The Pianists' Birthday Problem

We are used to the idea that common birthdays are not that unusual.  I recently attended a
chamber music concert involving the young German pianist Markus Groh.  A quick look at
his website revealed a rather extreme version of birthday matching:  Groh was born January 5th,
the same day as Alfred Brendel, Maurizo Pollini, and Arturo Benedetti Michelangeli!

Requirements for Academic Work

Inquiring minds often wanted know:  What sort of qualifications were necessary for academic
positions?  Finally we have an answer from the University of Arkansas.  In addition to passing
background checks for prior criminal records one must be capable of:

Sedentary Work - Exerting 10 pounds: Occasionally, Light Work - Exerting up to 20 pounds: Occasionally, Kneeling: Occasionally, Climbing (Stairs, Ladders, etc.): Occasionally, Lifting 5 -10 lbs: Occasionally, Lifting 10-25 lbs: Occasionally, Carrying 5-10 lbs: Occasionally, Pushing/pulling 10-25 lbs: Occasionally, Sitting for long periods of time: Occasionally, Standing for long periods of time: Occasionally, Speaking; Essential, Hearing: Essential, Vision: Ability to distinguish similar colors, depth perception, close vision: Essential, Walking - Short Distances: Frequently, Walking - Moderate Distances; Occasionally.

Ab Uno Disce Omnes

Virgil's dictum:  "From one example, all is revealed,"  would seem to be the very antithesis of
statistical thinking, so it seems surprising to discover that a single observation is enough to
construct a confidence interval for the mean in the standard Gaussian model with unknown
mean and variance.  The construction is described below and comes from class notes of Charles Stein,related to me by Steve Portnoy.  Any further information about the origins of this problem
or its solution would be most welcome.

Details in html
Details in pdf

Pricing the Internet

More or less by accident I ran across http://www.dtc.umn.edu/~odlyzko/doc/smart.pricing.pdf
an analysis of prospects for internet pricing by Andrew Odlyzko, an old Bell Labs hand now
at the U. of Minnesota.  He makes the case against congestion pricing, arguing that consumers
and perhaps business as well prefer simple flat rates, i.e. usage independent pricing and that
technology is capable of expanding to meet this preference.  Having argued the other side
of this case in http://comjnl.oxfordjournals.org/content/27/1/8.full.pdf  long ago, I was a bit
surprised,  and am still not entirely persuaded.  Maybe this only reflects that I haven't fully
accepted recent developments in behavioral economics?

Amsterdam Econometrics Games 2015

This year for the first time we sent a UIUC team
to the Econometric Games in Amsterdam.  This is a 3 day competition among
30 Universities; there is a preliminary round to select 10 finalists and then a
second round to determine the three prize winners.  The topic this year was
Longevity and Longevity Risk.  Details of this year's competition are available
here   http://www.econ.uiuc.edu/~roger/EGames/Case1.pdf   and
here  http://www.econ.uiuc.edu/~roger/EGames/Case2.pdf

Our team:   Nicolas Bottan, Cesare Buiatti, Julia Gonzalez and Jiaying Gu
placed second in this competition outperforming perennial favorites like
Copenhagen, Aarhus, Amsterdam, Carlos III as well as Oxford, Cambridge
and Harvard.  Our team deserves a ticker tape parade when they return
this weekend, unfortunately ticker tape is scarce these days.  So we will have
a celebration of their remarkable achievement on April 17th as part of the
Fourth Annual Boneyard Conference of Econometrics.  Details here:
http://www.econ.uiuc.edu/~roger/seminar/Boneyard15.pdf

So the time has come put your brackets on the table, here is a random realization of a bracket from
the QBracketology model complete with scores, and survival curves for the various teams based on
1000 realizations of the Tournament.  As you can see, not surprisingly, Kentucky is an overwhelming
favorite, with a probability of 0.407 of winning.  Only time will tell whether the estimated probabilities of the model are competitive in the Kaggle competition.

Mea Copula Redux

Never one to leave bad enough alone,  I've yet again returned to Quantile Bracketology as a
March diversion,  in lieu of watching any basketball.  This year Kaggle (sponsored by HP) is
again offering modest prizes for predicting probabilities of the NCAA Tournament, and this
year they provide somewhat better data:  30 years of past seasonal results as well as the tournament
outcome data.

I gave a talk about my technology for this a week or so ago in the Stat Department, slides for
that talk are linked here:  http://www.econ.uiuc.edu/~roger/research/bracketology/MM.html

A question that puzzled me last year was whether it might help to shrink the model's predicted
probabilities toward 1/2.  In an effort to explore this, I estimated models and predicted tournament
probabilities for each of the last 30 years.  A naive shrinkage rule was employed which simply
took the model's original probabilities as if they were based on the frequency of successes out
of 20 trials, and used a Beta(a,a) prior to do the shrinkage.  This yields a linear shrinkage of
modest amout for a taking values 0, 1, ... , 5,  where 0 corresponds to no shrinkage at all.
The results are rather mixed.  In the figure below I plot the logistic loss achieved for each
year for the various levels of a, with the black line representing no shrinkage and the various
colored lines the various degrees of shrinkage.  In 2/3 of the years no shrinkage is best.  In
one year, 2011, in which the model is most disastrous, maximal shrinkage is optimal.  Comparison
of the mean performance over the whole 30 year span yields:

   a =  0    a =  1    a =  2    a =  3    a =  4    a =  5 

0.5403810 0.5419280 0.5464682 0.5515166 0.5566610 0.5617073 

So, it would appear that shrinkage just tends to make the predictions more bland without really

helping much at all.