scholarly journals Efficient simulation for tail probabilities of Gaussian random fields

2008 ◽  
Author(s):  
Robert J. Adler ◽  
Jose Blanchet ◽  
Jingchen Liu
Keyword(s):  
Random Fields ◽  
Gaussian Random Fields ◽  
Tail Probabilities ◽  
Efficient Simulation

scholarly journals Rare-event simulation and efficient discretization for the supremum of Gaussian random fields

2015 ◽  
Vol 47 (03) ◽  
pp. 787-816
Author(s):  
Xiaoou Li ◽  
Jingchen Liu
Keyword(s):  
Random Fields ◽  
Gaussian Random Field ◽  
Rare Event ◽  
Gaussian Random Fields ◽  
Compact Set ◽  
Tail Probabilities ◽  
Hölder Continuous ◽  
Event Simulation ◽  
Classic Problem ◽  
Monte Carlo Algorithms

In this paper we consider a classic problem concerning the high excursion probabilities of a Gaussian random fieldfliving on a compact setT. We develop efficient computational methods for the tail probabilitiesℙ{supTf(t) >b}. For each positive ε, we present Monte Carlo algorithms that run inconstanttime and compute the probabilities with relative error ε for arbitrarily largeb. The efficiency results are applicable to a large class of Hölder continuous Gaussian random fields. Besides computations, the change of measure and its analysis techniques have several theoretical and practical indications in the asymptotic analysis of Gaussian random fields.

scholarly journals Rare-event simulation and efficient discretization for the supremum of Gaussian random fields

2015 ◽  
Vol 47 (3) ◽  
pp. 787-816 ◽  
Author(s):  
Xiaoou Li ◽  
Jingchen Liu
Keyword(s):  
Random Fields ◽  
Gaussian Random Field ◽  
Rare Event ◽  
Gaussian Random Fields ◽  
Compact Set ◽  
Tail Probabilities ◽  
Hölder Continuous ◽  
Event Simulation ◽  
Classic Problem ◽  
Monte Carlo Algorithms

In this paper we consider a classic problem concerning the high excursion probabilities of a Gaussian random fieldfliving on a compact setT. We develop efficient computational methods for the tail probabilitiesℙ{supTf(t) >b}. For each positive ε, we present Monte Carlo algorithms that run inconstanttime and compute the probabilities with relative error ε for arbitrarily largeb. The efficiency results are applicable to a large class of Hölder continuous Gaussian random fields. Besides computations, the change of measure and its analysis techniques have several theoretical and practical indications in the asymptotic analysis of Gaussian random fields.

scholarly journals Maxima of moving sums in a Poisson random field

2009 ◽  
Vol 41 (03) ◽  
pp. 647-663
Author(s):  
Hock Peng Chan
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Occupation Measure ◽  
Tail Probabilities ◽  
Alternative Representation ◽  
Asymptotic Formulae ◽  
Shape And Size ◽  
Asymptotic Tail

In this paper we examine the extremal tail probabilities of moving sums in a marked Poisson random field. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. We also provide an alternative representation of the constants of the asymptotic formulae in terms of the occupation measure of the conditional local random field at zero, and extend these representations to the constants of asymptotic tail probabilities of Gaussian random fields.

scholarly journals Maxima of moving sums in a Poisson random field

2009 ◽  
Vol 41 (3) ◽  
pp. 647-663 ◽  
Author(s):  
Hock Peng Chan
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Gaussian Random Fields ◽  
Occupation Measure ◽  
Tail Probabilities ◽  
Alternative Representation ◽  
Asymptotic Formulae ◽  
Shape And Size ◽  
Asymptotic Tail

In this paper we examine the extremal tail probabilities of moving sums in a marked Poisson random field. These sums are computed by adding up the weighted occurrences of events lying within a scanning set of fixed shape and size. We also provide an alternative representation of the constants of the asymptotic formulae in terms of the occupation measure of the conditional local random field at zero, and extend these representations to the constants of asymptotic tail probabilities of Gaussian random fields.

scholarly journals Fast generation of isotropic Gaussian random fields on the sphere

2018 ◽  
Vol 24 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Peter E. Creasey ◽  
Annika Lang
Keyword(s):  
Efficient Method ◽  
Unit Sphere ◽  
Random Fields ◽  
Fourier Transforms ◽  
Gaussian Random Fields ◽  
Covariance Matrices ◽  
Conditional Covariance ◽  
Efficient Simulation ◽  
Set Up ◽  
Markov Properties

Abstract The efficient simulation of isotropic Gaussian random fields on the unit sphere is a task encountered frequently in numerical applications. A fast algorithm based on Markov properties and fast Fourier transforms in 1d is presented that generates samples on an {n\times n} grid in {\operatorname{O}(n^{2}\log n)} . Furthermore, an efficient method to set up the necessary conditional covariance matrices is derived and simulations demonstrate the performance of the algorithm. An open source implementation of the code has been made available at https://github.com/pec27/smerfs.

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

Sign in / Sign up

Export Citation Format

Share Document