**AAS 197, January 2001**

*Session 22. New Results from ``Back-to-Basics" Data Analysis: Special Tutorials on Timing and Fitting*

Special Session Oral, Monday, January 8, 2001, 10:30am-12:00noon, Royal Palm 3/4
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## [22.04] A Maximum-Entropy Approach to Hypothesis Testing: An Alternative to the p-Value Approach

*P.A. Sturrock (Stanford University)*

In problems of the Bernoulli type, an experiment or
observation yields a count of the number of occurrences of
an event, and this count is compared with what it to be
expected on the basis of a specified and unremarkable
hypothesis. The goal is to determine whether the results
support the specified hypothesis, or whether they indicate
that some extraordinary process is at work. This evaluation
is often based on the ``p-value" test according to which one
calculates, on the basis of the specific hypothesis, the
probability of obtaining 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."

The Bayesian approach does make it possible to answer this
question. As in any Bayesian analysis, it 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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