blockBAGENI {baygel}

Type I naive Bayesian adaptive graphical elastic net block Gibbs sampler for Gaussian graphical models.

Description

Implements the Type I naive Bayesian adaptive graphical elastic net block Gibbs sampler to simulate the posterior distribution of the precision matrix for Gaussian graphical models.

Usage

blockBAGENI(
  X,
  burnin,
  iterations,
  verbose = TRUE,
  r = 0.001,
  s = 0.01,
  a = 0.001,
  b = 0.1
)

Arguments

X

A numeric matrix, assumed to be generated from a multivariate Gaussian distribution.

burnin

An integer specifying the number of burn-in iterations.

iterations

An integer specifying the length of the Markov chain after the burn-in iterations.

verbose

A logical determining whether the progress of the MCMC sampler should be displayed.

r

A double specifying the value of the shape parameter for the gamma prior associated with the Bayesian graphical lasso penalty term.

s

A double specifying the value of the scale parameter for the gamma prior associated with the Bayesian graphical lasso penalty term.

a

A double specifying the value of the shape parameter for the inverse gamma prior associated with the Bayesian graphical ridge penalty term.

b

A double specifying the value of the scale parameter for the inverse gamma prior associated with the Bayesian graphical ridge penalty term.

Value

A list containing precision 'Omega' and covariance 'Sigma' matrices from the Markov chains.

Examples

# Generate true precision matrix:
p             <- 10
n             <- 500
OmegaTrue    <- pracma::Toeplitz(c(0.7^rep(1:p-1)))
SigTrue      <- pracma::inv(OmegaTrue)
# Generate expected value vector:
mu            <- rep(0,p)
# Generate multivariate normal distribution:
set.seed(123)
X             <- MASS::mvrnorm(n, mu = mu, Sigma = SigTrue)
# Generate posterior distribution:
posterior     <- blockBAGENI(X, iterations = 1000, burnin = 500)
# Estimated precision matrix using the mean of the posterior:
OmegaEst      <- apply(simplify2array(posterior$Omega), 1:2, mean)