Bayesian Inference in the NY Times

In today’s Sunday NY Times Magazine, there’s a long article by psychologist Steven Pinker, on “Personal Genomics”, the growing ability for individuals to get information about their genetic inheritance. He discusses the evolution of psychological traits versus intelligence, and highlights the complicated interaction amongst genes, and between genes and society.

But what caught my eye was this paragraph:

What should I make of the nonsensical news that I… have a “twofold risk of baldness”? … 40 percent of men with the C version of the rs2180439 SNP are bald, compared with 80 percent of men with the T version, and I have the T. But something strange happens when you take a number representing the proportion of people in a sample and apply it to a single individual…. Anyone who knows me can confirm that I’m not 80 percent bald, or even 80 percent likely to be bald; I’m 100 percent likely not to be bald. The most charitable interpretation of the number when applied to me is, “If you knew nothing else about me, your subjective confidence that I am bald, on a scale of 0 to 10, should be 8.” But that is a statement about your mental state, not my physical one. If you learned more clues about me (like seeing photographs of my father and grandfathers), that number would change, while not a hair on my head would be different. [Emphasis mine].

That “charitable interpretation” of the 80% likelihood to be bald is exactly Bayesian statistics (which I’ve talked about, possibly ad nauseum, before) : it’s the translation from some objective data about the world — the frequency of baldness in carriers of this gene — into a subjective statement about the top of Pinker’s head, in the absence of any other information. And that’s the point of probability: given enough of that objective data, scientists will come to agreement. But even in the state of uncertainty that most scientists find themselves, Bayesian probability forces us to enumerate the assumptions (usually called “prior probabilities”) that enter into our assignments reasoning along with the data. Hence, if you knew Pinker, your prior probability is that he’s fully hirsute (perhaps not 100% if you allow for the possibility of hair extensions and toupees); but if you didn’t then you’d probably be willing to take 4:1 odds on a bet about his baldness — and you would lose to someone with more information.

In science, of course, it usually isn’t about wagering, but just about coming to agreement about the state of the world: do the predictions of a theory fit the data, given the inevitable noise in our measurements, and the difficulty of working out the predictions of interesting theoretical ideas? In cosmology, this is particularly difficult: we can’t go out and do the equivalent of surveying a cross section of the population for their genes: we’ve got only one universe, and can only observe a small patch of it. So probabilities become even more subjective and difficult to tie uniquely to the data. Hence the information available to us on the very largest observable scales is scarce, and unlikely to improve much, despite tantalizing hints of data discrepant with our theories, such as the possibly mysterious alignment of patterns in the Cosmic Microwave Background on very large angles of the sky (discussed recently by Peter Coles here). Indeed, much of the data pointing to a possible problem was actually available from the COBE Satellite; results from the more recent and much more sensitive WMAP Satellite have only reinforced the original problems — we hope that the Planck Surveyor — to be launched in April! — will actually be able to shed light on the problem by providing genuinely new information about the polarization of the CMB on large scales to complement the temperature maps from COBE and WMAP.