## The Annals of Statistics

- Ann. Statist.
- Volume 13, Number 3 (1985), 1129-1139.

### A Bayesian Nonparametric Sequential Test for the Mean of a Population

#### Abstract

We may take observations sequentially from a population with unknown mean $\theta$. After this sampling stage, we are to decide whether $\theta$ is greater or less than a known constant $\nu$. The net worth upon stopping is either $\theta$ or $\nu$, respectively, minus sampling costs. The objective is to maximize the expected net worth when the probability measure of the observations is a Dirichlet process with parameter $\alpha$. The stopping problem is shown to be truncated when $\alpha$ has bounded support. The main theorem of the paper leads to bounds on the exact stage of truncation and shows that sampling continues longest on a generalized form of neutral boundary.

#### Article information

**Source**

Ann. Statist., Volume 13, Number 3 (1985), 1129-1139.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176349660

**Digital Object Identifier**

doi:10.1214/aos/1176349660

**Mathematical Reviews number (MathSciNet)**

MR803762

**Zentralblatt MATH identifier**

0585.62137

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62L15: Optimal stopping [See also 60G40, 91A60]

Secondary: 62C10: Bayesian problems; characterization of Bayes procedures

**Keywords**

Dirichlet process sequential decisions optimal stopping

#### Citation

Clayton, Murray K. A Bayesian Nonparametric Sequential Test for the Mean of a Population. Ann. Statist. 13 (1985), no. 3, 1129--1139. doi:10.1214/aos/1176349660. https://projecteuclid.org/euclid.aos/1176349660