A characterization of the Dirichlet process. (English) Zbl 0736.62007

Lo, Albert Y.

Stat. Probab. Lett. 12, No. 3, 185-187 (1991).

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:

62E10

Characterization and structure theory of statistical distributions

Keywords:

linear posterior means; posterior mean of a random probability; sample empirical distribution function; Dirichlet random probability

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