  Familiar statistical tests and estimates are obtained by the direct
observation of cases of interest: a clinical trial of a new drug, for instance,
will compare the drug's effects on a relevant set of patients and controls.
Sometimes, though, indirect evidence may be temptingly available, perhaps the
results of previous trials on closely related drugs. Very roughly speaking, the
difference between direct and indirect statistical evidence marks the boundary
between frequentist and Bayesian thinking. Twentieth-century statistical
practice focused heavily on direct evidence, on the grounds of superior
objectivity. Now, however, new scientific devices such as microarrays routinely
produce enormous data sets involving thousands of related situations, where
indirect evidence seems too important to ignore. Empirical Bayes methodology
offers an attractive direct/indirect compromise. There is already some evidence
of a shift toward a less rigid standard of statistical objectivity that allows
better use of indirect evidence. This article is basically the text of a recent
talk featuring some examples from current practice, with a little bit of
futuristic speculation.
