learning from the experience of others - stanford...

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Learning from theExperience of Others

Bradley EfronStanford University

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What is “Statistics”?

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The Puzzled Physicist

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Bayes’ Rule (1763)

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Learning from Experience

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Eighteen Baseball Players

0.265.265.265Grand Average0.239.200.1567/4518. Alvis0.244.316.1788/4517. Munson0.249.286.2009/4516. Campaneris0.254.226.22210/4515. E Rodriguez0.254.264.22210/4514. Petrocelli

:::::0.277.222.33315/454. Johnstone0.281.276.35616/453. F Howard0.286.298.37817/452. F Robinson0.290.346.40018/451. Clemente

James-Stein“TRUTH”Avehits/ABNameObserved

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Regression to the Mean (Galton 1886)

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James-Stein Estimation (1956)

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Stein’s Paradox

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Corbet’s Butterflies(Malaysia 1943)

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Learning from Other Butterflies

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Proving the Magic Formula

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Shakespeare’s Word Counts

837 …104314632292434314376?

6 …543210

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Shakespeare’s Missing Words

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Gene 4124: Prostate Cancer Study

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Hypothesis Test

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Prostate Cancer Study

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Doing 6033 Hypothesis Tests at Once

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False Discovery Rates(Benjamini and Hochberg 1995)

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False Discovery Control Algorithm

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Learning from the Other z-Values

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References