We propose an Iterative Nonlinear Gaussianization Algorithm (INGA) which seeks a nonlinear map from a set of dependent random variables to independent Gaussian random variables. A direct motivation of INGA is to extend principal component analysis (PCA), which transforms a set of correlated random variables into uncorrelated (independent up to second order) random variables, and Independent Com...

We consider a distributed source coding problem of L correlated Gaussian observations Yi, i = 1, 2, · · · , L. We assume that the random vector Y L = t(Y1, Y2, · · · , YL) is an observation of the Gaussian random vector X = t(X1, X2, · · · , XK), having the form Y L = AX +N , where A is a L×K matrix and N = t(N1, N2, · · · , NL) is a vector of L independent Gaussian random variables also indepe...

Arthur Charpentier (see Arthur’s blog) was recently contacted by some researchers willing to test if a multivariate copula is or not Gaussian. They use a test proposed in Malevergne and Sornette (2003) stating that one should simply test for pairwise normality. This test may be of importance in finance, in actuarial science, and in risk management in general: for example, given 120 financial as...

Introduction: Diffusion Weighted Magnetic Resonance Imaging (DWMRI) provides visual contrast, depends on Brownian motion of water molecules. The diffusive behavior of water in cells alters in many disease states. Dephasing is a factor of magnetic field inhomogeneity, heterogeneity of tissue and etc., which is associated with the signal amplitude. In a series of DWI acquisition...

Definition 1.1. A Gaussian process {Xt }t∈T indexed by a set T is a family of (real-valued) random variables Xt , all defined on the same probability space, such that for any finite subset F ⊂ T the random vector XF := {Xt }t∈F has a (possibly degenerate) Gaussian distribution; if these finitedimensional distributions are all non-degenerate then the Gaussian process is said to be nondegenerate....