ANMC_Gauss: ANMC estimate for the remainder

In dazzimonti/ConservativeEstimates: Conservative estimates for excursion sets

Description

Asymmetric nested Monte Carlo estimation of P(max X^{-q} > Thresh | max X^{q} ≤ Thresh) where X is a normal vector.

Usage

ANMC_Gauss(compBdg, problem, delta = 0.4, type = "M", typeReturn = 0,
  verb = 0)

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 0.4), the actual proportion used might be smaller.
type	type of excursion: "m", for minimum below threshold or "M", for maximum above threshold.
typeReturn	integer chosen between 0 a number with only the probability estimation; 1 light return: a list with the probability estimator, the variance of the estimator, the vectors of conditional quantities used to obtain m^* and the system dependent parameters; 2 heavy return: the same list as light return with also the computational times and additional intermediate parameters.
verb	level of verbosity (0,1 for this function), also sets the verbosity of trmvrnorm_rej_cpp (to verb-1).

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

Dickmann, F. and Schweizer, N. (2014). Faster comparison of stopping times by nested conditional Monte Carlo. arXiv preprint arXiv:1402.0243.

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.