anMC
is a R package to efficiently compute orthant probabilities of
high-dimensional Gaussian vectors. The method is applied to compute
conservative estimates of excursion sets of functions under Gaussian
random field priors. This is an upgrade on the previously existent
package
ConservativeEstimates.
See the paper Azzimonti, D. and Ginsbourger D.
(2018) for more details.
The package main functions are:
-
ProbaMax
: the main function for high dimensional othant probabilities. Computes P(max X > t), where X is a Gaussian vector and t is the selected threshold. The function computes the probability with the decomposition explained here. It implements both theGMC
andGANMC
algorithms. It allows user-defined functions for the core probability estimate (defaults topmvnorm
of the packagemvtnorm
) and the truncated normal sampler (defaults totrmvrnorm_rej_cpp
) required in the method. -
ProbaMin
: analogous ofProbaMax
but used to compute P(min X < t), where X is a Gaussian vector and t is the selected threshold. This function computes the probability with the decomposition explained here. It implements both theGMC
andGANMC
algorithms. -
conservativeEstimate
: the main function for conservative estimates computation. Requires the mean and covariance of the posterior field at a discretization design.
To install the latest version of the package run the following code from a R console:
if (!require("devtools"))
install.packages("devtools")
devtools::install_github("dazzimonti/anMC")
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. DOI: 10.1080/10618600.2017.1360781. Preprint at hal-01289126
Azzimonti, D. (2016). Contributions to Bayesian set estimation relying on random field priors. PhD thesis, University of Bern. Available at link