blockGLasso {BayesianGLasso}

Block Gibbs sampler function

Description

Blockwise sampling from the conditional distribution of a permuted column/row for simulating the posterior distribution for the concentration matrix specifying a Gaussian Graphical Model

Usage

blockGLasso(X, iterations = 2000, burnIn = 1000, lambdaPriora = 1,
  lambdaPriorb = 1/10, verbose = TRUE)

Arguments

X

Data matrix

iterations

Length of Markov chain after burn-in

burnIn

Number of burn-in iterations

lambdaPriora

Shrinkage hyperparameter (lambda) gamma distribution shape

lambdaPriorb

Shrinkage hyperparameter (lambda) gamma distribution scale

verbose

logical; if TRUE return MCMC progress

Details

Implements the block Gibbs sampler for the Bayesian graphical lasso introduced in Wang (2012). Samples from the conditional distribution of a permuted column/row for simulating the posterior distribution for the concentration matrix specifying a Gaussian Graphical Model

Value

Sigma

List of covariance matrices from the Markov chain

Omega

List of concentration matrices from the Markov chains

Lambda

Vector of simulated lambda parameters

Author(s)

Patrick Trainor (University of Louisville)

Hao Wang

References

Wang, H. (2012). Bayesian graphical lasso models and efficient posterior computation. Bayesian Analysis, 7(4). <doi:10.1214/12-BA729> .

Examples

# Generate true covariance matrix:
s<-.9**toeplitz(0:9)
# Generate multivariate normal distribution:
set.seed(5)
x<-MASS::mvrnorm(n=100,mu=rep(0,10),Sigma=s)
blockGLasso(X=x)

# Same example with short MCMC chain:
s<-.9**toeplitz(0:9)
set.seed(6)
x<-MASS::mvrnorm(n=100,mu=rep(0,10),Sigma=s)
blockGLasso(X=x,iterations=100,burnIn=100)