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Type:

Package

Title:

L1-Ball Prior for Sparse Regression

Version:

0.1.0

Author:

Maoran Xu and Leo L. Duan

Maintainer:

Maoran Xu <maoranxu@ufl.edu>

Description:

Provides function for the l1-ball prior on high-dimensional regression. The main function, l1ball(), yields posterior samples for linear regression, as introduced by Xu and Duan (2020) <doi:10.48550/arXiv.2006.01340>.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Depends:

R (≥ 3.1.0)

Imports:

VGAM, stats

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

7.1.0

NeedsCompilation:

Packaged:

2020-07-20 01:52:51 UTC; maoran

Repository:

CRAN

Date/Publication:

2020-07-24 17:10:02 UTC

Fit the L1 prior

Description

This package provides an implementation of the Gibbs sampler, for using l1-ball prior with the regression likelihood y_i = X_i\theta+ \epsilon_i, \epsilon_i\sim {N}(0,\sigma^2).

Arguments

y

A data vector, n by 1

X

A design matrix, n by p

b_w

The parameter in Beta(1, p^{b_w}) for w, default b_w=1

step

Number of steps to run the Markov Chain Monte Carlo

burnin

Number of burn-ins

b_lam

The parameter in \lambda_i \sim Inverse-Gamma(1, b_\lambda), default b_\lambda=10^{-3}. To increase the level of shrinkage, use smaller b_\lambda.

Value

The posterior sample collected from the Markov Chain:

trace_theta: \theta
trace_NonZero: The non-zero indicator 1(\theta_i\neq 0)
trace_Lam: \lambda_i
trace_Sigma: \sigma^2

Examples

n = 60
p = 100
X <- matrix(rnorm(n*p),n,p)
d = 5
w0 <- c(rep(0, p-d), rnorm(d)*0.1+1)
y = X%*% w0 + rnorm(n,0,.1)
trace <- l1ball(y,X,steps=2000,burnin = 2000)
plot(colMeans(trace$trace_theta))