Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Performance of Test Supermartingale Confidence Intervals for the Success
  Probability of Bernoulli Trials   Given a composite null hypothesis H, test supermartingales are non-negative
supermartingales with respect to H with initial value 1. Large values of test
supermartingales provide evidence against H. As a result, test supermartingales
are an effective tool for rejecting H, particularly when the p-values obtained
are very small and serve as certificates against the null hypothesis. Examples
include the rejection of local realism as an explanation of Bell test
experiments in the foundations of physics and the certification of entanglement
in quantum information science. Test supermartingales have the advantage of
being adaptable during an experiment and allowing for arbitrary stopping rules.
By inversion of acceptance regions, they can also be used to determine
confidence sets. We use an example to compare the performance of test
supermartingales for computing p-values and confidence intervals to
Chernoff-Hoeffding bounds and the "exact" p-value. The example is the problem
of inferring the probability of success in a sequence of Bernoulli trials.
There is a cost in using a technique that has no restriction on stopping rules,
and for a particular test supermartingale, our study quantifies this cost.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph