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Vector autoregressions (VARs) with multivariate stochastic volatility are widely used for structural analysis. Often the structural model identified through economically meaningful restrictions--e.g., sign restrictions--is supposed to be…
Complex multivariate time series arise in many fields, ranging from computer vision to robotics or medicine. Often we are interested in the independent underlying factors that give rise to the high-dimensional data we are observing. While…
This paper introduces a Bayesian vector autoregression (BVAR) with stochastic volatility-in-mean and time-varying skewness. Unlike previous approaches, the proposed model allows both volatility and skewness to directly affect macroeconomic…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…
We consider the problem of modeling the dependence among many time series. We build high dimensional time-varying copula models by combining pair-copula constructions (PCC) with stochastic autoregressive copula (SCAR) models to capture…
Consider the empirical autocovariance matrix at a given non-zero time lag based on observations from a multivariate complex Gaussian stationary time series. The spectral analysis of these autocovariance matrices can be useful in certain…
A stochastic Navier-Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure \mu_{\nu} whose covariance is given in terms of the enstrophy. Pathwise uniqueness for…
The prevalence of spatially referenced multivariate data has impelled researchers to develop a procedure for the joint modeling of multiple spatial processes. This ordinarily involves modeling marginal and cross-process dependence for any…
Vector autoregressive (VAR) models have become a staple in the analysis of multivariate time series and are formulated in the time domain as difference equations, with an implied covariance structure. In many contexts, it is desirable to…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments…
In this paper, we study the problem of how to optimally steer the state covariance of a general continuous-time linear stochastic system over a finite time interval subject to additive noise. Optimality here means reaching a target state…
In practice, observations are often contaminated by noise, making the resulting sample covariance matrix to be an information-plus-noise-type covariance matrix. Aiming to make inferences about the spectra of the underlying true covariance…
The aim of this study is to extend the scope and applicability of the level-crossing method to discrete-time stochastic processes and generalize it to enable us to study multiple discrete-time stochastic processes. In previous versions of…
We propose a novel approach to intrinsic decoherence without adding new assumptions to standard Quantum Mechanics. We generalize the Liouville equation just by requiring the dynamical semigroup property of time evolution and dropping the…
Exploiting the theory of state space models, we derive the exact expressions of the information transfer, as well as redundant and synergistic transfer, for coupled Gaussian processes observed at multiple temporal scales. All of the terms,…
Accurately estimating the statistical properties of noise is important in data analysis for space-based gravitational wave detectors. Noise in different time-delay interferometry channels correlates with each other. Many studies often…
Mode shape information play the essential role in deciding the spatial pattern of vibratory response of a structure. The uncertainty quantification of mode shape, i.e., predicting mode shape variation when the structure is subjected to…