Related papers: Mean-dependent nonstationary spatial models

Spatial-temporal forecasting plays an important role in many real-world applications, such as traffic forecasting, air pollutant forecasting, crowd-flow forecasting, and so on. State-of-the-art spatial-temporal forecasting models take…

Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome…

Spatially-explicit estimates of population density, together with appropriate estimates of uncertainty, are required in many management contexts. Density Surface Models (DSMs) are a two-stage approach for estimating spatially-varying…

To mitigate the risk posed by extreme rainfall events, we require statistical models that reliably capture extremes in continuous space with dependence. However, assuming a stationary dependence structure in such models is often erroneous,…

A rich set of frequentist model averaging methods has been developed, but their applications have largely been limited to point prediction, as measuring prediction uncertainty in general settings remains an open problem. In this paper we…

State-space models are ubiquitous in the statistical literature since they provide a flexible and interpretable framework for analyzing many time series. In most practical applications, the state-space model is specified through a…

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…

This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…

We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…

Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…

Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…

While most spatial data can be modeled with the assumption that distant points are uncorrelated, some problems require dependence at both far and short distances. We introduce a model to directly incorporate dependence in phenomena that…

We derive the properties and demonstrate the desirability of a model-based method for estimating the spatially-varying effects of covariates on the quantile function. By modeling the quantile function as a combination of I-spline basis…

In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…

We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…

Machine learning (ML) has often been applied to space weather (SW) problems in recent years. SW originates from solar perturbations and is comprised of the resulting complex variations they cause within the systems between the Sun and…

In stationary subspace analysis (SSA) one assumes that the observable p-variate time series is a linear mixture of a k-variate nonstationary time series and a (p-k)-variate stationary time series. The aim is then to estimate the unmixing…

Distinguishing long-memory behaviour from nonstationarity is challenging, as both produce slowly decaying sample autocovariances. Existing stationarity tests either fail to account for long-memory processes or exhibit poor empirical size,…

A crucial assumption to reduce computational complexity in spatial-temporal data analysis is separability, which factors the covariance structure into a purely spatial and a purely temporal component. In this paper, we develop statistical…

Geoscientific systems tend to be characterized by pronounced temporal non-stationarity, arising from seasonal and climatic variability in hydrometeorological drivers, and from natural and anthropogenic changes to land use and cover. As has…