Transcript The Bayesian Songbook - University of Washington

The Bayesian Songbook
(heavily dependent on prior results)
Y
M
C
A
I SBA
Wakefield et al (2000)
featuring
You
Sexy
Thing
by
Hot Chocolate
… you need to believe in miracles!
Thinking Outside The (George) Box
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!
FISHER
Sir Ronald Aylmer
1890-1962
PEARSON
Egon Sharpe
1895-1980
KOLMOGOROV
Andrei Nikolaevich
1907-1987
The Frequentist Songbook?
Thinking Outside The (George) Box
There's no theorem
like… Bayes' theorem
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’
IMS? ISI?
Efron et al (200?)
Theorem 1.1
The YMCA / ISBA result
holds only for a four-letter
acronym
Corollary 1.2
Empirical Bayes methods do
not guarantee coherence
“O(n)-computable kernel density estimate”
“approx non-parametric Bayesian posterior”
“Let’s call the
whole thing f( )”
IN
2. Get a prior OUT
1. Put the data
3. Put the data back
IN!
OUT!
IN!
OUT!
…wave your hands about?
Empirical Bayes Analysis of
1-1 matching (in hippos)
*
Ken Rice1,2, Thomas Lumley1,3,
1.
2.
3.
*
University of Washington, Department of Biostatistics
Seattle Symphony Chorale
Seattle Choral Company
featuring a special tribute to Kolmogorov
Hippos (overview)
1. Background, definitions
2. Review of 1-1 matching, genderspecific 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.
2.
3.
4.
Glory
Temperature control
Attraction
Stress relief
HippopotamA (fair, uni-parented)
HippopotamA (fair, uni-parented)
Колмогоров-Смирнов
Mud
1. Glory
Гразь, гразь, чудная
гразь!
2. Temperature control
Пучшее средство как
кожная мазь
3. Attraction
4. Stress relief
Так возьми ж свою
даму и поведи ее в
яму
И там мы окунемся в
чудную гразь!
HippopotamAE (plural, sublime)
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!