Nonparametric models are versatile, albeit computationally expensive, tool for modeling mixture models. In this paper, we introduce spectral methods for the two most popular nonparametric models: the Indian Buffet Process (IBP) and the Hierarchical Dirichlet Process (HDP). We show that using spectral methods for the inference of nonparametric models are computationally and statistically efficie...

In this paper we investigate a continuous-time MA (moving average) process (Xt)t≥0 sampled at an equally spaced time grid {∆,2∆, . . . ,n∆}, where the grid distance ∆ > 0 is fixed and n denotes the number of observations, in the frequency domain. We derive for the process (Xk∆)k∈N with finite second moments the asymptotic behavior of the periodogram and of the lag-window spectral density estima...

This study investigates the effects of stress on the spectral properties of fricative noise in Standard Modern Greek (SMG). Twenty female speakers of SMG participated in the study. Fricatives were produced in stressed and unstressed positions in two vowel place positions: back and front vowels. Acoustic measurements were taken and the temporal and spectral properties of fricatives—using spectra...

An exact spectral analysis of the Markov propagator for the voter model is presented for the complete graph and extended to the complete bipartite graph and uncorrelated random networks. Using a well-defined Martingale approximation in diffusion-dominated regions of phase space, which is almost everywhere for the voter model, this method is applied to compute analytically several key quantities...

A spectral representation for regularly varying Lévy processes with index between one and two is established and the properties of the resulting random noise are discussed in detail giving also new insight in the L2-case where the noise is a random orthogonal measure. This allows a spectral definition of multivariate regularly varying Lévy-driven continuous time autoregressive moving average (C...

An analytical method for evaluating pole-residues in spectral method of moments (MoM) formulations is presented. Spectral integral formulations for periodic structures involve the inverse of the MoM matrix, which exhibits a periodic set of pole singularities, corresponding to the zeros of the matrix’s determinant. So far, these singularities have not been extracted and the corresponding pole-re...

Consider the ensemble of real symmetric Toeplitz matrices, each independent entry an i.i.d. random variable chosen from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. Previous investigations showed that the limiting spectral measure (the density of normalized eigenvalues) converges (weakly and almost surely), independent of p, to a distribution which is alm...

We study the spectral measure of large Euclidean random matrices. The entries of these matrices are determined by the relative position of n random points in a compact set Ωn of R. Under various assumptions we establish the almost sure convergence of the limiting spectral measure as the number of points goes to infinity. The moments of the limiting distribution are computed, and we prove that t...

We present evidence that the power law part of the quiescent x-ray emissions of neutron stars in low mass x-ray binaries is magnetospheric in origin. It can be very accurately calculated from known rates of spin and magnetic moments obtained from the ∼ 103−4 times brighter luminosity at the hard spectral state transition. This strongly suggests that the spectral state transition to the low hard...

The calculation of perturbative corrections to the spectral moments observable in hadronic τ decays is reconsidered. The exact order-αs results and the resummation procedure of Le Diberder and Pich are compared with a partial resummation of the perturbative series based on the analysis of so-called renormalon chains. The perturbative analysis is complemented by a model-independent description o...