There's no theorem like Bayes' theorem Like no theorem I know Everything about it is appealing Everything about it is a wow! Let out all that a priori feeling - that you've been afraid of up to now! Thinking Outside The (George) Box
The Frequentist Songbook? FISHER PEARSON KOLMOGOROV Sir Ronald Aylmer Egon Sharpe Andrei Nikolaevich 1890-19621895-1980 1907-1987
There's no theorem like… Bayes' theorem Thinking Outside The (George) Box A GLIVENKO-CANTELLI THEOREM AND STRONG LAWS OF LARGE NUMBERS FOR FUNCTIONS OF ORDER STATISTICS B Y J ON A. W ELLNER
Theorem 1.1 Theresult holds only for a four-letter acronym YMCA / ISBA Corollary 1.2 Empirical Bayes methods do not guarantee coherence
“ O(n) -computable kernel density estimate” “Let’s call the whole thing f( ) ” “approx non-parametric Bayesian posterior”
1.Put the data IN 2.Get a prior OUT …wave your hands about? 3. Put the data back IN! OUT! IN! OUT!
Empirical Bayes Analysis of 1-1 matching (in hippos) Ken Rice 1,2, Thomas Lumley 1,3, 1.University of Washington, Department of Biostatistics 2.Seattle Symphony Chorale 3.Seattle Choral Company featuring a special tribute to Kolmogorov * *
Hippos (overview) 1.Background, definitions 2.Review of 1-1 matching, gender- specific effects, parent-of-origin effects 3.Acknowledgement of (Russian) priority 4.Your input, comments, …scope for further improvement?