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)


[Package BBSSL version 0.1.0 Index]