Gibbs sampler for Bayesian Graphical LASSO and extensions

Main sampling algorithm of Glasso model, note that the mean is in CAR parameterization

bGlasso(
  data,
  link = "identity",
  r_Omega = 1,
  delta_Omega = 0.01,
  n_iter = 2000,
  n_burn_in = 1000,
  thin_by = 10,
  ns = 1000,
  m = 20,
  emax = 64,
  progress = TRUE,
  verbos = TRUE
)

Arguments

data	A data.frame with all response, row as observations
link	String name of link function? Currently can be "identity" for normal response, "probit" for binary, "log" for counting, "logit" for compositional. Note that when use "logit", the last response will be used as reference.
r_Omega	Hyper-parameter for precision matrix, shape parameter of Gamma. Should be a scalar
delta_Omega	Hyper-parameter for precision matrix, rate parameter of Gamma. Shoule be a scalar
n_iter	Number of sampling iterations (i.e. after burn in) for the Gibbs sampler
n_burn_in	Number of burn in iterations for the Gibbs sampler
thin_by	Final sample was thin by this number
ns	parameter for ARS, maximum number of hulls, only used when link is "log" and "logit"
m	parameter for ARS, initial number of hulls, only used when link is "log" and "logit"
emax	parameter for ARS, tolerance for small values being 0, larger meaning we tolerate smaller values, only used when link is "log" and "logit"
progress	Bool, whether report progress from C++
verbos	Bool, whether show warnings and messages.

Value

A bglasso_out object with elements:

• $point_est

  • $Omega: Posterior mean of precision matrix

• $nodes

  • $responses: node name of responses

• $data

  • $response: response matrix

• $settings: all settings sent to the algorithm, exclude data

• $MCMC_output

  • $mu: A coda::mcmc object, each row was an MCMC sample of the mean vector

  • $Omega: A coda::mcmc object, each row was an MCMC sample of the upper triangular part (with diagonal) of precision matrix Omega

  • $lambda: A coda::mcmc object, first column was the shrinkage parameter lambda for regression coefficient and the second column was shrinkage parameter lambda for precision matrix

Examples

set.seed(42)
dt <- simu_AR1()
glassores <- bGlasso(data = dt[,1:5])
#> Algorithm start...
#> 
#> progress:
#> 
#> 
#> done
#> 
plot(glassores)