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...

In this work, we discuss the problem of approximating a multivariate function by polynomials via `1 minimization method, using a random chosen sub-grid of the corresponding tensor grid of Gaussian points. The independent variables of the function are assumed to be random variables, and thus, the framework provides a non-intrusive way to construct the generalized polynomial chaos expansions, ste...

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...

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...

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...

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...

A Gaussian polytope is the convex hull of normally distributed random points in a Euclidean space. We give an improved error bound for the expected number of facets of a Gaussian polytope when the dimension of the space is fixed and the number of points tends to infinity. The proof applies the theory of the asymptotic distribution of the top order statistic of a collection of independently dist...

Hierarchical mixed models are used to account for dependence between correlated data, in particular dependence created by a group structure within the sample. In such models, the correlation between observations is modelled by including, in the regression model, group-indexed parameters regarded as random variables, so called random eeects. Gaussian distributions are commonly used for the rando...