Bayesian inference for logistic models using Pólya-Gamma latent variables. We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Pólya-Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effect models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple, effective methods for posterior inference that (1) circumvent the need for analytic approximations, numerical integration, or Metropolis-Hastings; and (2) outperform other known data-augmentation strategies, both in ease of use and in computational efficiency. All methods, including an efficient sampler for the Pólya-Gamma distribution, are implemented in the R package BayesLogit. Supplementary materials for this article are available online.

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  1. Durante, Daniele; Dunson, David B.: Bayesian inference and testing of group differences in brain networks (2018)
  2. Johndrow, James; Bhattacharya, Anirban: Optimal Gaussian approximations to the posterior for log-linear models with Diaconis-Ylvisaker priors (2018)
  3. Paci, Lucia; Finazzi, Francesco: Dynamic model-based clustering for spatio-temporal data (2018)
  4. Cadonna, Annalisa; Kottas, Athanasios; Prado, Raquel: Bayesian mixture modeling for spectral density estimation (2017)
  5. Syring, Nicholas; Martin, Ryan: Gibbs posterior inference on the minimum clinically important difference (2017)
  6. Elibol, Huseyin Melih; Nguyen, Vincent; Linderman, Scott; Johnson, Matthew; Hashmi, Amna; Doshi-Velez, Finale: Cross-corpora unsupervised learning of trajectories in autism spectrum disorders (2016)
  7. Peng, Lijun; Carvalho, Luis: Bayesian degree-corrected stochastic blockmodels for community detection (2016)
  8. Tian, Wei; Li, Xiaoyi; Fu, Zhihui: Bayesian inference for logistic models in R language (2016)
  9. Montesinos-López, Osval A.; Montesinos-López, Abelardo; Pérez-Rodríguez, Paulino; Eskridge, Kent; He, Xinyao; Juliana, Philomin; Singh, Pawan; Crossa, José: Genomic prediction models for count data (2015)
  10. Durante, Daniele; Dunson, David B.: Bayesian dynamic financial networks with time-varying predictors (2014)
  11. McClintock, Brett T.; Bailey, Larissa L.; Dreher, Brian P.; Link, William A.: Probit models for capture-recapture data subject to imperfect detection, individual heterogeneity and misidentification (2014)
  12. Choi, Hee Min; Hobert, James P.: The Pólya-gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic (2013)
  13. Polson, Nicholas G.; Scott, James G.; Windle, Jesse: Bayesian inference for logistic models using Pólya-Gamma latent variables (2013)