My theorem becomes ever more famous

After only about 250 years, it seems the mainstream and the laypeople
are at last hearing about the eponymous Bayes' Theorem. (What a shame that some professional mathematicians have not managed to do the same). Here's a review from the Boston Globe (the Boston in the New World, that
is) about the "first-ever account of Bayes’ rule for general readers",
according to its publishers:
'The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma
Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two
Centuries of Controversy' by Sharon Bertsch McGrayne. Read quite a lot of it for free at Google Books, or --- like me --- buy a copy pour encourager les autres.

Bayes Theorem is independently (exchangeably?) proven again!

Back in 1763 the World Wide Web wasn't yet fully developed [we only
had gophers for communication back then], so I can accept that not
everybody has heard of my Theorem, nowadays kindly called Bayes'
Theorem by those in the know.

But even now, it seems, some poor souls have only got up to 17th
century mathematics, such as calculus and the Bernoulli distribution,
but ultra-modern 18th century stuff like my Theorem. And so these antediluvians have had to prove it all over again.

Seriously. And then they go on to call it the "exact method" (as
opposed to the frequentist "method" which assumes too much and answers
too little, but is clearly much more famous than my apparently
old-fashioned Theorem), wondering

It is not clear why the exact method isn’t mentioned in
most textbooks or, indeed, why it isn’t universally used instead of
the standard method. Apparently the exact method is not well
known.

Indeed not.

[A tip of the hat to Xi'an
(a.k.a. Christian P. Robert) for the generous promulgation of this
delightful finding]

Most unusual Bayesian application of the day [or decade]: The Bayesian-Moroni Prayer Analysis Calculator

http://www.lds4u.com/lesson1/bayesian.htm

From the site:

The last chapter of the Book of Mormon contains a promise to everyone who reads it. The promise states that if you read the book and ask God about it with a sincere heart, "real intent" and faith in Christ, then he will tell you the book is true by the gift of the Holy Ghost (See Moroni 10:3-5). The problem with this promise is that if the book isn't true, then God really didn't make the promise in the first place. The reader finds himself in a loop of circular reasoning where the way to find out if the book is true is based upon the premise that it is in fact true.

Is this a sincere effort or not? Only a Bayesian analysis can help with that one...

I'm not actually sure it is a valid calculator, actually, but it's too ridiculous a premise to look into too much anyway. Although, on reconsideration, Pascal's Wager is a similar-ish sort of argument what with trying to use probability theory to help with struggles of faith in God. The article about that at http://plato.stanford.edu/entries/pascal-wager/ is well worth working through, by candlelight if necessary.

--

A supposed Bayesian analysis of whether the Swedish police actions against Julian Assange are politically motivated

Bayesian methods are perfect for forensic and other police
investigations. A couple of books that show how in very different ways
are A Probabilistic Analysis of the Sacco and Vanzetti Evidence (Wiley Series in Probability and Statistics) and Bayesian Networks and Probabilistic Inference in Forensic Science. I'm sure there are many, many others.

The New York Times in-house stats-blogger Nate Silver has tried to write a model analysis using Bayesian thinking of whether the ongoing Swedish sex crimes case against Julian Assange, the personage most widely associated with the Wikileaks website (and whose OKCupid profile you can pruriently find at http://www.okcupid.com/profile/HarryHarrison), is politically motivated. After starting with a frankly facile argument about whether his fellow passenger on the bullet train in Japan is Japanese, Caucasian, or a combination of the two, Silver goes on to provide not
light, but conspiracy theory heat, about that important question. It
boils down to saying that because he's a high-profile figure who has
annoyed many powerful people, including governments around the world,
that therefore it increases the probability that the current
shenanigans are politically motivated. Therefore, Mr. Silver
concludes, we should be more sceptical that the investigations are
done purely for crime-prevention purposes. The crucial two paragraphs:

What is less ambiguous here, however — as in the case of my bullet
train analogy — is the underlying context. The handling of the charges
suggests that the motivation for bringing them against Mr. Assange is
political. If the motivation is political, then the merits of the
charges might matter less. Even if they fail to result in a
conviction, the authorities might nevertheless succeed in, in essence,
incapacitating Mr. Assange for several months, and preventing him from
releasing further documents through WikiLeaks. They might also injure
Mr. Assange’s reputation among the public: certainly I have learned
more about details Mr. Assange’s personal life in recent days than I
would care to know.

Under these circumstances, then, it becomes more likely that the
charges are indeed weak (or false) ones made to seem as though they
are strong. Conversely, if there were no political motivation, then
the merits of the charges would be more closely related to
authorities’ zealousness in pursing them, and we could take them more
at face value.

Two quick points: Bayesianism doesn't have one right answer; it is
subjectivist. This analysis can be argued over by reasonable people.
I, for one, consider it simplistic. (For example, Silver points out
that the only other Interpol Red Alert against a sex offender issued
by Sweden this year was for a man accused of multiple sexual assaults
against children; a different kettle of pervert-fish indeed. But
what's the denominator? In other words, how many suspects of Swedish
sex crimes were abroad this year at the moment when the Swedes wanted
to talk to them? This is a crucial question without which a useful
likelihood function cannot really be constructed, hence no useful
Bayesian analysis).

But a more important point to make is: so what? Simply because of
Assange's notoriety, according to this analysis, we must conclude that
political motivations are more likely factors for what is going on.
But only a fool would leave it at that and decide the whole case is
suspect, before making a placard and protesting outside the English
courthouses whether Assange will be extradited. Most people would
continue to do what they did before --- i.e. let the legal process
take its course --- and hopefully realise, if they hadn't up until
this point, how incredibly unjust the whole system of European Arrest
Warrants are.

The promotion of Bayesian methods amongst the general public is a joy
to see, but it has to be done rigorously, otherwise laypeople will
justifiably see it as just another way to reinforce one's own
prejudices as opposed to exposing them.

Statistics is rapidly going mainstream

UPDATE: The programme is now available in full on Youtube. I found out from the always-enjoyable Revolution blog.

Statistics is going mainstream, and I know this from just one data 

point: Hans Rosling's new documentary for the BBC, "The Joy of
Stats". It's an hour-long propaganda piece on why statistics is not
the dry, boring subject you were taught at school, but an exciting and
actually indispensable tool for understanding the world.

Statistics is science. Statistics is philosophy. Statistics is
knowledge and power. With cheap computation and storage, the golden
age of statistics is upon us. Watch the start of this new age at
http://www.bbc.co.uk/iplayer/episode/b00wgq0l/The_Joy_of_Stats/

If you're not in the UK, or the expiry time of 4:29AM GMT Wed, 15 Dec
2010 has passed, you can instead see some clips at
http://www.open.ac.uk/openlearn/whats-on/the-joy-stats

And the film might end up on Rosling's Gapminder website at some
point, according to one ccomment I saw online, a drop in the
universe-ocean of data. He's so passionate I can believe he'll do it.

If I have one criticism --- and I have to have at least one to make it
worth your while to read the above sycophancy --- is that there wasn't
enough emphasis on how ordinary people can use statistics in their
lives. There was a section on citizens of San Francisco bringing
online maps of crime report statistics to meetings with
policepeople. All very well; but how about using statistics as we live
our lives and need to make decisions? A lively discussion of
rationality versus intuition could have been really fascinating and a
little more engaging than yet another story about big telescopes.

But I'm being picky. Please watch "The Joy of Stats" now if you
haven't already, and hug your nearest statistician (or "statso", if
you prefer) at your leisure. We'll really appreciate it.

That link again: http://www.bbc.co.uk/iplayer/episode/b00wgq0l/The_Joy_of_Stats/

Sunday R trick

This is not particularly Bayesian... you might think. But actually, computer graphics is a favourite hobby of mine, despite my having lived during the 18th century. Prince of Persia was good enough for us back then. I still remember drawing a Mandelbrot set on a graphical calculator.

Anyway, Bill Venables of CSIRO on the other side of the world from the Motherland sent the following delightful parlour trick to the R-help mailing list. Running the jif function with no parameters (i.e. by typing in jif() at the R command line) displays the image further down. I don't think complex numbers are required for this to be implemented, but at least now I know how plot works with complex numbers, which I guess was the point of the exercise.

Original posting follows:

I was looking for an example of complex variables in R.  This one is trivial, but rather cute (though World War II aficionados may 'come over all funny').

See if you can guess the image before you try the function.  It's not difficult.


This leads to the following image being drawn. Trying to work out how (or why) this happens is quite fun. Can you draw other Axis flags? (They lost WW2, so the least we can do in return is to use their flags as programming exercises).

Jif

Illegal statistics

Even the Supreme Court of the United States of America can't define a p-value properly:

Our experience with this case also suggests the judiciary would benefit from a better understanding of fundamental concepts of hypothesis testing. Both the U.S. and Michigan Supreme Court opinions state, “Standard deviation analysis seeks to determine the probability that the disparity between a group’s jury-eligible population and the group’s percentage in the qualified jury pool is attributable to random chance.” The probability referred to, of course, is the p-value, which is calculated assuming random (chance) selection of the jury pool from the eligible population.