B0185
Title: Ultimate Polya gamma samplers: Efficient MCMC for possibly imbalanced binary and categorical data
Authors: Sylvia Fruehwirth-Schnatter - WU Vienna University of Economics and Business (Austria)
Gregor Zens - Bocconi University (Italy) [presenting]
Helga Wagner - Johannes Kepler University (Austria)
Abstract: Modeling binary and categorical data is one of the most commonly encountered tasks of applied statisticians and econometricians. While Bayesian methods in this context have been available for decades now, they often require a high level of familiarity with Bayesian statistics or suffer from issues such as low sampling efficiency. To contribute to the accessibility of Bayesian models for binary and categorical data, we introduce novel latent variable representations based on Polya Gamma random variables for a range of commonly encountered discrete choice models. New Gibbs sampling algorithms for binary, binomial and multinomial logistic regression models are derived from these latent variable representations. All models allow for a conditionally Gaussian likelihood representation, rendering extensions to more complex modeling frameworks such as state-space models straight-forward. However, sampling efficiency may still be an issue in these data augmentation based estimation frameworks. To counteract this, MCMC boosting strategies are developed and discussed in detail. The merits of our approach are illustrated through extensive simulations and a real data application.
