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# anMC

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[![CRAN
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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](https://github.com/dazzimonti/ConservativeEstimates).
See the paper [Azzimonti, D. and Ginsbourger D.
(2018)](https://hal.science/hal-01289126) 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](https://hal.science/hal-01289126). 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](https://hal.science/hal-01289126). 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:

``` r
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](https://doi.org/10.1080/10618600.2017.1360781).
Preprint at
[hal-01289126](https://hal.science/hal-01289126)

Azzimonti, D. (2016). Contributions to Bayesian set estimation relying
on random field priors. PhD thesis, University of Bern. Available at
[link](https://biblio.unibe.ch/download/eldiss/16azzimonti_d.pdf)
