Related papers: The Bispectrum and Its Relationship to Phase-Ampli…
A number of popular measures of dependence between pairs of band-limited signals rely on analytic phase. A common misconception is that the dependence revealed by these measures must be specific to the spectral range of the filtered input…
In this work, we present the misspecified Gaussian Cram\'er-Rao lower bound for the parameters of a harmonic signal, or pitch, when signal measurements are collected from an almost, but not quite, harmonic model. For the asymptotic case of…
We investigate the relative merit of phase-based methods---mean phase coherence, unweighted and weighted phase lag index---for estimating the strength of interactions between dynamical systems from empirical time series which are affected…
Mapping human genetic variation is fundamentally interesting in fields such as anthropology and forensic inference. At the same time patterns of genetic diversity confound efforts to determine the genetic basis of complex disease. Due to…
The population of compact extragalactic sources contribute to the non-Gaussianity at Cosmic Microwave Background frequencies. We study their non-Gaussianity using publicly available full-sky simulations. We introduce a parametrisation to…
The bispectrum, the three-point function of density fluctuations in Fourier space, is the lowest order statistic that carries information about the spatial coherence of large-scale structures. For Gaussian initial conditions, when the…
The measurements of the statistical properties of the Cosmic Microwave Background (CMB) fluctuations enable us to probe the physics of the very early Universe especially at the epoch of inflation. A particular interest lays on the detection…
Vibrational spectroscopy is a powerful technique to characterize the near-equilibrium dynamics of molecules in the gas- and the condensed-phase. This contribution summarizes efforts from computer-based methods to gain insight into the…
Electroencephalography (EEG) underpins neuroscience, clinical neurophysiology, and brain-computer interfaces (BCIs), yet pronounced inter- and intra-subject variability limits reliability, reproducibility, and translation. This systematic…
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…
The bispectrum provides a characteristic signature of gravitational instability that can be used to probe the Gaussianity of the initial conditions and the bias of the galaxy distribution. We study how this signature is affected by redshift…
This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…
Spectral analysis using overlapping sliding windows is among the most widely used techniques in analyzing non-stationary time series. Although sliding window analysis is convenient to implement, the resulting estimates are sensitive to the…
Raman spectroscopy's capability to provide meaningful composition predictions is heavily reliant on a pre-processing step to remove insignificant spectral variation. This is crucial in biofluid analysis. Widespread adoption of diagnostics…
An increasing number of studies use the spectrum of cardiac signals for analyzing the spatiotemporal dynamics of complex cardiac arrhythmias. However, the relationship between the spectrum of cardiac signals and the spatiotemporal dynamics…
Bayesian parametric analytic continuation (BPAC) is proposed for the analytic continuation of noisy imaginary-time Green's function data as, e.g., obtained by continuous-time quantum Monte Carlo simulations (CTQMC). Within BPAC, the…
A multispeckle technique for efficiently measuring correctly ensemble-averaged intensity autocorrelation functions of scattered light from non-ergodic and/or non-stationary systems is described. The method employs a CCD camera as a…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
Principal component analysis (PCA) is a popular method for projecting data onto uncorrelated components in lower dimension, although the optimal number of components is not specified. Likewise, multiple signal classification (MUSIC)…
We study the problem of passive imaging through convolutive channels. A scene is illuminated with an unknown, unstructured source, and the measured response is the convolution of this source with multiple channel responses, each of which is…