ANMC_Gauss {anMC}  R Documentation 
ANMC estimate for the remainder
Description
Asymmetric nested Monte Carlo estimation of P(max X^{q} > threshold  max X^{q} \le threshold)
where X is a normal vector. It is used for the bias correction in ProbaMax
and ProbaMin
.
Usage
ANMC_Gauss(
compBdg,
problem,
delta = 0.4,
type = "M",
trmvrnorm = trmvrnorm_rej_cpp,
typeReturn = 0,
verb = 0
)
Arguments
compBdg 
total computational budget in seconds. 
problem 
list defining the problem with mandatory fields

delta 
total proportion of budget assigned to initial estimate (default 0.4), 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 
typeReturn 
integer chosen between

verb 
level of verbosity (0,1 for this function), also sets the verbosity of trmvrnorm (to verb1). 
Value
A list containing the estimated probability of excursion, see typeReturn
for details.
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
Azzimonti, D. (2016). Contributions to Bayesian set estimation relying on random field priors. 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.