Skip to contents

Prior effective sample size for a Gaussian graphical model

Source: R/family-ggm.R
prior_ess.ggm_elicited.Rd

Computes the prior ESS of an elicited prior distribution for the parameters in a Gaussian graphical model. The matrix estimators (VR, PR) work with matrices (Fisher information matrix and prior variance matrix) and need to be reduced to a scalar first, the remaining estimators do not. For the G-Wishart prior the quantities involved have no closed form and are approximated by Monte Carlo simulations.

Usage

# S3 method for class 'ggm_elicited'
prior_ess(
  params,
  estimator = NULL,
  aggregation = c("det", "tr", "mean"),
  sampler = c("direct", "gibbs"),
  n_samples = 1000L,
  tol = 1e-06,
  itermax = 1000L,
  burnin = 500L,
  init = NULL,
  compute_cond = FALSE,
  ...
)

Arguments

params

A ggm_elicited object, as returned by elicit_prior.

estimator

Character vector selecting the estimators, or NULL (default) to compute all available estimators for the family/prior. Several estimators are available "VR", "PR", "MTM", "PT", and "ELIR".

aggregation

Character scalar selecting the aggregation method to reduce the estimator to a scalar: "det" (default), "tr", or "mean". Applies only to the matrix estimators (VR, PR).

sampler

Monte Carlo sampler for the G-Wishart prior, either "direct" (default) or "gibbs" (Edge-wise Gibbs sampler). Ignored for the Wishart prior and the scalar estimators.

n_samples

Number of Monte Carlo samples for the G-Wishart prior. Default 1000.

tol

Convergence tolerance for the direct sampler. Default 1e-6.

itermax

Number of maximum iterations for the direct sampler. Default 1000. This number caps the iterative procedure for one draw of the direct sampler.

burnin

Number of burn-in iterations discarded by the Gibbs sampler. Default 500.

init

Starting value for the Gibbs sampler, a p by p symmetric positive-definite precision matrix on the same scale as the returned samples, which are centered on the elicited precision matrix. Entries where the graph has no edge must be zero: the sampler never updates them, so whatever is defined there is carried into every draw. NULL (default) starts from a diagonal matrix of the marginal precisions implied by the elicited prior (diag(params$nu / diag(solve(params$scale)))).

compute_cond

Logical: whether to compute the condition number of numerator and denominator of VR and PR (default FALSE).

...

Ignored, present for consistency with the generic prior_ess().

Value

A prior_ess object for the ggm family. Its estimates component is a named numeric vector with one entry per estimator. print and summary methods are available.

A prior_ess object for the ggm family. Its estimates component is a named list, one element per estimator, each with a global value and a parameterwise table (for the matrix estimators). When compute_cond = TRUE those elements also carry cond_numerator and cond_denominator. print and summary methods are available.

Details

The sampling arguments (sampler, n_samples, tol, itermax, burnin, init) apply to the G-Wishart prior only. Under the Wishart prior the quantities involved are available in closed form and nothing is simulated.

See also

Other prior ess: prior_ess()