Asymmetric nested Monte Carlo estimation of \(P(max X^{-q} > threshold | max X^{q} \le threshold)\) where X is a normal vector. It is used for the bias correction in ProbaMax and ProbaMin.
ANMC_Gauss(
compBdg,
problem,
delta = 0.4,
type = "M",
trmvrnorm = trmvrnorm_rej_cpp,
typeReturn = 0,
verb = 0
)A list containing the estimated probability of excursion, see typeReturn for details.
total computational budget in seconds.
list defining the problem with mandatory fields
muEq = mean vector of \(X^{q}\);
sigmaEq = covariance matrix of \(X^q\);
threshold = fixed threshold \(t\);
muEmq = mean vector of \(X^{-q}\);
wwCondQ = ``weights'' for \(X^{-q} | X^q\) [the vector \(\Sigma^{-q,q}(\Sigma^q)^{-1}\)];
sigmaCondQChol = Cholesky factorization of the conditional covariance matrix \(\Sigma^{-q | q}\);
total proportion of budget assigned to initial estimate (default 0.4), the actual proportion used might be smaller.
type of excursion: "m", for minimum below threshold or "M", for maximum above threshold.
function to generate truncated multivariate normal samples, it must have the following signature trmvrnorm(n,mu,sigma,upper,lower,verb), where
n: number of simulations;
mu: mean vector of the Normal variable of dimension \(d\);
sigma: covariance matrix of dimension \(d x d\);
upper: vector of upper limits of length d;
lower: vector of lower limits of length d;
verb: the level of verbosity 3 basic, 4 extended.
It must return a matrix \(d x n\) of realizations. If not specified, the rejection sampler trmvrnorm_rej_cpp is used.
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.
level of verbosity (0,1 for this function), also sets the verbosity of trmvrnorm (to verb-1).
Azzimonti, D. and Ginsbourger, D. (2018). Estimating orthant probabilities of high dimensional Gaussian vectors with an application to set estimation. Journal of Computational and Graphical Statistics, 27(2), 255-267. Preprint at hal-01289126
Azzimonti, D. (2016). Contributions to Bayesian set estimation relying on random field priors. PhD thesis, University of Bern.
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.