Ultimate Pólya Gamma Samplers – Efficient MCMC for possibly imbalanced binary and categorical data

Modeling binary and categorical data is one of the most commonly encountered tasks applied statisticians econometricians. While Bayesian methods in this context have been available for decades now, they often require a high level familiarity with statistics or suffer from issues such as low sampling efficiency. To contribute to accessibility models data, we introduce novel latent variable representations based on Pólya-Gamma random variables range logistic regression models. From these representations, new Gibbs algorithms binary, binomial, multinomial logit are derived. All allow conditionally Gaussian likelihood representation, rendering extensions more complex modeling frameworks state space straightforward. However, efficiency may still be an issue augmentation estimation frameworks. counteract this, marginal strategies developed discussed detail. The merits our approach illustrated through extensive simulations real applications.