MC_Gauss  R Documentation 
Standard Monte Carlo estimate for P(max X^{q} >threshold  max X^{q}≤ threshold) or P(min X^{q} <threshold  min X^{q}≥ threshold) where X is a normal vector. It is used for the bias correction in ProbaMax
and ProbaMin
.
MC_Gauss( compBdg, problem, delta = 0.1, type = "M", trmvrnorm = trmvrnorm_rej_cpp, typeReturn = 0, verb = 0, params = NULL )
compBdg 
total computational budget in seconds. 
problem 
list defining the problem with mandatory fields:

delta 
total proportion of budget assigned to initial estimate (default 0.1), the actual proportion used might be smaller. 
type 
type of excursion: "m", for minimum below threshold or "M", for maximum above threshold. 
trmvrnorm 
function to generate truncated multivariate normal samples, it must have the following signature trmvrnorm(n,mu,sigma,upper,lower,verb), where
It must return a matrix d x n of realizations. If not specified, the rejection sampler 
typeReturn 
integer: 0 (only the estimate) or 1 (heavy return with variance of the estimate, parameters of the estimator and computational times). 
verb 
the level of verbosity, also sets the verbosity of trmvrnorm (to verb1). 
params 
system dependent parameters (if NULL they are estimated). 
A list containing the estimated probability of excursion, see typeReturn
for details.
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
Azzimonti, D. (2016). Contributions to Bayesian set estimation relying on random field priors. PhD thesis, University of Bern.
Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1(2):141–149.
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