# Ultimate P'olya Gamma Samplers -- Efficient MCMC for possibly imbalanced binary and categorical data

arXiv: https://arxiv.org/abs/2011.06898 · HTML: https://mlsanity.com/paper/2011.06898/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2020.

## Built on by (most cited first, 4 of 4)

- [Gradient-free variational learning with conditional mixture networks](https://mlsanity.com/paper/2408.16429/) (2024)
- [Fast Mixing of Data Augmentation Algorithms: Bayesian Probit, Logit, and Lasso Regression](https://mlsanity.com/paper/2412.07999/) (2024)
- [Mixing times of data-augmentation Gibbs samplers for high-dimensional probit regression](https://mlsanity.com/paper/2505.14343/) (2025)
- [Mean-field Variational Bayes for Sparse Probit Regression](https://mlsanity.com/paper/2601.21765/) (2026)

## Abstract (arXiv)

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 P'olya-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.