Related papers: Test and Visualization of Covariance Properties fo…
Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as…
Surface metrology is the area of engineering concerned with the study of geometric variation in surfaces. This paper explores the potential for modern techniques from spatial statistics to act as generative models for geometric variation in…
We develop two new classes of space-time Gaussian process models by specifying covariance functions using what we call a half-spectral representation. The half-spectral representation of a covariance function, $K$, is a special case of…
Context: Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF). In order to successfully exploit such observables, a detailed…
Latent variable models are popularly used to measure latent factors (e.g., abilities and personalities) from large-scale assessment data. Beyond understanding these latent factors, the covariate effect on responses controlling for latent…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
The second-order, small-scale dependence structure of a stochastic process defined in the space-time domain is key to prediction (or kriging). While great efforts have been dedicated to developing models for cases in which the spatial…
A wide range of data that appear in scientific experiments and simulations are multivariate or multifield in nature, consisting of multiple scalar fields. Topological feature search of such data aims to reveal important properties useful to…
The classical Mat\'ern model has been a staple in spatial statistics. Novel data-rich applications in environmental and physical sciences, however, call for new, flexible vector-valued spatial and space-time models. Therefore, the extension…
Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong.…
Accurately specifying covariance structures is critical for valid inference in longitudinal and functional data analysis, particularly when data are sparsely observed. In this study, we develop a global goodness-of-fit test to assess…
This study investigates how conditional normalizing flows can be applied to remote sensing data products in climate science for spatio-temporal prediction. The method is chosen due to its desired properties such as exact likelihood…
We propose a fast bivariate smoothing approach for symmetric surfaces that has a wide range of applications. We show how it can be applied to estimate the covariance function in longitudinal data as well as multiple additive covariances in…
This paper deals with the time-varying high dimensional covariance matrix estimation. We propose two covariance matrix estimators corresponding with a time-varying approximate factor model and a time-varying approximate characteristic-based…
Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual…
Designing a covariance function that represents the underlying correlation is a crucial step in modeling complex natural systems, such as climate models. Geospatial datasets at a global scale usually suffer from non-stationarity and…
Variables contained within the global oceans can detect and reveal the effects of the warming climate as the oceans absorb huge amounts of solar energy. Hence, information regarding the joint spatial distribution of ocean variables is…
In this self-contained chapter, we revisit a fundamental problem of multivariate statistics: estimating covariance matrices from finitely many independent samples. Based on massive Multiple-Input Multiple-Output (MIMO) systems we illustrate…
Multiway data analysis aims to uncover patterns in data structured as multi-indexed arrays, with multiway covariance playing a crucial role in many applications. However, the high dimensionality of multiway covariance presents significant…
Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of…