Related papers: Review: Nonstationary Spatial Modeling, with Empha…
It is commonplace to encounter nonstationary data, of which the underlying generating process may change over time or across domains. The nonstationarity presents both challenges and opportunities for causal discovery. In this paper we…
Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial datasets. However, the large number of observations in modern datasets makes fitting such models computationally intractable with…
Cokriging is the common method of spatial interpolation (best linear unbiased prediction) in multivariate geostatistics. While best linear prediction has been well understood in univariate spatial statistics, the literature for the…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
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.…
Gaussian Process State Space Models (GP-SSMs) are a non-parametric model class suitable to represent nonlinear dynamics. They become increasingly popular in data-driven modeling approaches, i.e. when no first-order physics-based models are…
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…
Physical processes rarely occur in isolation, rather they influence and interact with one another. Thus, there is great benefit in modeling potential dependence between both spatial locations and different processes. It is the interaction…
Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…
This paper addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical…
The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…
We propose a new estimation methodology to address the presence of covariate measurement error by exploiting the availability of spatial data. The approach uses neighboring observations as repeated measurements, after suitably controlling…
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…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
In this paper we explore a covariance spectral modelling strategy for spatial-temporal processes which involves a spectral approach for time but a covariance approach for space.It facilitates the analysis of coherence between the temporal…
Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional methods frequently struggle with the inherent complexity,…
Spatial interpolation is a crucial task in geography. As perhaps the most widely used interpolation methods, geostatistical models -- such as Ordinary Kriging (OK) -- assume spatial stationarity, which makes it difficult to capture the…
This paper studies a regression model with functional dependent and explanatory variables, both of which exhibit nonstationary dynamics. The model assumes that the nonstationary stochastic trends of the dependent variable are explained by…
When modeling geostatistical or areal data, spatial structure is commonly accommodated via a covariance function for the former and a neighborhood structure for the latter. In both cases the resulting spatial structure is a consequence of…