ProbaMax: Probability of exceedance of maximum of Gaussian vector

In dazzimonti/ConservativeEstimates: Conservative estimates for excursion sets

Description

Computes P(max X > Thresh) with choice of algorithm between ANMC_Gauss and MC_Gauss. The two most expensive parts are computed with the RCpp functions.

Usage

ProbaMax(cBdg, Thresh, mu, Sigma, E = NULL, q = NULL, pn = NULL,
  lightReturn = T, method = 4, verb = 0, Algo = "ANMC")

Arguments

cBdg	computational budget.
Thresh	threshold.
mu	mean vector.
Sigma	covariance matrix.
E	discretization design for the field. If NULL, a simplex-lattice design n,n is used, with n=length(mu). In this case the choice of method=4,5 are not advised.
q	number of active dimensions. Can be passed either as an integer or as numeric vector of length 2. The vector is the range where to search for the best number of active dimensions. If NULL q is selected as the best number of active dimensions in the feasible range.
pn	coverage function vector.
lightReturn	boolean, if true light return.
method	method chosen to select the active dimensions.
verb	level of verbosity (0-5), selects verbosity also for ANMC_Gauss (verb-1) and MC_Gauss (verb-1).
Algo	choice of algorithm to compute the remainder Rq ("ANMC" or "MC").

Value

A list containing

• probability: The probability estimate

• variance: the variance of the probability estimate

• q:the number of selected active dimensions

If lightReturn=F then the list also contains:

• aux_probabilities: a list with the probability estimates: probability the actual probability, pq the biased estimator p_q, Rq the conditional probability R_q

• Eq: the points of the design E selected for p_q

• indQ: the indices of the active dimensions chosen for p_q

• resRq: The list returned by the MC method used for R_q

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

Chevalier, C. (2013). Fast uncertainty reduction strategies relying on Gaussian process models. 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.

dazzimonti/ConservativeEstimates documentation built on May 15, 2019, 1:19 a.m.