Suppose that the collection {ei}i=1 forms a frame for R, where each entry of the vector ei is a sub-Gaussian random variable. We consider expansions in such a frame, which are then quantized using a Sigma-Delta scheme. We show that an arbitrary signal in R can be recovered from its quantized frame coefficients up to an error which decays root-exponentially in the oversampling rate m/k. Here the...

The formula for the expectation of the product of four scalar real Gaussian random variables is generalized to matrix-valued (real or complex) Gaussian random variables. As an application of the extended formula, we present a simple derivation of the covariance matrix of instrumental variable (IV) estimates of parameters in multivariate linear regression models. (*) Faculty of Electrical Engine...

Bayesian networks provide a method of rep­ resenting conditional independence between random variables and computing the prob­ ability distributions associated with these random variables. In this paper, we ex­ tend Bayesian network structures to compute probability density functions for continuous random variables. We make this extension by approximating prior and conditional den­ sities using...

This paper presents a useful theorem for non-linear transformations of the sum of independent, zeromean, Gaussian random variables. It is proved that the linear regression coefficient of the non-linear transformation output with respect to the overall input is identical to the linear regression coefficient with respect to any Gaussian random variable that is part of the input. As a side-result,...

We maximized mutual information between the sensor locations (treated as random variables) to find a near-optimal choice of k sensors. In the original paper, the authors used a gaussian process to model the random variables and they therefore had analytical expressions for the mutual informations. Given data X1, . . . , Xn ∈ R (we have p possible sensor locations and n samples), they fit a gaus...

We consider two independent q-Gaussian random variables X0 and X1 and a function γ chosen in such a way that γ(X0) and X0 have the same distribution. For q ∈ (0, 1) we find that at least the fourth moments of X0 + X1 and γ(X0) + X1 are different. We conclude that no q-deformed convolution product can exist for functions of independent q-Gaussian random variables. 1995 PACS numbers: 02.50.Cw, 05...

x Introduction Literature Review Dissertation Organization and Contribution Abbreviations Array Signal Processing Fundamentals and Current Approaches Problem Formulation Maximum Likelihood DOA Estimation with Gaussian Distributions The Stochastic Maximum Likelihood Method The Deterministic Maximum Likelihood Method The Deterministic Cram er Rao Bound for Gaussian Noise Subspace Based DOA Estima...

The paper presents bounds for the distributions of suprema particular classes ϕ-sub-Gaussian random fields. Results stated depend on representations increments fields in different metrics. Several examples applications are provided to illustrate results, particular, related stochastic partial differential equations and with initial conditions.

This paper introduces the hybrid copula Bayesian network (HCBN) model, a generalization of the copula Bayesian network (CBN) model developed by Elidan (2010) for continuous random variables to multivariate mixed probability distributions of discrete and continuous random variables. To this end, we extend the theorems proved by Nešlehová (2007) from bivariate to multivariate copulas with discret...

1 Abstract A complex quantum system with energy dissipation is considered. The quantum Hamilto-nians H belong the complex Ginibre ensemble. The complex-valued eigenenergies Z i are random variables. The second differences ∆ 1 Z i are also complex-valued random variables. The second differences have their real and imaginary parts and also radii (moduli) and main arguments (angles). For N=3 dimen...