On the use of Cauchy prior distributions for Bayesian logistic regression

DOI10.1214/17-BA1051zbMath1407.62276arXiv1507.07170MaRDI QIDQ1631551

Yingbo Li, Joyee Ghosh, Robin Mitra

Publication date: 6 December 2018

Published in: Bayesian Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.07170

zbMATH Keywords

Markov chain Monte Carloseparationbinary regressionprobit regressionCauchy distributionsslow mixingexistence of posterior mean

Mathematics Subject Classification ID

Applications of statistics to biology and medical sciences; meta analysis (62P10) Bayesian inference (62F15) Generalized linear models (logistic models) (62J12)

Related Items (12)

Quantifying conditional probability tables in Bayesian networks: Bayesian regression for scenario-based encoding of elicited expert assessments on feral pig habitat ⋮ A comparative study on the performance of frequentist and Bayesian estimation methods under separation in logistic regression ⋮ Shrinkage with shrunken shoulders: Gibbs sampling shrinkage model posteriors with guaranteed convergence rates ⋮ Robust adaptive incorporation of historical control data in a randomized trial of external cooling to treat septic shock ⋮ Laplace approximations and Bayesian information criteria in possibly misspecified models ⋮ A novel variational Bayesian method for variable selection in logistic regression models ⋮ On the existence of posterior mean for Bayesian logistic regression ⋮ Penalising model component complexity: a principled, practical approach to constructing priors ⋮ Bayesian effect selection in structured additive distributional regression models ⋮ tglm ⋮ Shrinkage priors for Bayesian penalized regression ⋮ Mixtures ofg-Priors in Generalized Linear Models

Uses Software

• R
• CRAN
• BayesLogit
• Stan
• reglogit
• arm
• NUTS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo
• The Pólya-gamma Gibbs sampler for Bayesian logistic regression is uniformly ergodic
• Secure Bayesian model averaging for horizontally partitioned data
• Informative \(g\)-priors for logistic regression
• Robustness against separation and outliers in logistic regression
• A weakly informative default prior distribution for logistic and other regression models
• Slice sampling. (With discussions and rejoinder)
• Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation
• Bayesian variable selection using cost-adjusted BIC, with application to cost-effective measurement of quality of health care
• Simulation-based regularized logistic regression
• Hyper-\(g\) priors for generalized linear models
• Bayesian Variable Selection for Latent Class Models
• Rao–Blackwellization for Bayesian Variable Selection and Model Averaging in Linear and Binary Regression: A Novel Data Augmentation Approach
• Posterior expectations for large observations
• On the existence of maximum likelihood estimates in logistic regression models
• Bayesian Multivariate Logistic Regression
• On Bayesian Analysis of Generalized Linear Models Using Jeffreys's Prior
• Propriety of posterior distribution for dichotomous quantal response models
• Bias reduction of maximum likelihood estimates
• BAYESIAN REGRESSION ANALYSIS WITH SCALE MIXTURES OF NORMALS
• Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables
• Bayesian auxiliary variable models for binary and multinomial regression

This page was built for publication: On the use of Cauchy prior distributions for Bayesian logistic regression