The Annals of Statistics

A Bayesian Nonparametric Sequential Test for the Mean of a Population

Murray K. Clayton

Full-text: Open access

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


Export citation