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The Bayesian Songbook
(heavily dependent on prior results)
YYMMCCAA
II SSBBAAWakefield et al (2000)
featuring
YouSexyThing
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 appealingEverything 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 KOLMOGOROVSir Ronald Aylmer Egon Sharpe Andrei Nikolaevich
1890-1962 1895-1980 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
BY JON A. WELLNER
The Empirical Bayes Songbook! ‘My Way’
IMSIMS??
ISIISI??
Efron et al (200?)
Theorem 1.1The result holds only for a four-letter acronym
YMCAYMCA //
ISBAISBA
Corollary 1.2Empirical 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 IN2. 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 Rice1,2, Thomas Lumley1,3,
1. University of Washington, Department of Biostatistics
2. Seattle Symphony Chorale
3. Seattle Choral Companyfeaturing a special tribute to Kolmogorov
*
*
Hippos (overview)
1. Background, definitions2. 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)
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)
HippopotamA (fair, uni-parented)
Колмогоров-Смирнов
MudГразь, 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)
HippopotamAE (plural, sublime)
“Singing this haunting refrain”
MudMud, Mud, Glorious Mud!
Nothing quite like it for cooling the blood
So follow me, followDown to the hollow
And there let us wallow
in glo-o-o-o-ri-ous mud!