MBSGS (version 1.1.0)

BSGSSS: Bayesian Sparse Group Selection with Spike and Slab priors

Description

Run a gibbs sampler for a Bayesian sparse group selection model with spike and slab priors. This function is designed for an univariate response model and when the design matrix has a group structure.

Usage

BSGSSS(Y, X, group_size, niter = 10000, burnin = 5000,
pi0 = 0.5, pi1 = 0.5, num_update = 100, niter.update = 100,
alpha = 0.1, gamma = 0.1, a1 = 1, a2 = 1, c1 = 1, c2 = 1,
pi_prior = TRUE)

Arguments

Y

A numerical vector representing the univariate response variable.

X

A matrix respresenting the design matrix of the linear regression model.

group_size

Integer vector representing the size of the groups of the design matrix X

niter

Number of iteration for the Gibbs sampler.

burnin

Number of burnin iteration

pi0

Initial value for pi0 which will be updated if pi_prior="TRUE"

pi1

Initial value for pi1 which will be updated if pi_prior="TRUE"

num_update

Number of update regarding the scaling of the shrinkage parameter lambda which is calibrated by a Monte Carlo EM algorithm

niter.update

Number of itertion regarding the scaling of the shrinkage parameter lambda which is calibrated by a Monte Carlo EM algorithm

alpha

Shape parameter of the Inverse Gamma prior on the variance of the noise for the linear regression model.

gamma

Scale parameter of the Inverse Gamma prior on the variance of the noise for the linear regression model.

a1

First shape parameter of the conjugate beta hyper-prior for pi_0. Default is 1.

a2

Second shape parameter of the conjugate beta prior for pi_0. Default is 1.

c1

First shape parameter of the conjugate beta hyper-prior for pi_1. Default is 1.

c2

Second shape parameter of the conjugate beta prior for pi_1. Default is 1.

pi_prior

Logical. If "TRUE" beta priors are used for pi0 and pi1

Value

BSGSSS returns a list that contains the following components:

pos_mean

The posterior mean estimate of the regression coefficients

pos_median

The posterior mean estimate of the regression coefficients

coef

A matrix with the regression coefficients sampled at each iteration

References

B. Liquet, K. Mengersen, A. Pettitt and M. Sutton. (2016). Bayesian Variable Selection Regression Of Multivariate Responses For Group Data. Submitted in Bayesian Analysis.

Xu, X. and Ghosh, M. (2015). Bayesian Variable Selection and Estimation for Group Lasso. Bayesian Analysis, 10(4): 909<U+2013>936.

See Also

BGLSS

Examples

# NOT RUN {
## Simulation of datasets X and Y with group variables
set.seed(1)
data1 = gen_data_uni(nsample = 120,cor.var=0.5, ntrain = 80)
data1 = normalize(data1)

true_model <- data1$true_model
X <- data1$X
Y<- data1$Y
train_idx <- data1$train_idx
gsize <- data1$gsize
## We recommend to set niter=50000, burnin=10000
## num_update = 100 and niter.update = 100 
## to reach convergence

model <- BSGSSS(Y[,1],X,niter=500,burnin=100,group_size=gsize,
num_update = 20,niter.update = 20)
model$pos_median!=0
true_model
# }