The function selectQdims iteratively selects the number of active dimensions and the dimensions themselves for the computation of \(p_q\).
The number of dimensions is increased until \(p_{q}-p_{q-1}\) is smaller than the error of the procedure.
selectQdims(
E,
threshold,
mu,
Sigma,
pn = NULL,
method = 1,
reducedReturn = T,
verb = 0,
limits = NULL,
pmvnorm_usr = pmvnorm
)If reducedReturn=F returns a list containing
indQ: the indices of the active dimensions chosen for \(p_q\);
pq: the biased estimator \(p_q\) with attribute error, the estimated absolute error;
Eq: the points of the design \(E\) selected for \(p_q\);
muEq: the subvector of mu selected for \(p_q\);
KEq: the submatrix of Sigma composed by the indexes selected for \(p_q\).
Otherwise it returns only indQ.
discretization design for the field.
threshold.
mean vector.
covariance matrix.
coverage probability function based on threshold, mu and Sigma. If NULL it is computed.
integer chosen between
0 selects by taking equally spaced indexes in mu;
1 samples from pn;
2 samples from pn*(1-pn);
3 samples from pn adjusting for the distance (tries to explore all modes);
4 samples from pn*(1-pn) adjusting for the distance (tries to explore all modes);
5 samples with uniform probabilities.
boolean to select the type of return. See Value for further details.
level of verbosity: 0 returns nothing, 1 returns minimal info.
numeric vector of length 2 with q_min and q_max. If NULL initialized at c(10,300)
function to compute core probability on active dimensions. Inputs:
lower: the vector of lower limits of length d.
upper: the vector of upper limits of length d.
mean: the mean vector of length d.
sigma: the covariance matrix of dimension d.
returns a the probability value with attribute "error", the absolute error. Default is the function pmvnorm from the package mvtnorm.
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
Chevalier, C. (2013). Fast uncertainty reduction strategies relying on Gaussian process models. PhD thesis, University of Bern.
Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1(2):141--149.