l1ball: Fit the L1 prior

In l1ball: L1-Ball Prior for Sparse Regression

Description

This package provides an implementation of the Gibbs sampler, for using l1-ball prior with the regression likelihood y_i = X_iθ+ ε_i, ε_i\sim {N}(0,σ^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 λ_i \sim Inverse-Gamma(1, b_λ), default b_λ=10^{-3}. To increase the level of shrinkage, use smaller b_λ.

Value

The posterior sample collected from the Markov Chain:

• trace_theta: θ

• trace_NonZero: The non-zero indicator 1(θ_i\neq 0)

• trace_Lam: λ_i

• trace_Sigma: σ^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))

l1ball documentation built on July 25, 2020, 1:06 a.m.