Skip to contents

Describe a Gaussian-convolution simulation scenario

Source: R/02_03_scenario_descriptors.R
describe_simulation_scenario.Rd

Summarises the generating law \(\boldsymbol{y}\mid(\boldsymbol{\zeta},\boldsymbol{p})\sim \mathcal{N}_{G}(\boldsymbol{\mu}\boldsymbol{p}, \sum_j p_j^2\boldsymbol{\Sigma}_j)\) at five layers: composition, mean geometry, covariance / SPD diagnostics, network sparsity, and tangent Fisher information (mean versus covariance split). MixSim BarOmega and average pairwise Hellinger of the component Gaussians are kept in descriptors (Hellinger is the unweighted pairwise mean; hellinger_weighted is optional). Jeffreys / symmetrised KL is returned in supplementary. Mean-geometry columns include the highest pairwise cosine and the mean Euclidean (CLD) gap.

Usage

describe_simulation_scenario(
  true_theta,
  adjacency = NULL,
  active_tol = 1e-08,
  include_mixsim = TRUE
)

Arguments

true_theta

List with p, mu, and sigma (and optionally Theta precision). Parsed by check_true_theta() / .parse_true_theta().

adjacency

Optional \(G\times G\times J\) adjacency array, or a length-\(J\) list of adjacencies, used for network density when supplied.

active_tol

Threshold for counting an active simplex component.

include_mixsim

Logical. If TRUE (default), compute MixSim BarOmega via compute_average_overlap(). Set FALSE to skip.

Value

A list with:

  • theta_true: the convolution parameters p, mu, sigma;

  • descriptors: one-row tibble of kept scenario statistics in six families (composition, mean geometry, SPD of \(\boldsymbol{\Sigma}(\boldsymbol{p})\), tangent Fisher, network, component overlap). MixSim BarOmega uses compute_average_overlap() (Davies quadrature for \(G<4\), Sobol Monte Carlo otherwise). Average pairwise Hellinger and affine-invariant Riemannian distance of the \(\Sigma_j\) are kept alongside. hellinger_weighted is optional. SPD columns include both \(\kappa\{\boldsymbol{\Sigma}(\boldsymbol{p})\}\) (kappa_sigma_p) and the reciprocal \(\lambda_{\min}/\lambda_{\max}\) (kappa_sigma_reciprocal);

  • supplementary: one-row tibble of Jeffreys / symmetrised KL, recorded but not treated as a primary score;

  • call: the matched call (match.call()).

See also

run_simulation_benchmark(), expected_fisher_unconstrained(), compute_shannon_entropy(), composition_from_entropy(), helmert_basis(), compute_average_overlap(), compute_average_riemannian()

Examples

theta <- list(
  p = c(0.5, 0.5),
  mu = cbind(c(10, 0), c(0, 10)),
  sigma = array(c(diag(2), diag(2)), dim = c(2, 2, 2))
)
out <- describe_simulation_scenario(theta)
out$descriptors$h_star
#> [1] 1
out$call
#> describe_simulation_scenario(true_theta = theta)