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!