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Spatial functional data arise in many settings, such as particulate matter curves observed at monitoring stations and age population curves at each areal unit. Most existing functional regression models have limited applicability because…
For time series with long-range temporal dependence, inference for covariance and precision matrices is non-trivial. We propose a Berry-Esseen type Gaussian approximation result that gives a finite-sample bound for the Kolmogorov distance…
The data torrent unleashed by current and upcoming astronomical surveys demands scalable analysis methods. Many machine learning approaches scale well, but separating the instrument measurement from the physical effects of interest, dealing…
We discuss efficient Bayesian estimation of dynamic covariance matrices in multivariate time series through a factor stochastic volatility model. In particular, we propose two interweaving strategies (Yu and Meng, Journal of Computational…
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open…
As a computational alternative to Markov chain Monte Carlo approaches, variational inference (VI) is becoming more and more popular for approximating intractable posterior distributions in large-scale Bayesian models due to its comparable…
In this paper, a regression algorithm based on Green's function theory is proposed and implemented. We first survey Green's function for the Dirichlet boundary value problem of 2nd order linear ordinary differential equation, which is a…
Profile likelihoods are rarely used in geostatistical models due to the computational burden imposed by repeated decompositions of large variance matrices. Accounting for uncertainty in covariance parameters can be highly consequential in…
Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be stationary over the whole region of interest. In…
Due to their flexibility, frames of Hilbert spaces are attractive alternatives to bases in approximation schemes for problems where identifying a basis is not straightforward or even feasible. Computing a best approximation using frames,…
We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and…
Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…
Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
When a large body of data from diverse experiments is analyzed using a theoretical model with many parameters, the standard error matrix method and the general tools for evaluating errors may become inadequate. We present an iterative…
This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a…
Covariance matrices are important tools for obtaining reliable parameter constraints. Advancements in cosmological surveys lead to larger data vectors and, consequently, increasingly complex covariance matrices, whose number of elements…
Datasets in the fields of climate and environment are often very large and irregularly spaced. To model such datasets, the widely used Gaussian process models in spatial statis- tics face tremendous challenges due to the prohibitive…
We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…
Covariate shift in regression problems and the associated distribution mismatch between training and test data is a commonly encountered phenomenon in machine learning. In this paper, we extend recent results on nonparametric convergence…