I Think I'm a Radical Baysean

To learn something that isn't math, I've been picking up the readings from some of my friends' classes if they look interesting. This last week I read a pair of articles by Kahneman and Tversky about flaws in heuristic reasoning and an objection by the frequentist Gigerenzer.

K&T illustrate one of the flaws of heuristic reasoning by asking people to evaluate the probability that a particular woman is a librarian or a librarian and feminist, given a description of her that fits the stereotype of a feminist. Many people say the latter is more probable, when in fact the probability of any subset (that someone is both A and B) must be less than the probability of the superset (that someone is A). They call this the "representativeness" error -- that is, that if a particular event is very representative of a particular class, then people overestimate its likelihood. An example of the same effect is that people consider the sequence of flips of a fair coin "H-T-H-H-T" more likely than the sequence "H-H-H-H-H" because the first evokes randomness more, even though we know that any particular sequence must have equal probability.

Gigerenzer objects to this in a couple of ways. One is that people, when asked to evaluate two possibilities, A or A and B, they naturally assume that the asker actually means "A and not B" or "A and B", since otherwise it's kind of a stupid question. This makes sense to me. His second objection is the one I really want to talk about, though, and that is that it doesn't make sense to ascribe probability to a single, non-repeatable event.

In case you don't know, like I didn't before I came here, there are two different schools of thought concerning probability: the Frequentists and the Bayseans. The former believe, like Gigerenzer, that in order for an event to have meaningful probability, it must be repeatable, and that the probability is interpreted as the limit of the frequency of occurances as the number of samples goes to infinity. Bayseans allow one to speak about the probability even of events that occur only once, such as a particular team winning the twentieth Superbowl, and interpret probability as a measure of certainty concerning a particular outcome.

I take great objection to the Frequentist point of view, not only in cases where we are evaluating the probability of a single event, but also when the measured outcome is "repeatable". For example, take the flipping of a coin. The fact that when I flip a coin, we reasonably describe the probability of it coming up heads has nothing to do with the fact that many coins have been flipped before, or the possibility of flipping the coin many more times. It has to do with the symmetry between the two sides, the information loss introduced by the flipping action (negating the asymmetry of the coin starting either heads up or heads down), and a reasonable physical model of the world that suggests that symmetric outcomes should happen with equal likelihood. Were this theory in doubt, a coin has added benefit that we can flip it many times and get a more rigorous estimate of the likelihood of it coming up heads through the reasonable assumptions of statistical inference, but this possibility can't reasonably be said to inform our estimate of the probability of heads. The first coin that was ever flipped, long before statistics textbooks, had just as much of a fifty-fifty chance of heads and tails as any coin today. (Ignoring recent improvements in the manufacture of symmetric coins, I suppose.)

In fact, the moment the coin has left your thumb, the outcome is as determined as the profession of an unknown person. Depending on what your ideas about free will are, you could say it is determined even before that. We describe its outcome in probabilistic terms because of a lack of information, not because of its similarity to possible future situations. Looking at it this way, there's no basic philosophical difference between a coin flip and evaluating the probability that a single person has a particular profession -- we are just able, through simplifying physical assumptions and statistical inference, to make a much better estimate of the probability of the latter knowing very little about the particular event.

Statistics and probability are primarily concerned with trying to make inferences about situations about which there is insufficient information. The notion of "probability" is simply a convenient way of thinking about deterministic and determined events that we cannot observe completely. When we say an event is "repeatable", we simply mean that a series of events in time are similar enough with respect to the variables we can observe and think are salient to its outcome. This allows us to use convenient mathematical models and make accurate predictions about the future. Random events have a continuum of repeatability, but they all have one thing in common, whether they happen once or many times: we don't know enough about them to predict their outcomes, and this is what allows us to speak of their probability.

I think this makes me a radical Baysean, a label that I think sounds pretty cool. (Ever since my friend Fred described himself as a "radical agronomist" this summer, I think I've wanted to be a radical something.) Of course, my understanding of this issue is still pretty shallow, and probably biased by the fact that I've now read heavyweight Bayseans (Kahneman won the Nobel prize in economics) and a less prestigious Frequentist. I'm sure you're all sitting on the edge of your seats, wondering how this will all turn out.

To Kazakhs.

I believe in supporting satire, free speech, and non-PC cultural criticism, but these things do hurt people sometimes. This isn't an argument for self-censorship or timidity, but for sympathetic efforts to bridge gaps when misunderstandings occur. I know I already wrote a Borat post, but a Kazakh friend of mine living in America wrote me feeling upset about the movie. This is part of my reply to her, which I would address to all Kazakhs living here. There are no new ideas from my last post, just a different tone.

---

When I was in Kokshetau, a journalist wrote an article about me as an American that made me look very stupid and rude. Lots of people in Kokshetau saw it, and I felt ashamed to show my face for weeks. You have to live with the Borat posters everywhere. It's very hard to live in a foreign country and culture, when you feel like you're always being watched and judged. To be in America when your country, which you rightly feel very proud of, seems to be mocked in a popular movie must be very difficult.

But let me try to convince you of something that might sound strange at first, but which is very true: the Borat movie is not about Kazakhstan. I know, he says he's from Kazakhstan, and he waves a Kazakh flag, but that is where the similarity with the real Kazakhstan ends. The language he speaks isn't Kazah, the Cyrillic is gibberish, the people and houses don't look like Kazakhstan, and of course all the "culture" is completely made up. The -only- reason he chose "Kazakhstan" is because nobody had heard of it. I heard that he originally wanted to be from Albania, but it was thought that too many people knew where Albania was. In other words, it could be anywhere, as long as Americans haven't heard of it.

And it's true that before this movie, most Americans had never heard of Kazakhstan. I know, I had to explain to people where I was moving to. This is not something you should be ashamed of as a Kazakh, it's Americans who should be ashamed of their own ignorance.

This American ignorance is exactly what Borat is making fun of. This movie has nothing at all to do with the real Kazakhstan, but it has a lot to do with the real America. Borat's whole act is to behave like a boorish, ignorant, dirty man, and cleverly show that Americans have a lot in common with him.

For example, anti-Semitism is not a problem in Kazakhstan, but it is a problem here. So when Borat gets an Arizona bar to sing along with a song called "Throw the Jew Down the Well", who is being made fun of? Is it Kazakhstan or America? When a stadium of sports-fans nearly riots when he sings the National Anthem wrong, is it Americans or Kazakhs ashamed of hyper-nationalism? Isn't the very fact that most people know so little about Kazakhstan more the subject of Borat than anything to do with the real Kazakhstan?

I deeply believe that this is not a movie about Kazakhstan, it's a movie about America. It takes place in America, and with real Americans, not actors. It is American culture that he probes, not Kazakhstan's. The "Kazakhstan" of Borat is a fiction designed to probe America's flaws.

I think most Americans understand this. Everyone I talk to, everything I read, shows that people know that Borat does not represent the real Kazakhstan. And if someone doesn't understand that, then it is exactly these ignorant people that Borat is poking fun at. So you don't need to feel ashamed. On the contrary, you should act proud to be a Kazakh, and take this chance to teach people a little about what being Kazakh really means.

Slavic Political Turns of Phrase.

I was playing go with a Russian fellow, and we began describing the board in terms of cold-war geography. This part well on my side was France, this island that I temporarily controlled but was unable to protect was Cuba, this part kind of between us but likely to fall to my opponent was Poland. And he taught me a Russian saying: "курица не птица -- Польша за граница" -- "A hen is a not a bird like Poland is outside Russian borders". (You'll be happy to hear that in go, as with the real Soviet Union, the West was victorious.)

And I was listening to a talk by the former Ukranian finance minister and ambassador to the EU, and he said of Ukraine's relationship with America (I paraphrase): "America is more concerned with Russia than with the Ukraine itself. It is like hunter trying to wake bear with stick: he does not care much what happens to the stick."

My Chinese Flatmates, and a Different Sort of Tragedy of the Commons.

It's well-known that when scarce goods are held collectively, and individuals can utilise them without individually paying for what they themselves use, people will often shirk their contribution to the group store, causing the proverbial "tragedy of the commons". However, in some cases, if people have strong disinclinations to be perceived as shirking, the opposite can happen, and non-optimal equilibria exist where people over-contribute to the store. A case study: my flat's kitchen's dishsoap.

Kazakhstan Plans to Switch to the Latin Alphabet. Don't They Have Better Things to Do?

According to interfax, Kazakhstan is planning on joining Uzbekistan and Turkmenistan in officially transitioning their Turkic language from the Cyrillic to Latin script. The only reasons I can imagine to do this are to pander to a Kazakh nationalism that seeks to divide ethnic Russians and Kazakhs, or to make Kazakh marginally easier for Westerners to learn. The first is obviously not a good reason, and there are much, much cheaper, much much more effective things the Kazakh government could do to effect the second. Publishing a decent Kazakh-English dictionary would be a good start.

A Poem.

I study this, I study that.
I estimate the sigma-hat.
Heteroskedastic error terms
Really make my stomach churn.