A Bayesian Maximum-Entropy Approach to Hypothesis Testing, for Application to RNG and Similar Experiments

Abstract- In assessing the results of RNG (random number generator) ex-periments, and in similar problems of the Bernoulli type, one needs to evalu-ate 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 hy-pothesis, 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 re-quires that we consider not just one hypothesis but a complete set of hypothe-ses. This may be achieved very simply by supplementing the specific hy-pothesis 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