The Bayesian Songbook (heavily dependent on prior results)

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Presentation transcript:

The Bayesian Songbook (heavily dependent on prior results)

Y M C A

ISBA Wakefield et al (2000)

featuring You Sexy Thing by Hot Chocolate

… you need to believe in miracles!

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

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

The Empirical Bayes Songbook! ‘My Way’

IMS?ISI? Efron et al (200?)

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?

Hippopotamus (male,bold)

Shalimar (cool, wide)

HippopotamA (female, fair)

HippopotamUS (non-ignoramus)

Mud (key points) 1.Glory 2.Temperature control 3.Attraction 4.Stress relief

HippopotamA (fair, uni-parented)

Колмогоров-Смирнов

Mud Гразь, гразь, чудная гразь! Пучшее средство как кожная мазь Так возьми ж свою даму и поведи ее в яму И там мы окунемся в чудную гразь! 1.Glory 2.Temperature control 3.Attraction 4.Stress relief

HippopotamAE (plural, sublime)

“Singing this haunting refrain”

Mud Mud, Mud, Glorious Mud! Nothing quite like it for cooling the blood So follow me, follow Down to the hollow And there let us wallow in glo-o-o-o-ri-ous mud!