selectActiveDims {anMC}

Select active dimensions for small dimensional estimate

Description

The function selectActiveDims selects the active dimensions for the computation of p_q with an heuristic method.

Usage

selectActiveDims(
  q = NULL,
  E,
  threshold,
  mu,
  Sigma,
  pn = NULL,
  method = 1,
  verb = 0,
  pmvnorm_usr = pmvnorm
)

Arguments

q

either the fixed number of active dimensions or the range where the number of active dimensions is chosen with selectQdims. If NULL the function selectQdims is called.

E

discretization design for the field.

threshold

threshold.

mu

mean vector.

Sigma

covariance matrix.

pn

coverage probability function based on threshold, mu and Sigma. If NULL it is computed.

method

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.

verb

level of verbosity: 0 returns nothing, 1 returns minimal info

pmvnorm_usr

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.

Value

A vector of integers denoting the chosen active dimensions of the vector mu.

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), 255-267. Preprint at hal-01289126

Azzimonti, D. (2016). Contributions to Bayesian set estimation relying on random field priors. PhD thesis, University of Bern.

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.