| Gibbs {BBSSL} | R Documentation |
Gibbs
Description
This function runs SSVS for linear regression with Spike-and-Slab LASSO prior. By default, this function uses the speed-up trick in Bhattacharya et al. (2016) when p > n.
Usage
Gibbs(y, X, a, b, lambda, maxiter, burn.in, initial.beta = NULL, sigma = 1)
Arguments
y |
A vector of continuous responses (n x 1). |
X |
The design matrix (n x p), without an intercept. |
a, b |
Parameters of the prior. |
lambda |
A two-dim vector = c(lambda0, lambda1). |
maxiter |
An integer which specifies the maximum number of iterations for MCMC. |
burn.in |
An integer which specifies the maximum number of burn-in iterations for MCMC. |
initial.beta |
A vector of initial values of beta to used. If set to NULL, the LASSO solution with 10-fold cross validation is used. Default is NULL. |
sigma |
Noise standard deviation. Default is 1. |
Value
A list, including matrix 'beta' ((maxiter-burn.in) x p), matrix 'tau2' ((maxiter-burn.in) x p), matrix 'gamma' ((maxiter-burn.in) x p), vector 'theta' ((maxiter-burn.in) x 1).
Author(s)
Lizhen Nie lizhen@statistics.uchicago.edu, Veronika Rockova Veronika.Rockova@chicagobooth.edu
References
Nie, L., & Ročková, V. (2020). Bayesian Bootstrap Spike-and-Slab LASSO. arXiv:2011.14279.
Bhattacharya, A., Chakraborty, A., & Mallick, B. K. (2016). Fast sampling with Gaussian scale mixture priors in high-dimensional regression. Biometrika, 103(4):985.
Examples
n = 50; p = 12;
truth.beta = c(1.3, 1.3, 1.3, 1.3);
truth.sigma = 1
data = Generate_data(truth.beta, p, n, truth.sigma = 1, rho = 0.6,"block",4)
y = data$y; X = data$X; beta = data$beta
# --------------- set parameters -----------------
lambda0 = 7; lambda1 = 0.15; lambda = c(lambda0, lambda1)
a = 1; b = p #beta prior for theta
# this is for demonstration of usage only
# in practice, you may want to use more iterations!
MCchain1 = Gibbs(y, X, a, b, lambda, maxiter = 1000, burn.in = 100)