A new look at logit likelihoods

We propose a new data-augmentation scheme for estimating models with logit likelihoods. This talk will build up the relevant theory involving Polya-Gamma distributions, and demonstrate three useful features of the approach. First, it leads to simple EM and Gibbs-sampling algorithms, circumventing the need for analytic approximations, numerical integration, or Metropolis-Hastings. Second, it allows modelers great flexibility in choosing priors beyond the usual Dirichlet or logistic-normal family. Finally, our approach naturally suggests a default logistic-Z prior, which is strongly related to Jeffreys' prior for the binomial. To illustrate the method we focus on two cases: multiway tables with fixed margins, and logistic regression. But the approach encompasses many other common situations, including topic models, network models, the Cox model, and discrete-choice models.Joint with: Nick Polson, Liang Sun, Jesse WindleReception following seminar in 211 Old Chemistry