anMC-package: anMC: Compute High Dimensional Orthant Probabilities

In anMC: Compute High Dimensional Orthant Probabilities

anMC: Compute High Dimensional Orthant Probabilities

Description

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.

Details

Efficient estimation of high dimensional orthant probabilities. 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. It implements the GANMC algorithm and allows for user-defined sampler and core probability estimates.

• ProbaMin: analogous of ProbaMax for the problem P(min X < t), where X is a Gaussian vector and t is the selected threshold. It implements the GANMC algorithm and allows for user-defined sampler and core probability estimates.

• conservativeEstimate: the main function for conservative estimates computation. Requires the mean and covariance of the posterior field at a discretization design.

Note

This work was supported in part by the Swiss National Science Foundation, grant number 146354 and the Hasler Foundation, grant number 16065. Thanks to David Ginsbourger for the fruitful discussions and his continuous help in testing and improving the package.

Author(s)

Maintainer: Dario Azzimonti [e-mail] (ORCID) [copyright holder]

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10618600.2017.1360781")}

Azzimonti, D. (2016). Contributions to Bayesian set estimation relying on random field priors. PhD thesis, University of Bern.

Bolin, D. and Lindgren, F. (2015). Excursion and contour uncertainty regions for latent Gaussian models. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 77(1):85–106.

Chevalier, C. (2013). Fast uncertainty reduction strategies relying on Gaussian process models. PhD thesis, University of Bern.

Dickmann, F. and Schweizer, N. (2014). Faster comparison of stopping times by nested conditional Monte Carlo. arXiv preprint arXiv:1402.0243.

Genz, A. (1992). Numerical computation of multivariate normal probabilities. Journal of Computational and Graphical Statistics, 1(2):141–149.

Genz, A. and Bretz, F. (2009). Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics 195. Springer-Verlag.

Horrace, W. C. (2005). Some results on the multivariate truncated normal distribution. Journal of Multivariate Analysis, 94(1):209–221.

Robert, C. P. (1995). Simulation of truncated normal variables. Statistics and Computing, 5(2):121–125.

See Also

Useful links:

• \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/10618600.2017.1360781")}

anMC documentation built on Aug. 22, 2023, 5:08 p.m.