blockGLasso: Block Gibbs sampler for Bayesian Graphical Lasso
In trainorp/BayesianGLasso: Bayesian Graphical Lasso

Description Usage Arguments Details Value Author(s) References Examples

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

blockGLasso(X, iterations = 2000, burnIn = 1000, adaptive = FALSE,
  lambdaPriora = 1, lambdaPriorb = 1/10, adaptiveType = c("norm",
  "priorHyper"), priorHyper = NULL, gammaPriors = 1, gammaPriort = 1,
  lambdaii = 1, keepLambdas = TRUE, illStart = c("identity", "glasso"),
  rho = 0.1, verbose = TRUE, ...)

`X`	Data matrix
`iterations`	Length of Markov chain after burn-in
`burnIn`	Number of burn-in iterations
`adaptive`	Logical; Adaptive graphical lasso (TRUE) or regular (FALSE). Default is FALSE.
`lambdaPriora`	Shrinkage parameter (lambda) gamma distribution shape hyperparameter (Ignored if adaptive=TRUE)
`lambdaPriorb`	Shrinkage parameter (lambda) gamma distribution scale hyperparameter (Ignored if adaptive=TRUE)
`adaptiveType`	Choose of adaptive type. Options are "norm" for norm of concentration matrix based adaptivity and "priorHyper" for informative adaptivity
`priorHyper`	Matrix of gamma scale hyper parameters (Ignord if adaptiveType="norm")
`gammaPriors`	labmda_ij gamma distribution shape prior (Ignored if adaptive=FALSE)
`gammaPriort`	lambda_ij gamma distribution rate prior (Ignored if adaptive=FALSE)
`lambdaii`	lambda_ii hyperparameter (Ignored if adaptive=FALSE)
`keepLambdas`	Logical: Should lambda MCMC chain (vector / matrix) be kept?
`illStart`	Method for generating a positive definite estimate of the sample covariance matrix if sample covariance matrix is not semi-positive definite
`rho`	Regularization parameter for the graphical lasso estimate of the sample covariance matrix (if illStart="glasso")
`verbose`	logical; if TRUE return MCMC progress

Implements the block Gibbs sampler for the posterior distribution of a GGM concentration matrix estimated via the Bayesian Graphical Lasso introduced by Wang (2012) or the Bayesian Adaptive Graphical Lasso. For the adaptive case, the element-wise shrinkage parameter is drawn from a gamma distribution where the scale parameter is adaptively modulated directly from the estimated concentration matrix or a user can supply their own informative prior.

`Omega`	List of concentration matrices from the Markov chains
`Lambda`	Vector of simulated lambda parameters

Patrick Trainor (University of Louisville)

Hao Wang

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

# 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)