Computationally efficient method to estimate orthant probabilities of high-dimensional Gaussian vectors. Further implements a function to compute conservative estimates of excursion sets under Gaussian random field priors.
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
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
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:
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
Fixed an issue in
trmvrnorm_rej_cpp that could prevent a call to the function
conservativeEstimate from inside another package.
The package requires a C++11 compiler.
The time measurements now are taken with the
chrono library from C++11.
Dropped dependency on
selectEq is now called
Thresh is now called
ProbaMin now have a user option to choose the function
trmvrnorm to generate truncated multivariate normal samples. The default option is