Related papers: The Bispectrum and Its Relationship to Phase-Ampli…

Electroencephalograms (EEG) are noninvasive measurement signals of electrical neuronal activity in the brain. One of the current major statistical challenges is formally measuring functional dependency between those complex signals. This…

A class of multivariate spectral representations for real-valued nonstationary random variables is introduced, which is characterised by a general complex Gaussian distribution. In this way, the temporal signal properties -- harmonicity,…

Living systems have time-evolving interactions that, until recently, could not be identified accurately from recorded time series in the presence of noise. Stankovski et al. (Phys. Rev. Lett. 109 024101, 2012) introduced a method based on…

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore…

In practice, observations are often contaminated by noise, making the resulting sample covariance matrix a signal-plus-noise sample covariance matrix. Aiming to make inferences about the spectral distribution of the population covariance…

Longslit spectroscopy is entering an era of increased spatial and spectral resolution and increased sample size. Improved instruments reveal complex velocity structure that cannot be described with a one-dimensional rotation curve, yet…

A statistical framework is presented for the study of the orthogonally polarized modes of radio pulsar emission via the covariances between the Stokes parameters. To accommodate the typically heavy-tailed distributions of single-pulse radio…

Chain Event Graphs (CEGs) are a widely applicable class of probabilistic graphical model that can represent context-specific independence statements and asymmetric unfoldings of events in an easily interpretable way. Existing model…

We identify universal signatures in the bispectrum arising from a transient tachyonic instability of entropic fluctuations during inflation, a phenomenon that naturally arises in hyperbolic field-space geometries. We perform exact numerical…

Over the last decade, large-scale multiple testing has found itself at the forefront of modern data analysis. In many applications data are correlated, so that the observed test statistic used for detecting a non-null case, or signal, at…

This chapter discusses correlation analysis of stationary multivariate Gaussian time series in the spectral or Fourier domain. The goal is to identify the hub time series, i.e., those that are highly correlated with a specified number of…

The aim of this article is to establish asymptotic distributions and consistency of subsampling for spectral density and for magnitude of coherence for non-stationary, almost periodically correlated time series. We show the asymptotic…

Optical pump-probe spectroscopy is a powerful tool for the study of non-equilibrium electronic dynamics and finds wide applications across a range of fields, from physics and chemistry to material science and biology. However, a shortcoming…

The analysis of high spectral resolution spectroscopic and spectropolarimetric observations constitute a very powerful way of inferring the dynamical, thermodynamical, and magnetic properties of distant objects. However, these techniques…

We consider cross-spectral purity in random nonstationary electromagnetic beams in terms of the Stokes parameters representing the spectral density and the spectral polarization state. We show that a Stokes parameter being cross-spectrally…

Background: There is increasing interest in approaches for analyzing the effect of exposure mixtures on health. A key issue is how to simultaneously analyze often highly collinear components of the mixture, which can create problems such as…

Electroencephalography signals allow to explore the functional activity of the brain cortex in a non-invasive way. However, the analysis of these signals is not straightforward due to the presence of different artifacts and the very low…

Coherent two-dimensional electronic spectroscopy probes ultrafast dynamics using femtosecond pulses. In case the timescale of the studied dynamics become comparable to the pulse duration, pulse overlap effects may compromise the…

The measurement of a reaction cross section from a pulse height spectrum is a ubiquitous problem in experimental nuclear physics. In $\gamma$-ray spectroscopy, this is accomplished frequently by measuring the intensity of full-energy…

We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of…