Interesting Stuff

Thinking about publishing a 1% effect?  Think again!  and again!

Bayesian approach to clustering.

Worried that the world will end when world's largest atom-smasher starts collisions?
Read this.

A good review on Bayesian statistics as applied to cosmology by Roberto Trotta.

Let's face it.  Unbinned comparisions of distributions are cool.  
The following are some
of my favorite papers:
One way of approaching these unbinned problems is use rank tests.  For instance, as
in the Kolmogorov-Smirnov test, one might take a set of measurements from two experiments, rank the values in order of least to greatest, then ask whether or not they increase in the same way.
The Baskerville and Solomon reviews how one might view a rank test in terms of probability theory.  Also, Conover's "A Kolmogorov Goodness-of-Fit Test for Discontinuous Distributions"
is also interesting for those show seek a different (more general?) formulation of the KS-test.

Edwin Pliny Seaver's Mathematical Handbook - includes old but good integral tables.

Are Ants Conscious?  This paper claims to show mathematically that they aren't!

Information entropy: entropy is characterized by certain criteria.  That is,
its measure should be continuous, the measure should be unchanged if the outcomes of
the random variable are re-ordered, the measure should be a maximum if all the outcomes
are equally likely, and the amount of entropy should be independent of whether I
add up the entropy from many 'sub-systems' or as a whole.  
Anyway, often in explanations of entropy people just give the function that
satisfies these criteria without really explaining where it comes from.  
Chaundy and McLeod derived that function and, although
you can't get the paper online, here is the
reference to it called "On a Functional Equation".  It's an easy but mathy read and worth
your time if you're into understanding entropy from a statistical/mathematical
point of view (e.g., in understanding Jaynes' "MaxEnt").  

Become a card-carrying Bayesian

"Bayesian Analysis of Multi-Source Data" by P.C. Bhat, H.B. Prosper and S.S. Snyder - one can do a lot of analysis with this paper

Here's a basic version of what Bhat, Prosper and Snyder did in the "Bayesian Analysis..." paper above by
R. Barlow and C. Beeston (Computer Physics Communications 77 (1993) 219).  Both papers are worth the read.
The advantage of the Barlow+Beeston paper is that it is analytic - however it is hard to see how one fits in additional
prior information.
(Beware, the two papers seem to contradict each other where it concerns finding the best estimate for x by maximizing L(x). 
Barlow+Beeston say one can find the best estimate for x by simply maximizing L(x).  Bhat et al. say one needs a correction factor
and, in practice, it is necessary to calculate L(x+N) where N is the number of bins. 
Barlow+Beeston's method is analytic where Bhat et al.'s is not - I'm not sure why this would make a difference.  Both papers
give good arguments for where the best estimate should be.  I've found Bhat et al. to work with the correction. 
I've never tried Barlow+Beeston's method, but ROOT apparently uses it in TFractionFitter without complaints.)

Check out Mathematical Statistics with Applications by Asha Seth Kapadia Wenyaw Chan and Lemuel Moye
This is book was written to bridgeb the gap between purely mathematical statistics like
Jun Shao's Mathematical Statistics and more application-centered texts like Glen
Cowan's Statistical Data Analysis, D.S. Sivia's Data Analysis: A Bayesian Tutorial,
Sir Harold Jeffreys's classic, Theory of Probability and Edwin T. Jaynes' Probability Theory: The Logic
of Science.  The explanations in Kapadia et al.'s book are clear and the book is loaded with examples. 
Plus, it's written so that you could almost read it cover-to-cover!

For an alternative (some may argue dated) point of view on the Bayesian approach
see  A.W.F. Edwards' book, "Likelihood".  Edwards, a student/colleague of Fisher's, gives a scathing critique of Bayesians
and much food for thought.  If  you look at the dust jacket, the book as sold as containing
some serious philosophical points on probability - I didn't find anything philosophically
earth-shattering, although this might be due to the fact that the book was written in different
times.

The Gutenberg Project

Speaking of Information Criteria, there is an excellent review of the Bayes Factor (i.e. marginalized likelihood ratio) by Kass and Raftery here.  If you ever wondered where the Bayesian Information Criteria came from, this is your paper.
(Basically, you use LaPlace's method of approximating the integral over the parameters.)
Also, here is a paper written by an all-star cast of authors (Sellke, Bayarri and Berger) on relating the Bayes Factor
(which some see as anti-intuitive) to p-values.

Excellent Review of Hadronic Generators for Extensive Air Showers by J. Knapp et al.

JStor

Discussions of string theory: Peter Woit (anti-string) and Lubos Motl (pro-string) - beware of Lubos' site - I find that
it crashes my redhat OS when I run it on an old version of mozilla.

The Fastest Human Ever

Tommie Smith and John Carlos - 1968 Mexico City

The First Four Minute Mile

Don Connolly's Racing Web Page

Instant Run-Off Voting

Math Geneology Project:  Who was your advisor's advisor's advisor?  Click here to find out.

Film of Emil Zatopek, greatest distance runner of all time.

Speaking of greats from Czechoslovakia, here's someone who has been robbed of the literature Nobel Prize for 30 years.


Abraham Wald was one of the earlier developers of modern sequential analysis techniques - along
with the great statistician Milton Friedman.  The idea of the technique is as follows.  Suppose you have
an auto assembly line and you want to know the % of defective cars coming out of my factory.  If the % of defects is larger than (say)
10% then you shut down the plant down and re-think how you're producing cars.  Now you could say that you're going
to produce 100 cars and if the number of defects is greater than 10, you shut the plant down, but what if the
first 11 cars are defects?  What's the point of producing more cars?  Also, what do you do about the fact
that you could produce 11/100 defects in one run, but if you produced another 100, there would be 2/100?  That is, what if the
11 were a statistical fluctuation? 
Sequential analysis allows one to make  a decision to reject or accept the null hypothesis using as few `events' (in this
case, cars) as possible, accounting for statistical fluctuations in the sample.  The sequential analysis technique he developed was so
powerful that it was classified during WWII to decide at what point an aircraft has sustained too many
hits and should turn back (or never return home).  This technique is used in medical studies, where
it is simply unethical not to.  You can read his semi-readable paper on his sequential
analysis technique here or buy is even more readable book.  The final pieces of Wald's contribution to
the war effort were declassified in the 90's, and a very historical, highly technical and, moreover, 
extremely interesting account of his work is found here and here.  Here's our paper on applying the
method to the problem of finding the origins of ultrahigh energy cosmic rays!

Speaking of aircraft, here's an interesting paper about fighter aces.  It turns out
that the best fighter aces of WWI may not have been that great after all, but
merely really lucky.
Coolest name for a paper ever: "Separating Hyperplanes and the Authorship of the Disputed Federalist Papers". 
The idea is that the authorship of 12 federalist papers were (and I guess still are)
under dispute.  The disputed papers were authored by James Madison, Alexander Hamilton or John Jay.  Madison
and Hamilton authored most of them, so the debate is whether they were Madison's or Hamilton's. 
Mosteller and Wallace wrote a book (the book) about a statistical study they did looking at the frequency of
certain words and found that they were Madison's.   Anyway, in the "Separating Hyperplanes.." paper,
they associate "each paper with a point in 70-dimensional space.  
This is done by computing how many times, per 1000 words of text, each
of 70 differnt function words (commonly used prepositions, adverbs, pronouns,
articles, and the like) appears in eachpaper.  In the second step of the method,
we search for a hyperplane that has all of the undiputed Hamilton points
on one side and all of the undisputed Madison points on the other side."
In other words, it's sort of a poor-man's neural network... but nevertheless interesting.

I'm not big on rhetoric - but here is MacArthur's farwell speech to
West Point (a.k.a. "Duty, Honor, Country" speech).  It's uber-sad, but it's brilliantly written.
 Be sure to click on the link and hear the ghostly voice of the old general himself say:

"The shadows are lengthening for me. The twilight is here. My days of old have vanished, tone and tint. They have gone glimmering through the dreams of things that were. Their memory is one of wondrous beauty, watered by tears, and coaxed and caressed by the smiles of yesterday. I listen vainly, but with thirsty ears, for the witching melody of faint bugles blowing reveille, of far drums beating the long roll. In my dreams I hear again the crash of guns, the rattle of musketry, the strange, mournful mutter of the battlefield."
The simpsons made fun of this speech in "The Secret War of Lisa" episode.  The commandant says:
"The wars of the future will not be fought on the battlefield or at sea.
They will be fought in space, or possibly on top of a very tall
mountain.  In either case, most of the actual fighting will be done by
small robots.  And as you go forth today remember always your duty is
clear:  To build and maintain those robots.  Thank you."

MacArthur says in his speech:
"We speak in strange terms: of harnessing the cosmic energy; of making winds
and tides work for us; of creating unheard synthetic materials to supplement or even replace
our old standard basics; to purify sea water for our drink; of mining ocean floors for new
fields of wealth and food; of disease preventatives to expand life into the hundreds of years;
of controlling the weather for a more equitable distribution of heat and cold, of rain
and shine; of space ships to the moon; of the primary target in war, no longer 
limited to the armed forces of an enemy, but instead to include his civil populations; of ultimate conflict
between a united human race and the sinister forces of some other planetary galaxy;
of such dreams and fantasies as to make life the most exciting of all time.  
And through all this welter of change and development, your mission
remains fixed, determined, inviolable: it is to win our wars."
Here's my favorite monster truck.  Watch megasaurus "come to life",
breath fire on a sub-compact car, and munch on it.

Sloane Tanen is one of my favorite authors who documents the life of some chicks.

Using the fractal dimension to measure the order in a system has been used for many things.
It has been everywhere from studying the structure of the universe to authenticating Jackson Pollock
paintings.  The latter has caused some debate.  See, for instance, these articles and this article.

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