Ultimate Pólya Gamma Samplers–Efficient MCMC for Possibly Imbalanced Binary and Categorical Data

Gregor Zens*, Sylvia Frühwirth-Schnatter, Helga Wagner

*Corresponding author for this work

Publication: Scientific journalJournal articlepeer-review


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 Pólya-Gamma random variables for a range of commonly encountered logistic regression models. From these latent variable representations, new Gibbs sampling algorithms for binary, binomial, and multinomial logit models are derived. All models allow for a conditionally Gaussian likelihood representation, rendering extensions to more complex modeling frameworks such as state space models straightforward. However, sampling efficiency may still be an issue in these data augmentation based estimation frameworks. To counteract this, novel marginal data augmentation strategies are developed and discussed in detail. The merits of our approach are illustrated through extensive simulations and real data applications. Supplementary materials for this article are available online.

Original languageEnglish
JournalJournal of the American Statistical Association
Early online dateSept 2023
Publication statusE-pub ahead of print - Sept 2023

Bibliographical note

Publisher Copyright:
© 2023 The Author(s). Published with license by Taylor & Francis Group, LLC.


  • Bayesian
  • Data augmentation
  • Gibbs sampling
  • MCMC boosting
  • Parameter expansion

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