Estimating Orthant Probabilities of High-Dimensional Gaussian Vectors with An Application to Set Estimation

DOI10.1080/10618600.2017.1360781OpenAlexW2301321238MaRDI QIDQ3391109

Dario Filippo Azzimonti, David Ginsbourger

Publication date: 28 March 2022

Published in: Journal of Computational and Graphical Statistics (Search for Journal in Brave)

Full work available at URL: https://boris.unibe.ch/112863/1/mainArticle.pdf

zbMATH Keywords

Monte CarloGaussian random fieldsGaussian probabilitiesconservative set estimation

Mathematics Subject Classification ID

Statistics (62-XX)

Related Items (7)

Extrapolation of stationary random fields via level sets ⋮ Skew Gaussian processes for classification ⋮ An \(O(N)\) algorithm for computing expectation of \(N\)-dimensional truncated multi-variate normal distribution. I: Fundamentals ⋮ A class of random fields with two-piece marginal distributions for modeling point-referenced data with spatial outliers ⋮ Gaussian process optimization with failures: classification and convergence proof ⋮ Exploiting low-rank covariance structures for computing high-dimensional normal and Student-\(t\) probabilities ⋮ A unified framework for closed-form nonparametric regression, classification, preference and mixed problems with skew Gaussian processes

Uses Software

• R
• mvtnorm
• ggplot2
• TOMS659
• AS 195
• Orthants
• KrigInv
• QSIMVN
• tmg

Cites Work

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• Some results on the multivariate truncated normal distribution
• Spatio-temporal exceedance locations and confidence regions
• Sequential design of computer experiments for the estimation of a probability of failure
• Computation of multivariate normal and \(t\) probabilities
• The multivariate normal distribution
• Design and analysis of computer experiments. With comments and a rejoinder by the authors
• \textit{KrigInv}: an efficient and user-friendly implementation of batch-sequential inversion strategies based on kriging
• Simulation of multivariate normal rectangle probabilities and their derivatives. Theoretical and computational results
• Monte Carlo and quasi-Monte Carlo sampling
• Computation of Gaussian orthant probabilities in high dimension
• Tables for Computing Bivariate Normal Probabilities
• Algorithm AS 195: Multivariate Normal Probabilities with Error Bound
• THE MONTE CARLO EVALUATION OF ORTHANT PROBABILITIES FOR MULTIVARIATE NORMAL DISTRIBUTIONS
• A Simple Approximation for Bivariate and Trivariate Normal Integrals
• A New Reconstruction of Multivariate Normal Orthant Probabilities
• Algorithm 659
• The Evaluation of General Non-Centred Orthant Probabilities
• OH Radical-Initiated Reaction of 3-Hexene-2,5-dione:  Formation of Methylglyoxal
• Methods of Reducing Sample Size in Monte Carlo Computations
• Excursion and Contour Uncertainty Regions for Latent Gaussian Models
• Theory of Random Sets

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