
The purpose of this note is to point out that if the posterior mean of a random probability $$P$$ given a sample $$X_ 1,\ldots,X_ n$$ from $$P$$ is linear in the sample empirical distribution function, then $$P$$ is a Dirichlet random probability.

##### MSC:
 6.2e+11 Characterization and structure theory of statistical distributions
Full Text:
##### References:
 [1] Diaconis, P.; Ylvisaker, D., Conjugate priors for exponential families, Ann. statist., 7, 269-281, (1979) · Zbl 0405.62011 [2] Doksum, K.A., Tailfree and neutral random probabilities and their posterior distributions, Ann. probab., 2, 183-201, (1974) · Zbl 0279.60097 [3] Ericson, W.A., Subjective Bayesian models in sampling finite populations, J. roy. statist. soc. ser. B, 31, 195-224, (1969) · Zbl 0186.51901 [4] Feller, W., An introduction to probability theory and its applications, (1971), Wiley New York · Zbl 0219.60003 [5] Ferguson, T.S., A Bayesian analysis of some nonparametric problems, Ann. statist., 1, 209-230, (1973) · Zbl 0255.62037 [6] Good, I.J., The estimation of probabilities: an essay on modern Bayesian methods. research monograph no. 30, (1965), MIT Press Cambridge, MA · Zbl 0168.39603 [7] Zabell, S.L., W.E. Johnson’s “sufficientness” postulate, Ann. statist., 10, 1091-1099, (1981) · Zbl 0512.62007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.