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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 the GMC and GANMC algorithms.
It allows user-defined functions for the core probability estimate
(defaults to pmvnorm of the package mvtnorm)
and the truncated normal sampler (defaults to
trmvrnorm_rej_cpp) required in the method.
ProbaMin: analogous of ProbaMax 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 the
GMC and GANMC 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
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.