selectQdims {anMC}  R Documentation 
Iteratively select active dimensions
Description
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_{q1}
is smaller than the error of the procedure.
Usage
selectQdims(
E,
threshold,
mu,
Sigma,
pn = NULL,
method = 1,
reducedReturn = T,
verb = 0,
limits = NULL,
pmvnorm_usr = pmvnorm
)
Arguments
E 
discretization design for the field. 
threshold 
threshold. 
mu 
mean vector. 
Sigma 
covariance matrix. 
pn 
coverage probability function based on 
method 
integer chosen between

reducedReturn 
boolean to select the type of return. See Value for further details. 
verb 
level of verbosity: 0 returns nothing, 1 returns minimal info. 
limits 
numeric vector of length 2 with q_min and q_max. If 
pmvnorm_usr 
function to compute core probability on active dimensions. Inputs:
returns a the probability value with attribute "error", the absolute error. Default is the function 
Value
If reducedReturn=F
returns a list containing
indQ
: the indices of the active dimensions chosen forp_q
;pq
: the biased estimatorp_q
with attributeerror
, the estimated absolute error;Eq
: the points of the designE
selected forp_q
;muEq
: the subvector ofmu
selected forp_q
;KEq
: the submatrix ofSigma
composed by the indexes selected forp_q
.
Otherwise it returns only indQ
.
References
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), 255267. Preprint at hal01289126
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.