Efficient sampling for Gaussian linear regression with arbitrary priors

TL;DR

This paper introduces a novel slice sampler for Bayesian linear regression with arbitrary priors, offering faster performance and greater flexibility than existing methods, especially for large models and new shrinkage priors.

Contribution

It develops a versatile, efficient sampler that works with any prior with a computable density, improving sampling speed and enabling exploration of new shrinkage priors without custom algorithms.

Findings

Faster than many existing implementations for large regressors

Compatible with any prior with a density function up to a normalizing constant

Produces better effective sample size per second than alternative approaches

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.