# Mhorseshoe

## Overview

Mhorseshoe is a package for a high-dimensional Bayesian linear modeling algorithm using a horseshoe prior. A feature of this package is that it implements approximate MCMC algorithm from Johndrow et al. (2020) and provides a horseshoe estimator that can effectively reduce computational costs for high-dimensional sparse data. This package provides two different algorithm functions :

-exact_horseshoe() Run the horseshoe estimator.

-approx_horseshoe() Run the horseshoe estimator with the approximate algorithm applied.

## Installation

install.package("Mhorseshoe")

## Usage

The following linear model assumptions are made.

$L(y\ |\ x, \beta, \sigma^2) = (\frac{1}{\sqrt{2\pi}\sigma})^{-N/2}exp \{ -\frac{1}{2\sigma^2}(y-X\beta)^T(y-X\beta)\},\\ X \in \mathbb{R}^{N \times p},\ y \in \mathbb{R}^{N},\ \beta \in \mathbb{R}^{p}$

• $$X \in \mathbb{R}^{N \times p}$$ : Matrix of covariates.
• $$y \in \mathbb{R}^{N}$$ : Response variable.
# Run functions from the Mhorseshoe package
ex_result <- exact_horseshoe(X, y, burn = 5000, iter = 10000)
ap_result <- approx_horseshoe(X, y, burn = 5000, iter = 10000)

# posterior mean of beta
ex_betahat <- ex_result$BetaHat ap_betahat <- ap_result$BetaHat

# 95% posterior credible intervals
ex_LeftCI <- ex_result$LeftCI ex_RightCI <- ex_result$RightCI
ap_LeftCI <- ap_result$LeftCI ap_RightCI <- ap_result$RightCI

## References

Johndrow, J., Orenstein, P., & Bhattacharya, A. (2020). Scalable Approximate MCMC Algorithms for the Horseshoe Prior. In Journal of Machine Learning Research (Vol. 21).

If you would like to discuss this package, please email leehuimin115@g.skku.edu