Abstract. Slepian and Sudakov-Fernique type inequalities, which compare expectations of maxima of Gaussian random vectors under certain restrictions on the covariance matrices, play an important role in probability theory, especially in empirical process and extreme value theories. Here we give

Random elements of measurable spaces: proofs,

Sampling from Gaussian Markov random fields (GMRFs), that is multivariate Gaussian ran-dom vectors that are parameterised by the inverse of their covariance matrix, is a fundamental problem in computational statistics. In this paper, we show how we can exploit arbitrarily accu-rate approximations

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For the probabilities of large deviations of Gaussian random vectors an asymptotic expansion is derived. Based upon a geometric measure representation for the Gaussian law the interactions between global and local geometric properties both of the distribution and of the large deviation domain

Structural reliability theory has a significant impact on the development of modern design codes. Much of its success could be attributed to the advent of the first-order reliability method (FORM). This paper presents a state-of-the art review on modeling dependent non-Gaussian random vectors

Abstract-In this paper, we compute E[Q( X ], where X is an n × 1 complex circularly Gaussian vector, X is the L 2 norm of X and E[ ] is the expectation operator. This is done by finding the characteristic function of the decision variable and subsequently applying the inversion formula to obtain a

We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian

.i.d.) Gaussian random vector that is imperceptibly inserted in a spread-spectrum-like fashion into the perceptually most significant spectral components of the data. We argue that insertion of a watermark under this regime makes the watermark robust to signal processing operations (such as lossy compression