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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