A generalized Isserlis theorem for location mixtures of Gaussian random vectors

Autoregressive Gaussian Random Vectors of First Order

autoregressive gaussian random vectors of first order

Gaussian Random Vectors

1. The multivariate normal distribution Let X := (X1 � � � � �X�) be a random vector. We say that X is a Gaussian random vector if we can write X = μ + AZ� where μ ∈ R, A is an � × � matrix and Z := (Z1 � � � � �Z�) is a �-vector of i.i.d. standard normal random variables. Proposition 1. Let X be a Gaussian random vector, as above. Then, EX = μ� Var(X) := Σ = AA� and MX(�) = e � μ+ 1 2 �A���2 =...

Generalized Marginal Likelihood for Gaussian mixtures

The dominant approach in Bernoulli-Gaussian myopic deconvolution consists in the joint maximization of a single Generalized Likelihood with respect to the input signal and the hyperparameters. The aim of this correspondence is to assess the theoretical properties of a related Generalized Marginal Likelihood criterion in a simpliied framework where the lter is reduced to identity. Then the outpu...

Circularly-Symmetric Gaussian random vectors

A number of basic properties about circularly-symmetric Gaussian random vectors are stated and proved here. These properties are each probably well known to most researchers who work with Gaussian noise, but I have not found them stated together with simple proofs in the literature. They are usually viewed as too advanced or too detailed for elementary texts but are used (correctly or incorrect...