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An Approximate Iterative Algorithm for Modeling of Non-Gaussian Vectors with Given Marginal Distributions and Covariance Matrix
AbstractA new iterative method for modeling of non-Gaussian random vectors with given marginal distributions and a covariance matrix is proposed in...
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Continuous Random Vectors
Having studied discrete random variables, that is, random variables taking their values in a finite or countable set, we now introduce random...
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Gaussian scrolls, Gaussian flags and duality
A projective variety whose Gauss map has positive dimensional fibres corresponds to a special kind of scroll called Gaussian . A Gaussian scroll is a...
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Hybrid Gaussian/Non-Gaussian Quality-Related Nonlinear Process Monitoring
In complex industrial processes, the mixed characteristics of Gaussian/non-Gaussian and nonlinear data are a common phenomenon. This process is...
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Distribution of the Volume of Weighted Gaussian Simplex
Let X 0 ,..., X l be independent standard Gaussian vectors in ℝ d such that l ≤ d . An explicit formula is obtained for the distribution of the volume of a...
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The Gaussian Free Field
The Gaussian free field is defined in this chapter and the identity in law between the vertex occupation field of loop ensembles of intensity ½ or 1...
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Infinite-dimensional distances and divergences between positive definite operators, Gaussian measures, and Gaussian processes
This paper presents a survey of recent results on the generalization of distances and divergences on the set of symmetric, positive definite (SPD)...
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Convex Hulls of Several Multidimensional Gaussian Random Walks
Explicit formulas for the expected volume and expected number of facets of the convex hull of several multidimensional Gaussian random walks are...
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Conditional Gaussian Densities
Gaussian probability distributions are the workhorse in Bayesian scientific computing, providing a well understood subclass of distributions that...
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Grassmann Angles and Absorption Probabilities of Gaussian Convex Hulls
Let M be an arbitrary subset in ℝ n with a conic (or positive) hull C . Consider its Gaussian image AM , where A is a k × n -matrix whose entries are...
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Spectral Methods for Gaussian Processes
The quantization theory of Gaussian random vectors in a Hilbert space is ruled by the eigenvalues and eigenvectors of their covariance operators....
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Bernstein–Jackson Inequalities on Gaussian Hilbert Spaces
Estimates of best approximations by exponential type analytic functions in Gaussian random variables with respect to the Malliavin derivative in the...
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Gaussian Measures and Families
This chapter deals with some of the properties of Gaussian measures and the construction of families of Gaussian random variables.
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Random Vectors
While Chap. 2 investigates one real random variable at a time, the present chapter is dedicated to studying...
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Average-case analysis of the Gaussian elimination with partial pivoting
The Gaussian elimination with partial pivoting (GEPP) is a classical algorithm for solving systems of linear equations. Although in specific cases...
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Non-Gaussian Process Monitoring and Fault Diagnosis
Compared with PLS and PCA, independent component analysis (ICA) uses higher-order statistical information (above third-order) of the signal, so as to...
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Conditional Gaussian Nonlinear Systems
In this chapter, a nonlinear modeling framework, called the conditional Gaussian nonlinear system (CGNS), is introduced. The CGNS contains a rich...
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Multiple intersections of space-time anisotropic Gaussian fields
Let X = { X ( t ) ∈ ℝ d , t ∈ℝ N } be a centered space-time anisotropic Gaussian field with indices H = ( H 1 , ⋯, H N ) ∈ (0, 1) N , where the components X i ( i =...
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On the Gaussian Surface Area of Spectrahedra
We show that for sufficiently large \(n\geq 1\) and...