# Modeling and emulation of nonstationary Gaussian fields

@article{Nychka2018ModelingAE, title={Modeling and emulation of nonstationary Gaussian fields}, author={Douglas W. Nychka and Dorit M. Hammerling and Mitchell Krock and Ashton Wiens}, journal={Spatial Statistics}, year={2018} }

Geophysical and other natural processes often exhibit non-stationary covariances and this feature is important to take into account for statistical models that attempt to emulate the physical process. A convolution-based model is used to represent non-stationary Gaussian processes that allows for variation in the correlation range and vari- ance of the process across space. Application of this model has two steps: windowed estimates of the covariance function under the as- sumption of local… Expand

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#### References

SHOWING 1-10 OF 50 REFERENCES

A Generalized Convolution Model and Estimation for Non-stationary Random Functions

- Mathematics
- 2014

Standard geostatistical models assume second order stationarity of the underlying Random Function. In some instances, there is little reason to expect the spatial dependence structure to be… Expand

Estimation and Prediction of a Class of Convolution-Based Spatial Nonstationary Models for Large Spatial Data

- Mathematics
- 2010

In this article we address two important issues common to the analysis of large spatial datasets. One is the modeling of nonstationarity, and the other is the computational challenges in doing… Expand

Spatial Modelling Using a New Class of Nonstationary Covariance Functions.

- Computer Science, Medicine
- Environmetrics
- 2006

A new class of nonstationary covariance functions for spatial modelling, which includes a non stationary version of the Matérn stationary covariance, in which the differentiability of the spatial surface is controlled by a parameter, freeing one from fixing the differentiable in advance. Expand

Exploring a New Class of Non-stationary Spatial Gaussian Random Fields with Varying Local Anisotropy

- Mathematics
- 2013

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… Expand

Spectral methods for nonstationary spatial processes

- Mathematics
- 2002

SUMMARY We propose a nonstationary periodogram and various parametric approaches for estimating the spectral density of a nonstationary spatial process. We also study the asymptotic properties of the… Expand

A Multiresolution Gaussian Process Model for the Analysis of Large Spatial Datasets

- Mathematics
- 2015

We develop a multiresolution model to predict two-dimensional spatial fields based on irregularly spaced observations. The radial basis functions at each level of resolution are constructed using a… Expand

An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach

- Mathematics
- 2011

Continuously indexed Gaussian fields (GFs) are the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive… Expand

A process-convolution approach to modelling temperatures in the North Atlantic Ocean

- Computer Science
- Environmental and Ecological Statistics
- 2004

A Bayesian approach is taken here which relies on Markov chain Monte Carlo for exploring the posterior distribution of the convolution kernel in a process-convolution approach for space-time modelling. Expand

Kriging and automated variogram modeling within a moving window

- Mathematics
- 1990

Abstract A spatial estimation procedure based on ordinary kriging is described and evaluated which consists of using only sampling sites contained within a moving window centered at the estimate… Expand

Local likelihood estimation for nonstationary random fields

- Computer Science, Mathematics
- J. Multivar. Anal.
- 2011

A weighted local likelihood estimate for the parameters that govern the local spatial dependency of a locally stationary random field is developed that smoothly downweights the influence of faraway observations, works for irregular sampling locations, and when designed appropriately, can trade bias and variance for reducing estimation error. Expand