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September, 1985 A Bayesian Nonparametric Sequential Test for the Mean of a Population
Murray K. Clayton
Ann. Statist. 13(3): 1129-1139 (September, 1985). DOI: 10.1214/aos/1176349660


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.


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Murray K. Clayton. "A Bayesian Nonparametric Sequential Test for the Mean of a Population." Ann. Statist. 13 (3) 1129 - 1139, September, 1985.


Published: September, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0585.62137
MathSciNet: MR803762
Digital Object Identifier: 10.1214/aos/1176349660

Primary: 62L15
Secondary: 62C10

Rights: Copyright © 1985 Institute of Mathematical Statistics


Vol.13 • No. 3 • September, 1985
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