### "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

Posted at September 24, 2013 16:00 | permanent link