Three-Toed Sloth

"Binomial Likelihoods and the Polya-Gamma Distribution" (Next Week at the Statistics Seminar)

Attention conservation notice: Only of interest if you (1) care about computational statistics, and (2) will be in Pittsburgh next Monday.

Having a talk on Bayesian computational statistics by a Dr. Scott worked so well last time, we're doing it again:

James Scott, "Binomial Likelihoods and the Polya-Gamma Distribution"

Abstract:Bayesian inference for the logistic regression model has long been recognized as a hard problem. By comparison, Bayesian inference for the probit model is much easier, owing to the simple latent-variable method of Albert and Chib (1993) for posterior sampling.

In the two decades since the work of Albert and Chib on the probit model, there have been many attempts to apply a similar computational strategy to the logit model. These efforts have had mixed results: all such methods are either approximate, or are significantly more complicated than the Albert/Chib method. Perhaps as a result, the Bayesian treatment of the logit model has not seen widespread adoption by non-statisticans in the way that, for example, the Bayesian probit model is used extensively in political science, market research, and psychometrics. The lack of a standard computational approach also makes it more difficult to use the logit link in the kind of rich hierarchical models that have become routine in Bayesian statistics.

In this talk, I propose a new latent-variable representation for binomial likelihoods. It appeals to a new class of distributions, called the Polya-Gamma family. Although our method involves a different missing-data mechanism from that of Albert and Chib, it is nonetheless a direct analogue of their construction, in that it is both exact and simple. I will describe the Polya-Gamma method in detail; demonstrate its superior efficiency; and highlight a few examples where it has proven helpful. I will conclude by drawing an interesting connection with variational methods.

Joint work with Jesse Windle and Nicholas Polson.

Time and place: 4:30--5:30 pm on Monday, 30 September 2013, place TBA (note unusual time)

Enigmas of Chance