# 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