Class, 11/19

Today I told you about the every-four-years Valencia conferences of Bayesians and the other series of meetings that happens two years after each Valencia conference. This conference has been going since, I think, 1978. A discussion of how the series began, written by Jose Bernardo (I mentioned him today) can be found here.

Because they have gotten quite large, in recent years the meetings have been held at a Mediterranean resort (one was held on the Canary Islands, part of Spain). One of the songs I played, "Frequentists and Bayesians," referred to that (Click here for music and lyrics). The songs and other things I mentioned come from the "Cabaret" that follows each of the roughly 5-day long meetings, when everyone is pretty exhausted and ready for some fun. The Cabarets feature songs with Bayesian flavor, set to well-known tunes (see the handout), skits, juggling, and other frivolity. Pictures of several of the Cabarets can be found here.

The song refers to MCMC, which stands for Markov chain Monte Carlo, which has pretty much become the default method of Bayesian calculations for the past 20 years. As I described it in class, it uses a "random walk" method to stagger from one state of nature to another one, in such a way that more time is spent on states of nature that have a high posterior probability. Then we can use the sample so generated to make the inferences we need, by just counting how often each state of nature is visited by the MCMC program; the proportion of time spent on a particular state of nature becomes an estimate of the posterior probability of that state of nature.

Another song I played, "These are Bayes," featured two things of interest. One is the mention of Sir Harold Jeffreys (no relation), who lived to almost 100 years of age and played a very important role over the years in making Bayesian statistics come into the mainstream. He invented a way of deciding on priors which, in the problems we have been doing, amounts to a uniform prior. (I met Sir Harold once, on the only trip he made to the U.S., when I was a graduate student. And, when I go to Bayesian meetings, the similarity between our last names is always a source of amusement.) The second thing is the running joke that Bayesians make about posteriors (Click here for music and lyrics).

There is a lively debate about how to choose priors. There's the Jeffreys prior, mentioned above, and other exotic things like Maximum Entropy priors, Reference priors, Group-theoretic priors and so on. We didn't discuss these at all since they are beyond the scope of the course, but one of the songs, "Confusing Priors," is really referring to this debate. It's on YouTube here.

Two other songs that are in the handout but which I did not play are "The MCMC Saga" and "Bayesian Believer". More YouTube clips of other songs can be found here. The lyrics of some of the earlier songs can be found on the Bayesian Songbook, which I excerpted for today's handout.