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Volume 11: Number 2: Article 5
A Bayesian Maximum-Entropy Approach to Hypothesis Testing, for Application to RNG and Similar Experiments
P. A. Sturrock, Center for Space Science and Astrophysics, Varian
302G, Stanford University, Stanford, CA 94305-4060
In assessing the results of RNG (random number generator) experiments,
and in similar problems of the Bernoulli type, one needs to evaluate
the proposition that the results are compatible with a specific hypothesis,
such as the so-called "null hypothesis" that no extraordinary process
is at work. This evaluation is often based on the "p-value" test according
to which one calculates the probability of obtaining, on the basis of
the specific hypothesis, the actual result or a "more extreme" result.
Textbooks caution that the p-value does not give the probability that
the specific hypothesis is true, and one recent textbook asserts "Although
that might be a more interesting question to answer, there is no way
to answer it." A Bayesian approach requires that we consider not just
one hypothesis but a complete set of hypotheses. This may be achieved
very simply by supplementing the specific hypothesis with the maximum-entropy
hypothesis that covers all other possibilities in a way that is maximally
non-committal. This procedure yields an estimate of the probability
that the specific hypothesis is true. This estimate is found to be more
conservative than that which one might infer from the p-value test.
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