Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables

REFERENCES

• Albert , J. H. and Chib , S. 1993 . Bayesian Analysis of Binary and Polychotomous Response Data . Journal of the American Statistical Association , 88 : 669 – 679 .
   Web of Science ®Google Scholar
• Andrews , D. and Mallows , C. 1974 . Scale Mixtures of Normal Distributions . Journal of the Royal Statistical Society, Series B , 36 : 99 – 102 .
   Google Scholar
• Barndorff-Nielsen , O. E. , Kent , J. and Sorensen , M. 1982 . Normal Variance-Mean Mixtures and z Distributions . International Statistical Review , 50 : 145 – 159 .
   Web of Science ®Google Scholar
• Bates , D. , Maechler , M. and Bolker , B. 2011 . mlmRev: Examples from Multilevel Modelling Software Review , Available at http://CRAN.R-project.org/package=mlmRev. R Package Version 1.0-1
   Google Scholar
• Biane , P. , Pitman , J. and Yor , M. 2001 . Probability Laws Related to the Jacobi Theta and Riemann Zeta Functions, and Brownian Excursions . Bulletin of the American Mathematical Society , 38 : 435 – 465 .
   Web of Science ®Google Scholar
• Blei , D. M. and Lafferty , J. 2007 . A Correlated Topic Model of Science . The Annals of Applied Statistics , 1 : 17 – 35 .
   Web of Science ®Google Scholar
• Carlin , J. 1992 . Meta-Analysis for 2 × 2 Tables: A Bayesian Approach . Statistics in Medicine , 11 : 141 – 158 .
   PubMed Web of Science ®Google Scholar
• Choi , H. M. and Hobert , J. P. 2013 . The Polya-Gamma Gibbs Sampler for Bayesian Logistic Regression is Uniformly Ergodic,” . Technical Report, University of Florida
   Google Scholar
• Ciesielski , Z. and Taylor , S. J. 1962 . First Passage Times and Sojourn Times for Brownian Motion in Space and the Exact Hausdorff Measure of the Sample Path . Transactions of the American Mathematical Society , 103 : 434 – 450 .
   Google Scholar
• Devroye , L. 1986 . Non-Uniform Random Variate Generation , Berlin : Springer . Available for download at http://luc.devroye.org/rnbookindex.html
   Google Scholar
• Devroye , L. 2009 . On Exact Simulation Algorithms for Some Distributions Related to Jacobi Theta Functions . Statistics & Probability Letters , 79 : 2251 – 2259 .
   Web of Science ®Google Scholar
• Frühwirth-Schnatter , S. and Frühwirth , R. 2007 . Auxiliary Mixture Sampling With Applications to Logistic Models . Computational Statistics and Data Analysis , 51 : 3509 – 3528 .
   Web of Science ®Google Scholar
• ——— . 2010 . “ Data Augmentation and MCMC for Binary and Multinomial Logit Models ” . In Statistical Modelling and Regression Structures , 111 – 132 . Berlin : Springer-Verlag . Available from UT library online
   Google Scholar
• Frühwirth-Schnatter , S. , Frühwirth , R. , Held , L. and Rue , H. 2009 . Improved Auxiliary Mixture Sampling for Hierarchical Models of Non-Gaussian Data . Statistics and Computing , 19 : 479 – 492 .
   Web of Science ®Google Scholar
• Fussl , A. , Frühwirth-Schnatter , S. and Frühwirth , R. 2013 . Efficient MCMC for Binomial Logit Models . ACM Transactions on Modeling and Computer Simulation , 22 : 1 – 21 .
   Web of Science ®Google Scholar
• Gamerman , D. 1997 . Sampling From the Posterior Distribution in Generalized Linear Mixed Models . Statistics and Computing , 7 : 57 – 68 .
   Web of Science ®Google Scholar
• Gelman , A. , Carlin , J. , Stern , H. and Rubin , D. 2004 . Bayesian Data Analysis (2nd ed.) , New York : Chapman and Hall/CRC .
   Google Scholar
• Gramacy , R. B. and Polson , N. G. 2012 . Simulation-Based Regularized Logistic Regression . Bayesian Analysis , 7 : 567 – 590 .
   Web of Science ®Google Scholar
• Holmes , C. and Held , L. 2006 . Bayesian Auxiliary Variable Models for Binary and Multinomial Regression . Bayesian Analysis , 1 : 145 – 168 .
   Web of Science ®Google Scholar
• Jackman , S. 2009 . Bayesian Analysis for the Social Sciences , New York : Wiley .
   Google Scholar
• McFadden , P. 1974 . “ Conditional Logit Analysis of Qualitative Choice Behavior ” . In Frontiers of Econometrics , Edited by: Zarembka , P. 105 – 142 . New York : Academic .
   Google Scholar
• O’Brien , S. M. and Dunson , D. B. 2004 . Bayesian Multivariate Logistic Regression . Biometrics , 60 : 739 – 746 .
   PubMed Web of Science ®Google Scholar
• Plummer , M. , Best , N. , Cowles , K. and Vines , K. 2006 . CODA: Convergence Diagnosis and Output Analysis for MCMC . R News , 6 : 7 – 11 . Available at http://CRAN.R-project.org/doc/Rnews/
   Google Scholar
• Polson , N. G. and Scott , J. G. 2012 . Local Shrinkage Rules, Lévy Processes, and Regularized Regression . Journal of the Royal Statistical Society, Series B , 74 : 287 – 311 .
   Google Scholar
• Polson , N. G. and Scott , J. G. 2013 . Data Augmentation for Non-Gaussian Regression Models Using Variance-Mean Mixtures . Biometrika , 100 : 459 – 471 .
   Web of Science ®Google Scholar
• Rossi , P. E. 2012 . Bayesm: Bayesian Inference for Marketing/Micro-Econometrics http://CRAN.R-project.org/package=bayesm. R Package Version 2.2-5
   Google Scholar
• Rossi , P. E. , Allenby , G. M. and McCulloch , R. E. 2005 . Bayesian Statistics and Marketing , New York : Wiley .
   Google Scholar
• Salakhutdinov , R. , Mnih , A. and Hinton , G. 2007 . Restricted Boltzmann Machines for Collaborative Filtering . Proceedings of the 24th Annual International Conference on Machine Learning , : 791 – 798 .
   Google Scholar
• Windle , J. , Polson , N. G. and Scott , J. G. 2013a . BayesLogit: Bayesian Logistic Regression http://cran.r-project.org/web/packages/BayesLogit/index.html. R Package Version 0.2-4
   Google Scholar
• Windle , J. , Polson , N. G. and Scott , J. G. 2013b . Improved Pólya-Gamma Sampling . Technical Report, University of Texas at Austin
   Google Scholar