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February 2016 Assigning probabilities to hypotheses in the context of a binomial distribution
Casper J. Albers, Otto J. W. F. Kardaun, Willem Schaafsma
Braz. J. Probab. Stat. 30(1): 127-144 (February 2016). DOI: 10.1214/14-BJPS264


Given is the outcome $s$ of $S\sim{\mathrm{B}}(n,p)$ ($n$ known, $p$ fully unknown) and two numbers $0<a\leq b<1$. Required are probabilities $\alpha_{<}(s)$, $\alpha_{a,b}(s)$, and $\alpha_{>}(s)$ of the hypotheses $\mathrm{H}_{<}$: $p<a$, $\mathrm{H}_{a,b}$: $a\leq p\leq b$, and $\mathrm{H}_{>}$: $p>b$, such that their sum is equal to 1. The degenerate case $a=b(=c)$ is of special interest. A method, optimal with respect to a class of functions, is derived under Neyman–Pearsonian restrictions, and applied to a case from medicine.


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Casper J. Albers. Otto J. W. F. Kardaun. Willem Schaafsma. "Assigning probabilities to hypotheses in the context of a binomial distribution." Braz. J. Probab. Stat. 30 (1) 127 - 144, February 2016.


Received: 1 January 2013; Accepted: 1 September 2014; Published: February 2016
First available in Project Euclid: 19 January 2016

zbMATH: 1381.62046
MathSciNet: MR3453518
Digital Object Identifier: 10.1214/14-BJPS264

Keywords: $P$-values , $q$-values , Hypothesis testing , squared error loss , weak unbiasedness

Rights: Copyright © 2016 Brazilian Statistical Association


Vol.30 • No. 1 • February 2016
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