Assigning probabilities to hypotheses in the context of a binomial distribution

@article{Albers2016AssigningPT,
title={Assigning probabilities to hypotheses in the context of a binomial distribution},
author={C. Albers and O. Kardaun and W. Schaafsma},
journal={Brazilian Journal of Probability and Statistics},
year={2016},
volume={30},
pages={127-144}
}

Given is the outcome s of S∼B(n,p) (n known, p fully unknown) and two numbers 0 (s) of the hypotheses 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.