Related papers: Modeling and emulation of nonstationary Gaussian f…

In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…

Continuously indexed datasets with multiple variables have become ubiquitous in the geophysical, ecological, environmental and climate sciences, and pose substantial analysis challenges to scientists and statisticians. For many years,…

For multivariate spatial Gaussian process (GP) models, customary specifications of cross-covariance functions do not exploit relational inter-variable graphs to ensure process-level conditional independence among the variables. This is…

Gaussian processes are Bayesian non-parametric models used in many areas. In this work, we propose a Non-stationary Heteroscedastic Gaussian process model which can be learned with gradient-based techniques. We demonstrate the…

Gaussian random fields (GRFs) constitute an important part of spatial modelling, but can be computationally infeasible for general covariance structures. An efficient approach is to specify GRFs via stochastic partial differential equations…

We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with $t$ marginals obtained through scale…

Spatiotemporal simulation of minimum and maximum temperature is a fundamental requirement for climate impact studies and hydrological or agricultural models. Particularly over regions with variable orography, these simulations are difficult…

A simple stochastic model of solute drag by moving grain boundaries (GBs) is presented. Using a small number of parameters, the model describes solute interactions with GBs and captures nonlinear GB dynamics, solute saturation in the…

Hydroclimatic processes are characterized by heterogeneous spatiotemporal correlation structures and marginal distributions that can be continuous, mixed-type, discrete or even binary. Simulating exactly such processes can greatly improve…

Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many…

Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…

Ambient air pollution measurements from regulatory monitoring networks are routinely used to support epidemiologic studies and environmental policy decision making. However, regulatory monitors are spatially sparse and preferentially…

Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…

We propose a computational procedure for identifying convection in heat transfer dynamics. The procedure is based on a Gaussian process latent force model, consisting of a white-box component (i.e., known physics) for the conduction and…

We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…

We construct a Gaussian random field (GRF) that combines fractional smoothness with spatially varying anisotropy. The GRF is defined through a stochastic partial differential equation (SPDE), where the range, marginal variance, and…

We study estimation and prediction of Gaussian processes with covariance model belonging to the generalized Cauchy (GC) family, under fixed domain asymptotics. Gaussian processes with this kind of covariance function provide separate…

This paper is concerned with the study of the embedding circulant matrix method to simulate stationary complex-valued Gaussian sequences. The method is, in particular, shown to be well-suited to generate circularly-symmetric stationary…

Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the…