Has the sun just gone nova? If we’re unsure, should we contact a Bayesian or a frequentist? (Or a psychoanalyst?)
The question is frivolous, but it may illustrate that some very weighty ideas are finding a mass audience.
The movements of asset prices, the probabilities of counterparty default, and other key variables are commonly modeled after all as Bayesian-Markov chains. The term itself combines the work of the 18th century English statistician Thomas Bayes portrayed here with that of a Russian mathematician of the late Czarist era, Andrey Markov, whose image you’ll see below.
Further, as Big Data comes to be ever more central to the hunt for alpha, the dispute between “frequentists” on the one hand and “Bayesians” on the other hand, as schools that claim to understand these accumulations of data and what they can do, becomes ever more intense. The frequentist approach aims at objectivity and timelessness. The Bayesian approach is both more subjective and more path-dependent (that is, if you will, it is sensitive to the history of a particular line of inquiry.)
So I sat up and took notice when, in the early days of February 2015, a cartoon offering a somewhat satirical take on those frequentist-Bayesian debates became a trending topic on social media.
A cartoon?
Are these geeky subjects being assimilated into pop culture? Well: yes. The cartoon in question appeared in the web comic xkcd. Click here. In the center of the first frame stands a table with a strange-looking box on it. The box, a neutrino detector, is supposed to let people know if the sun has just exploded, on the presumption that the people checking the detector wouldn’t otherwise know immediately, because “it’s night.”
But the neutrino detector is capable of lying. Before answering the question about the sun, it rolls two dice (virtual dice, presumably). If they both come up 6, it gives the wrong answer to the question “has the sun gone nova?”
So: on the night depicted by the cartoon, the box says the sun has gone nova. The frequentist statistician determines that the likelihood of both dice coming up 6 is only 1 in 32. That is a probability of less than 0.05, so he concludes that “the sun has exploded.”
The Bayesian supplies the punch line, “Bet you $50 it hasn’t.”
This, it is well to remember, is a joke. The cartoon format is a hint of that. Students of humor could dissect the punchline in a number of ways having nothing to do with the philosophy of statistics. They could discuss, for example, the futility of monetary transactions in the face of one’s own (and everybody else’s!) imminent death. But for the most part this is funny in the way that jokes about the absent-minded professor one-upped by some unimpressed possessor-of-common-sense are generally funny. And people have been telling jokes of that sort since a servant-girl rebuked the philosopher Thales.
Confidence Intervals
What is fascinating is that Bayesian statisticians can nowadays takes the role of the servant girl in such an exchange. If I understand the implication accurately, the Bayesian in the cartoon simply asked himself which is more likely: that two dice came up 6 or that the sun has just exploded? Since the former is much more likely than the latter, he was confident enough to offer the bet.
The frequentist erred by mechanical application of the 0.05 confidence interval. This is what put him in the position of Thales, history’s first philosopher and the man who according to legend once fell down a well because he was looking up at the stars too intently. It also puts the frequentist in the position of many a portfolio manager in the events leading up to the crises of 2007-08, the ones who took just this mechanical an approach to the Value at Risk metric.
What is also fascinating is the way this cartoon, apparently drawn four years ago, blew up into a nova of its own on social media just recently, apparently because a philosophy student in Mexico discovered it and posted the cartoon on his Facebook page.
The frequentists have taken offense, under the impression that it shows how smug Bayesians have become.
I’m not qualified either to take sides or to act smug, so I’ll just default to a belief in the ongoing development of technology. Big Data will develop, and much will be learned, much money will be made, regardless of what philosophical awning is thrown above it all.