Statistical Science

The Future of Indirect Evidence

Bradley Efron

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Abstract

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.

Article information

Source
Statist. Sci., Volume 25, Number 2 (2010), 145-157.

Dates
First available in Project Euclid: 19 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.ss/1290175835

Digital Object Identifier
doi:10.1214/09-STS308

Mathematical Reviews number (MathSciNet)
MR2789983

Zentralblatt MATH identifier
1328.62043

Keywords
Statistical learning experience of others Bayesian and frequentist James–Stein Benjamini–Hochberg False Discovery Rates effect size

Citation

Efron, Bradley. The Future of Indirect Evidence. Statist. Sci. 25 (2010), no. 2, 145--157. doi:10.1214/09-STS308. https://projecteuclid.org/euclid.ss/1290175835


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