# anMC

`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.

### Features

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.

### Installation

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")
```

### 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), 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