Conditionally Gaussian random sequences generalize State Space models along two relevant directions: (a) the parameters of the model depend in an arbitrary way from past observations, but once this dependence is realized, the randomness can be expressed in terms of Gaussian random variables, (b) correlation is introduced between the transition and measurement equations, through the presence of ...

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...