Efficient sampling for Gaussian linear regression with arbitrary priors

2018/06/14 by P. Richard Hahn, Jingyu He, Hahn, P. Richard +4
Chemistry · Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Machine Learning (stat.ML) #Spectroscopy and Chemometric Analyses #stat.CO #stat.ML

paper · pdf · doi:10.48550/arxiv.1806.05738

arxiv created 2018/06/14 · openalex publication_date 2018/06/14 · arxiv updated 2018/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper develops a slice sampler for Bayesian linear regression models with arbitrary priors. The new sampler has two advantages over current approaches. One, it is faster than many custom implementations that rely on auxiliary latent variables, if the number of regressors is large. Two, it can be used with any prior with a density function that can be evaluated up to a normalizing constant, making it ideal for investigating the properties of new shrinkage priors without having to develop custom sampling algorithms. The new sampler takes advantage of the special structure of the linear regression likelihood, allowing it to produce better effective sample size per second than common alternative approaches.

Related

• From Estimation to Sampling for Bayesian Linear Regression with Spike-and-Slab Prior
• Bayesian Regression Using a Prior on the Model Fit: The R2-D2 Shrinkage Prior
• Fast sampling with Gaussian scale-mixture priors in high-dimensional regression
• Slice sampling covariance hyperparameters of latent Gaussian models
• Bayesian shrinkage priors subject to linear constraints