## The Annals of Probability

- Ann. Probab.
- Volume 2, Number 2 (1974), 183-201.

### Tailfree and Neutral Random Probabilities and Their Posterior Distributions

#### Abstract

The random distribution function $F$ and its law is said to be neutral to the right if $F(t_1), \lbrack F(t_2) - F(t_1) \rbrack/\lbrack 1 - F(t_1)\rbrack, \cdots, \lbrack F(t_k) - F(t_{k-1}) \rbrack/\lbrack 1 - F(t_{k-1}) \rbrack$ are independent whenever $t_1 < \cdots < t_k$. The posterior distribution of a random distribution function neutral to the right is shown to be neutral to the right. Characterizations of these random distribution functions and connections between neutrality to the right and general concepts of neutrality and tailfreeness (tailfreedom) are given.

#### Article information

**Source**

Ann. Probab., Volume 2, Number 2 (1974), 183-201.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176996703

**Digital Object Identifier**

doi:10.1214/aop/1176996703

**Mathematical Reviews number (MathSciNet)**

MR373081

**Zentralblatt MATH identifier**

0279.60097

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60K99: None of the above, but in this section

Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 62G99: None of the above, but in this section

**Keywords**

Random probabilities posterior distributions processes Dirichlet process posterior mean of a process Bayes estimates tailfree neutral

#### Citation

Doksum, Kjell. Tailfree and Neutral Random Probabilities and Their Posterior Distributions. Ann. Probab. 2 (1974), no. 2, 183--201. doi:10.1214/aop/1176996703. https://projecteuclid.org/euclid.aop/1176996703