{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/bayesian-inference-for-logistic-models-using","title":"Bayesian inference for logistic models using Polya-Gamma latent variables","arxiv_id":"1205.0310","date":"2012-05-02","proceeding":null,"authors":["Nicholas G. Polson","James G. Scott","Jesse Windle"],"abstract":"We propose a new data-augmentation strategy for fully Bayesian inference in\nmodels with binomial likelihoods. The approach appeals to a new class of\nPolya-Gamma distributions, which are constructed in detail. A variety of\nexamples are presented to show the versatility of the method, including\nlogistic regression, negative binomial regression, nonlinear mixed-effects\nmodels, and spatial models for count data. In each case, our data-augmentation\nstrategy leads to simple, effective methods for posterior inference that: (1)\ncircumvent the need for analytic approximations, numerical integration, or\nMetropolis-Hastings; and (2) outperform other known data-augmentation\nstrategies, both in ease of use and in computational efficiency. All methods,\nincluding an efficient sampler for the Polya-Gamma distribution, are\nimplemented in the R package BayesLogit.\n  In the technical supplement appended to the end of the paper, we provide\nfurther details regarding the generation of Polya-Gamma random variables; the\nempirical benchmarks reported in the main manuscript; and the extension of the\nbasic data-augmentation framework to contingency tables and multinomial\noutcomes.","url_abs":"http://arxiv.org/abs/1205.0310v3","url_pdf":"http://arxiv.org/pdf/1205.0310v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"bayesian-inference-for-logistic-models-using","repo_url":"https://github.com/kushagragpt99/MCMC","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"bayesian-inference-for-logistic-models-using","repo_url":"https://github.com/zoj613/polya-gamma","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[{"task_slug":"bayesian-inference","task_name":"Bayesian Inference"},{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"data-augmentation","task_name":"Data Augmentation"},{"task_slug":"numerical-integration","task_name":"Numerical Integration"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"polya-gamma-augmentation","method_name":"Polya-Gamma Augmentation"}],"datasets_introduced":[],"methods_introduced":[{"slug":"polya-gamma-augmentation","name":"Polya-Gamma Augmentation","full_name":"Data augmentation using Polya-Gamma latent variables."}],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}