Numerical solutions of stochastic problems involving random processes X(t), which constitutes infinite families variables, require to represent these by finite dimensional (FD) models Xd(t), i.e., deterministic functions time depending on numbers d variables. Most available FD match the mean, correlation, and other global properties X(t). They provide useful information a broad range problems, ...

By way of the projected phase-space (PPS), we investigate relation between galaxy properties and cluster environment in a subsample groups from Yang Catalog. The sample is split according to gaussianity velocity distribution group into gaussian (G) non-gaussian (NG). Our limited massive clusters with $\rm M_{200} \geq 10^{14} M_{\odot}$ 0.03\leq z \leq 0.1$. NG are more massive, less concentrat...

In many practical applications, the data is organized along a manifold of lower dimension than the dimension of the embedding space. This additional information can be used when learning the model parameters of Gaussian mixtures. Based on a mismatch measure between the Euclidian and the geodesic distance, manifold constrained responsibilities are introduced. Experiments in density estimation sh...

A REMARK ON THE EQUIVALENCE OF GAUSSIAN PROCESSES HARRY VAN ZANTEN Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands email: [email protected] Submitted June 19, 2007, accepted in final form January 17, 2008 AMS 2000 Subject classification: 60G15, 60G30

In this paper two new fading distributions, the α−η−μ Distribution and α−κ−μ Distribution, are presented. The α − η − μ distribution includes the α − μ, Nakagami-m, Nakagami-q, Weibull, Hoyt, Rayleigh, Exponential, and the OneSided Gaussian distributions as special cases. The α − κ − μ distribution includes the α − μ, Nakagami-m, Weibull, Rice, Rayleigh, Exponential, and the One-Sided Gaussian ...

We consider the sequential Bayesian op-timization problem with bandit feedback,adopting a formulation that allows for the re-ward function to vary with time. We modelthe reward function using a Gaussian pro-cess whose evolution obeys a simple Markovmodel. We introduce two natural extensionsof the classical Gaussian process upper confi-dence bound (GP-UCB) algorit...

an estimation problem of the mean µ of an inverse gaussian distribution ig(µ, c µ) with known coefficient of variation c is treated as a decision problem with entropy loss function. a class of bayes estimators is constructed, and shown to include mrse estimator as its closure. two important members of this class can easily be computed using continued fractions

the complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. as a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.

the complete convergence is investigated for moving-average processes of doubly infinite sequence of negative dependence sub-gaussian random variables with zero means, finite variances and absolutely summable coefficients. as a corollary, the rate of complete convergence is obtained under some suitable conditions on the coefficients.