BSGSSS: Bayesian Sparse Group Selection with Spike and Slab priors

In MBSGS: Multivariate Bayesian Sparse Group Selection with Spike and Slab

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

Author(s)

Benoit Liquet, Matthew Sutton and Xiaofan Xu.

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<e2><80><93>936.

See Also

BGLSS

Examples

## 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

MBSGS documentation built on May 2, 2019, 4:18 a.m.