Inference with Pólya-Gamma Augmentation for US Election Law

Adam C. Hall and Joseph Kang ()
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Adam C. Hall: US Census Bureau, 4600 Silver Hill Rd., Washington, DC 20233, USA
Joseph Kang: US Census Bureau, 4600 Silver Hill Rd., Washington, DC 20233, USA

Mathematics, 2025, vol. 13, issue 6, 1-18

Abstract: Pólya-gamma (PG) augmentation has proven to be highly effective for Bayesian MCMC simulation, particularly for models with binomial likelihoods. This data augmentation strategy offers two key advantages. First, the method circumvents the need for analytic approximations or Metropolis–Hastings algorithms, which leads to simpler and more computationally efficient posterior inference. Second, the approach can be successfully applied to several types of models, including nonlinear mixed-effects models for count data. The effectiveness of PG augmentation has led to its widespread adoption and implementation in statistical software packages, such as version 2.1 of the R package BayesLogit. This success has inspired us to apply this method to the implementation of Section 203 of the Voting Rights Act (VRA), a US law that requires certain jurisdictions to provide non-English voting materials for specific language minority groups (LMGs). In this paper, we show how PG augmentation can be used to fit a Bayesian model that estimates the prevalence of each LMG in each US voting jurisdiction, and that uses a variable selection technique called stochastic search variable selection. We demonstrate that this new model outperforms the previous model used for 2021 VRA data with respect to model diagnostic measures.

Keywords: small area estimation; Pólya-gamma augmentation; stochastic search variable selection; Bayesian regression; Gibbs sampling; Voting Rights Act (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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