Related papers: Statistical Inference for Bures-Wasserstein Flows
Turbulent flows have historically presented formidable challenges to predictive computational modeling. Traditional numerical simulations often require vast computational resources, making them infeasible for numerous engineering…
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…
Starting from stationary bifurcations in Couette-Dean flow, we compute nontrivial stationary solutions in inertialess viscoelastic circular Couette flow. These solutions are strongly localized vortex pairs, exist at arbitrarily large…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
Although there is a rich literature on methods for allowing the variance in a univariate regression model to vary with predictors, time and other factors, relatively little has been done in the multivariate case. Our focus is on developing…
We develop and analyze a random field model for the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities provided by RANS simulations that is accessible to both a rigorous analytical validation…
Inverse statistical physics aims at inferring models compatible with a set of empirical averages estimated from a high-dimensional dataset of independently distributed equilibrium configurations of a given system. However, in several…
Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
Regression analysis with probability measures as input predictors and output response has recently drawn great attention. However, it is challenging to handle multiple input probability measures due to the non-flat Riemannian geometry of…
We study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
In this paper, we present a novel and effective inference approach to conduct both finite- and large-sample inference for high-dimensional linear regression models. This approach is developed under the so-called repro samples framework, in…
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…
In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…
The analysis of multivariate functional curves has the potential to yield important scientific discoveries in domains such as healthcare, medicine, economics and social sciences. However, it is common for real-world settings to present…
Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…
We propose a framework to understand input-output amplification properties of non- linear partial differential equation (PDE) models of wall-bounded shear flows, which are spatially invariant in one coordinate (e.g., streamwise-constant…
In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…