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The estimation of multivariate GARCH time series models is a difficult task mainly due to the significant overparameterization exhibited by the problem and usually referred to as the "curse of dimensionality". For example, in the case of…

We investigate the conditional distributions of two Banach space valued, jointly Gaussian random variables. In particular, we show that these conditional distributions are again Gaussian and that their means and covariances can be…

Spatial generalized linear mixed models (SGLMMs) are popular and flexible models for non-Gaussian spatial data. They are useful for spatial interpolations as well as for fitting regression models that account for spatial dependence, and are…

Air pollution remains a critical environmental and public health challenge, demanding high-resolution spatial data to better understand its spatial distribution and impacts. This study addresses the challenges of conducting multivariate…

We introduce a novel approach to inference on parameters that take values in a Riemannian manifold embedded in a Euclidean space. Parameter spaces of this form are ubiquitous across many fields, including chemistry, physics, computer…

Hyper-spectral satellite imagery is now widely being used for accurate disaster prediction and terrain feature classification. However, in such classification tasks, most of the present approaches use only the spectral information contained…

We consider the problem of inferring constraints on a high-dimensional parameter space with a computationally expensive likelihood function. We propose a machine learning algorithm that maps out the Frequentist confidence limit on parameter…

Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…

We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…

We develop goodness-of-fit tests for max-stable random fields, which are used to model heavy-tailed spatial data. The test statistics are constructed based on the Fourier transforms of the indicators of extreme values in the heavy-tailed…

A common way to learn and analyze statistical models is to consider operations in the model parameter space. But what happens if we optimize in the parameter space and there is no one-to-one mapping between the parameter space and the…

We consider the problem of estimating a high-dimensional covariance matrix from a small number of observations when covariates on pairs of variables are available and the variables can have spatial structure. This is motivated by the…

This article presents a neural network approach for estimating the covariance function of spatial Gaussian random fields defined in a portion of the Euclidean plane. Our proposal builds upon recent contributions, expanding from the purely…

Models that capture the spatial and temporal dynamics are applicable in many science fields. Non-separable spatio-temporal models were introduced in the literature to capture these features. However, these models are generally complicated…

A frame is a system of vectors $S$ in Hilbert space $\mathscr{H}$ with properties which allow one to write algorithms for the two operations, analysis and synthesis, relative to $S$, for all vectors in $\mathscr{H}$; expressed in…

Understanding centennial scale climate variability requires data sets that are accurate, long, continuous and of broad spatial coverage. Since instrumental measurements are generally only available after 1850, temperature fields must be…

Markov chain Monte Carlo (MCMC) methods are simulated by local exploration of complex statistical distributions, and while bypassing the cumbersome requirement of a specific analytical expression for the target, this stochastic exploration…

For spatial and network data, we consider models formed from a Markov random field (MRF) structure and the specification of a conditional distribution for each observation. Fast simulation from such MRF models is often an important…

It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…

The communications and interrelations between different locations on the Earth's surface have far-reaching implications for both social and natural systems. Effective spatial analytics ideally require a spatial representation, where…