MC_Gauss: MC estimate for the remainder

In dazzimonti/ConservativeEstimates: Conservative estimates for excursion sets

Description

Standard Monte Carlo estimate for P(max X^{-q} >Thresh | max X^{q}≤ Thresh) or P(min X^{-q} <Thresh | min X^{q}≥ Thresh) where X is a normal vector. Needed for the bias correction in ProbaMax and ProbaMin.

Usage

MC_Gauss(compBdg, problem, delta = 0.1, type = "M", typeReturn = 0,
  verb = 0, params = NULL)

Arguments

compBdg	total computational budget in seconds.
problem	list defining the problem with mandatory fields: muEq = mean vector of X^{q}; sigmaEq = covariance matrix of X^q; Thresh = threshold; muEmq = mean vector of X^{-q}; wwCondQ = “weights” for X^{-q} | X^q [ the vector Σ^{-q,q}(Σ^q)^{-1}]; sigmaCondQChol = Cholesky factorization of the conditional covariance matrix Σ^{-q | q}.
delta	total proportion of budget assigned to initial estimate (default 0.1), the actual proportion used might be smaller.
type	type of excursion: "m", for minimum below threshold or "M", for maximum above threshold.
typeReturn	integer: 0 (only the estimate) or 1 (heavy return with variance of the estimate, parameters of the estimator and computational times).
verb	the level of verbosity, also sets the verbosity of trmvrnorm_rej_cpp (to verb-1).
params	system dependent parameters (if NULL they are estimated).

Value

A list containing the estimated probability of excursion, see typeReturn for details.

References

Azzimonti, D. and Ginsbourger, D. (2016). Estimating orthant probabilities of high dimensional Gaussian vectors with an application to set estimation. Preprint at hal-01289126

Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1(2):141–149.

dazzimonti/ConservativeEstimates documentation built on May 15, 2019, 1:19 a.m.