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