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. 
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