Recent headline

New Jersey Firehouse Catches Fire.

What's next, New Jersey Police Station Robbed? New Jersey Hospital Gets Sick?

Four-point-four sigmas to the right

Here's something I've learned today from an Indian coworker of mine: in a comparison of the very best athletes from different sports, there is a clear all-time winner. It's an Australian cricketer Don Bradman (1908-2001). Below is a comparison of the top five greatest athletes of all time; the comparison metric is the number of standard deviations away from the mean of their respective disciplines.

Athlete Sport Statistic Sigmas 1 Don Bradman Cricket Batting Average 4.4 2 Pele Soccer Goals Per Game 3.7 3 Ty Cobb Baseball Batting Average 3.6 4 Jack Nicklaus Golf Major Titles 3.5 5 Michael Jordan Basketball Points Per Game 3.4

Judea Pearl wins the 2011 Turing Award

Judea Pearl has won the 2011 A. M. Turing Award. The citation reads: "For fundamental contributions to artificial intelligence through the development of a calculus for probabilistic and causal reasoning." The A. M. Turing Award, given annually since 1966 by the Association for Computing Machinery, is considered the "Nobel Prize of theoretical computer science." Among the recipients are Marvin Minsky, Donald Knuth and Edsger Dijkstra.

Oftentimes, notions that seem so obvious and fundamental that we take them for granted turn out to be much more complex than we initially gave them credit for. It took philosophy and science entire millenia to come up with the first logically correct and useful definition of truth, due to Alfred Tarski. It took a few more decades for Judea Pearl to do the same for the concept of cause and effect. For those of you who don't know Pearl's work, go read his book Causality; I guarantee you it will be one of the most important pieces of prose you'll ever read. (If you would like a short and non-technical introduction, just read the book's closing part Epilogue: The Art and Science of Cause and Effect.)

The gist of Pearl's idea for defining causality is that you cannot do this without first formalizing the notion of an intervention. An intervention is an act of assigning a specific value to a variable by means that are completely independent of that variable's "natural environment". In Pearl's notation, intervention is denoted by do(X = x); think of it as of choosing treatment in a randomized experiment, or as of using the assignment operator in computer programming. Pearl defines the causal effect of a variable X on variable Y as a probability distribution of Y induced by deliberately setting the value of X to x (i.e. "doing" the do(X = x)). Or, in other words, event A causes event B if and only if the smallest possible set of do() operations performed on the whole system that brings about the realization of A, brings about the realization of B as well.

This may all sound trivial, but it actually has some non-trivial implications for probabilistic reasoning, which Pearl works out in full detail. Another interesting feature of his formalization of causality is that it provides a natural framework for mathematically rigorous thinking about the old philosophical ideas of "possible worlds" and counterfactuals. For example, it makes counterfactuals non-tautological (that is, it makes them sometimes true and sometimes false, and thus interesting, as opposed to their treatment in vanilla propositional logic in which all counterfactuals are vacuously true and therefore completely useless). Here is a truth-condition of a counterfactual implied by Pearl's theory:

The proposition "If A were true then B would be true" is true if and only if in the possible world closest to ours in which A holds, B holds as well,

where world V is closest to world W iff there does not exist any world Z such that the set of do() operations required to transform W into Z is a proper subset of the set of do() operations required to transform W into V.

The law of large WTF?

Andrew Gelman recently pointed out that some financial folks have some very strange ideas about the law of large numbers. Apparently, those strange ideas are deeply ingrained. Here are some excerpts from Investopedia's entry on the law of large numbers:

Definition of 'Law of Large Numbers.' In statistical terms, a rule that assumes that as the number of samples increases, the average of these samples is likely to reach the mean of the whole population.

So far so good; it's an informal definition of the same concept that statisticians call the law of large numbers. But then when you read,

When relating this concept to finance, it suggests that as a company grows, its chances of sustaining a large percentage in growth diminish. This is because as a company continues to expand, it must grow more and more just to maintain a constant percentage of growth.

...you start scratching your head. The above statement, while definitely true, has precisely fuck-all to do with the law of large numbers. As does the next one:

As an example, assume that company X has a market capitalization of $400 billion and company Y has a market capitalization of $5 billion. In order for company X to grow by 50%, it must increase its market capitalization by $200 billion, while company Y would only have to increase its market capitalization by $2.5 billion. The law of large numbers suggests that it is much more likely that company Y will be able to expand by 50% than company X.

No matter how you look at it, this is not an example of the law of large numbers. Whoever wrote this entry does not understand the definition they provided.

Added: I missed the mistake in Investopedia's definition of the law: It's not an assumption, it's a theorem.

More Added: For the sake of comparison, here is Felix Salmon's example of a correct use of the law of large numbers in a business setting:

If you run a bunch of casinos with hundreds of thousands of punters coming and and betting hundreds of millions of dollars, then you can predict with high accuracy the amount of money you're going to make at the end of the quarter.

Farewell to a Hero

Major Michal Issajewicz, aged 91, died March 4 in Warsaw. Issajewicz was an officer of the Home Army. For the most of his military career, he served in Home Army's anti-gestapo unit code-named "Umbrella" (Parasol). He is most famous as an important participant of Operation Kutschera, which was a carefully planned execution of Franz Kutschera, the SS and Reich's Police Chief for Nazi-occupied Warsaw. The operation, the logistics and planning of which took many months, was carried out on February 1, 1944. Issajewicz participated in the assassination as a driver of the vehicle that was to stop Kutschera's limo by slamming into it, and as a third backup-executioner. As both first- and second-executioner were injured during the operation, Issajewicz turned out to be the one to actually finish Kutschera off; during retreat from the execution scene he had received a head wound. Before the war was over, Issajewicz had been arrested by the gestapo and survived an interrogation in its horrific Warsaw prison called Pawiak, as well as incarceration in an equally horrific Stutthof concentration camp, from which he eventually managed to escape.

Below is a short clip from a 1958 Polish movie called Zamach ("The Assassination") about Operation Kutschera. It contains a reconstruction (from what I know, quite an accurate one) of the actual execution.

Major Michal Issajewicz, R.I.P.

Predictive power

When the financial crisis broke in August 2007, David Viniar, chief financial officer of Goldman Sachs, famously commented that 25-standard deviation events had occurred on several successive days.

Taken literally, this is of course false; no one has ever seen even a single 25-standard deviation event, and no one ever will. What has occurred was probably the most spectacular failure of a mathematical model in the history of mathematical models.

(The source of the quote is here.)

The process of elimination

At the moment, the GOP electorate behaves a bit like a very indecisive student trying to guess the right answer among four in a multiple choice test question. By process of elimination, the student already figured out that choices B, C, and D are definitely not the right answers. However, he doesn't like choice A either, so he won't just cirlcle it and be done with the question; instead, he'll keep thinking about the answer some more. And then a little longer.

The rest is commentary

The first words of Steven Landsburg's great book The Armchair Economist are:

Most of economics can be summarized in four words: "People respond to incentives." The rest is commentary.

Love the book, hate the line. Sure, technically it's true, but it's true in a way that tautologies are. It's true but completely uninformative. How do they respond to what incentives? The devil's in the commentary. Saying that "People respond to incentives" is the essence of economics is kind of like saying that:

Most of physics can be summarized in four words: "Everything is a wave." 

Most of game theory can be summarized in two words: "People strategize." 

Most of biology can be summarized in five words: "Random mutation and natural selection." 

Most of evolutionary psychology can be summarized in three words: "Cognitive traits evolved." 

Most of statistics can be summarized in eleven words: "When repeated large number of times, random events show predictable patterns."

The rest is just commentary.

Nude security theater

It can't possibly be that easy to beat the TSA's billion-dollar body scanners right? TSA can't be that stupid can they?

Too ridiculous for words

Browsing various items relevant to the heated dispute over whether or not contraceptives should be subsidized, I've encountered a whole lot of beliefs that are not just false but quite obviously so. They're so ridiculous it's hard to believe there are people who actually have those beliefs. Here are some of those (in no particular order):

• Mandating insurance companies to cover contraception isn't asking taxpayers to pay for someone's contraception.
• Not requiring that insurance companies cover contraception is the same as denying access to contraception.
• The fact that the market price of contraceptives is high means there is a market failure.

If you believe any of those things, you should really be ashamed of your ignorance.

Hello, I'm a horrible person. Will you marry me?

A friend of mine is dating a man in a very bad situation. He's divorced and has two kids with his ex-wife who has full custody of their children and keeps suing him for more and more child support. The net amount he has to pay every year in child support, court costs and legal fees, hovers around $80,000. And it can get even worse any day. His ex-wife is not greedy (she's already remarried to a filthy rich guy). She's much worse than greedy; she's taking pleasure in his suffering. She once told my friend, "By the time I'm through with him, he'll beg for mercy."

You have no idea how many times I've heard people react to stories like this with a self-assuringly judgmental remark to the effect of "Why would you ever marry someone like that?" To all of you who ever said this about someone, here's something you might want to consider. Your wife may be someone like that. Your husband may be someone like that. You may be someone like that. Do you think people are stupid? No one ever marries anyone like that. It's just that one day some people have the bad luck to discover that their spouse isn't really the person they thought they were. Nicole Brown did not marry "the kind of guy who beats his wife, threatens to kill her, stalks her in order to consciously instill the sense of imminent doom in her, and then eventually does kill her." As one of my favorite lines in one of my favorite movies goes,

Nobody knows anybody. Not that well.

Even a broken clock is right twice a day

And so, every once in a while, will be Rush Limbaugh.

Statisticians are special

Says a statistician:

Statisticians are special because, deep in our bones, we know about uncertainty. Economists know about incentives, physicists know about reality, movers can fit big things in the elevator on the first try, evolutionary psychologists know how to get their names in the newspaper, lawyers know you should never never never talk to the cops, and statisticians know about uncertainty. Of that, I’m sure.