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Motivated by numerous questions in random geometry, given a smooth manifold $M$, we approach a systematic study of the differential topology of Gaussian random fields (GRF) $X:M\to \mathbb{R}^k$, that we interpret as random variables with…
Gaussian conditional random fields (GCRF) are a well-known used structured model for continuous outputs that uses multiple unstructured predictors to form its features and at the same time exploits dependence structure among outputs, which…
Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance…
We study the Hamiltonian formulation for a parametrized scalar field in a regular bounded spatial region subject to Dirichlet, Neumann and Robin boundary conditions. We generalize the work carried out by a number of authors on parametrized…
Modeling and inferring spatial relationships and predicting missing values of environmental data are some of the main tasks of geospatial statisticians. These routine tasks are accomplished using multivariate geospatial models and the…
Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…
Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is…
The covariance matrix of measurements of Markov random fields (processes) has useful properties that allow to develop effective computational algorithms for many problems in the study of Markov fields on the basis of field observations…
The problem of estimating the slope parameter in regression between two spatial processes under confounding by an unmeasured spatial process has received widespread attention in the recent statistical literature. Yet, a fundamental question…
In this paper, we first propose a Bayesian neighborhood selection method to estimate Gaussian Graphical Models (GGMs). We show the graph selection consistency of this method in the sense that the posterior probability of the true model…
The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…
The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the…
This work is motivated by constructing a weather simulator for precipitation. Temperature and humidity are two of the most important driving forces of precipitation, and the strategy is to have a stochastic model for temperature and…
This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on applications in computational mechanics and design optimization. We leverage Mat\'ern-type…
A non-stationary spatial Gaussian random field (GRF) is described as the solution of an inhomogeneous stochastic partial differential equation (SPDE), where the covariance structure of the GRF is controlled by the coefficients in the SPDE.…
This paper develops tests for the correct specification of the conditional variance function in GARCH models when the true parameter may lie on the boundary of the parameter space. The test statistics considered are of Kolmogorov-Smirnov…
Gaussian random fields are popular models for spatially varying uncertainties, arising for instance in geotechnical engineering, hydrology or image processing. A Gaussian random field is fully characterised by its mean function and…
Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…
This work aims to extend the existing results on the Hausdorff dimension of the classical thick point sets of a Gaussian free field (GFF) to a more general class of exceptional sets. We adopt the circle or sphere averaging regularization to…
The equations of a physical constitutive model for material stress within tantalum grains were solved numerically using a tetrahedrally meshed volume. The resulting output included a scalar vonMises stress for each of the more than 94,000…