Bayesian linear regression using the horseshoe prior

As a part of my research I've become interested in the bayesian horseshoe prior for linear regression. But I had a hard time to find the nitty-gritty details of the derivations of the MCMC sampler or a simple implementation of the full MCMC sampler. This repo contains both the nitty-gritty details in deriving the sampler and a naive (slow) implementation in R.

Reference

Carvalho, Carlos M., Nicholas G. Polson, and James G. Scott. "Handling sparsity via the horseshoe." International Conference on Artificial Intelligence and Statistics. 2009. It can be found here.

The nitty-gritty details of the sampler

The derivation of the sampler can be found here.

Implementation in R

A naive (slow) implementation in R as an R package has been put together in this repository. The main purposes is to have a reference implementation and code that can be shared and developed further for others interested in this sampler. A faster implementation can be found in the monomvn R package.

Install the package

install.packages("devtools")
devtools::install_github("MansMeg/hslm", subdir = "RPackage")

Basic usage

Training and test data (based on the diabetes dataset in the lars R package) is included to test the sampler.

data(diabetes_x_train)
data(diabetes_y_train)
hs_res <- hslm(diabetes_y_train, diabetes_x_train)
colMeans(hs_res$beta[-(1:1000]),] # Mean of beta parameters with burnin (1000) removed