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In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
Nonstationarity is a major challenge in analyzing spatial data. For example, daily precipitation measurements may have increased variability and decreased spatial smoothness in areas with high mean rainfall. Common nonstationary covariance…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…
Non-equilibrium systems have long-ranged spatial correlations even far away from critical points. This implies that the likelihoods of spatial steady state profiles of physical observables are nonlocal functionals. In this letter, it is…
Standard geostatistical models assume stationarity and rely on a variogram model to account for the spatial dependence in the observed data. In some instances, this assumption that the spatial dependence structure is constant throughout the…
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…
Multivariate spatial-statistical models are often used when modeling environmental and socio-demographic processes. The most commonly used models for multivariate spatial covariances assume both stationarity and symmetry for the…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
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…
High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…
Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the…
Multivariate spatial modeling is key to understanding the behavior of materials downstream in a mining operation. The ore recovery depends on the mineralogical composition, which needs to be properly captured by the model to allow for good…
A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stationarity in practice? We study the challenges involved in…
With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial…
Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…
We construct flexible spatio-temporal models through stochastic partial differential equations (SPDEs) where both diffusion and advection can be spatially varying. Computations are done through a Gaussian Markov random field approximation…
A stochastic model for a mobile network is studied. Users enter the network, and then perform independent Markovian routes between nodes where they receive service according to the Processor-Sharing policy. Once their service requirement is…