Modeling spatial data using local likelihood estimation and a Matérn to spatial autoregressive translation

  title={Modeling spatial data using local likelihood estimation and a Mat{\'e}rn to spatial autoregressive translation},
  author={Ashton Wiens and Douglas W. Nychka and William Kleiber},
  journal={arXiv: Methodology},
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 covariances that is efficient for large data sets. First, we use likelihood estimation in local, moving windows to infer spatially varying covariance parameters. These surfaces of covariance parameters can then be encoded into a global covariance model specifying the… Expand

Figures from this paper

Bayesian Nonstationary and Nonparametric Covariance Estimation for Large Spatial Data
Given replicate observations of a Gaussian spatial field, this work proposes nonstationary and nonparametric Bayesian inference on the spatial dependence and proposes a near-linear number of nonzero entries in a sparse Cholesky factor of the precision matrix. Expand
A functional-data approach to the Argo data
Spatio-temporal functional kriging methodology for mean and covariance estimation to predict temperature and salinity at a fixed location as a smooth function of depth to provide new tools for scientific problems where the dependence on depth must be considered. Expand
Nonrigid Registration Using Gaussian Processes and Local Likelihood Estimation
The nonrigid registration method is applied to a pair of massive remote sensing elevation data sets exhibiting complex geological terrain, with improved accuracy and uncertainty quantification in a cross validation study versus two rigid registration methods. Expand
Graph-based Prior and Forward Models for Inverse Problems on Manifolds with Boundaries
Graphical Matérn-type Gaussian field priors are introduced that enable flexible modeling near the boundaries, representing boundary values by superposition of harmonic functions with appropriate Dirichlet boundary conditions. Expand
The SPDE Approach to Matérn Fields: Graph Representations
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establishExpand


Estimation and Prediction of a Class of Convolution-Based Spatial Nonstationary Models for Large Spatial Data
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 doingExpand
Local likelihood estimation for covariance functions with spatially-varying parameters: the convoSPAT package for R
A new nonstationary covariance function for spatial Gaussian process models that allows for efficient computing in two ways: first, by representing the spatially-varying parameters via a discrete mixture or "mixture component" model, and second, by estimating the mixture component parameters through a local likelihood approach. Expand
Modeling and emulation of nonstationary Gaussian fields
Evidence is given to show that non-stationary covariance functions based on the Mat`ern family can be reproduced by the Lat- ticeKrig model, a flexible, multi-resolution representation of Gaussian processes that emulates spatial fields derived from numerical model simulations such as Earth system models. Expand
Kriging and automated variogram modeling within a moving window
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 estimateExpand
Nonparametric Estimation of Nonstationary Spatial Covariance Structure
Abstract Estimation of the covariance structure of spatial processes is a fundamental prerequisite for problems of spatial interpolation and the design of monitoring networks. We introduce aExpand
Exploring a New Class of Non-stationary Spatial Gaussian Random Fields with Varying Local Anisotropy
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 viaExpand
Non-stationary spatial regression for modelling monthly precipitation in Germany
Abstract It is widely accepted that spatial dependencies have to be acknowledged appropriately in data that are spatially aligned. However, most spatial models still assume that the dependenceExpand
Non-Stationary Spatial Modeling
A spatial model which allows the spatial dependence structure to vary as a function of location and is explained through a constructive "process-convolution" approach, which ensures that the re sulting covariance structure is valid. Expand
Does non-stationary spatial data always require non-stationary random fields?
It is shown that there is a real danger of over-fitting the model and that careful modelling is necessary in order to properly account for varying second-order structure, and that sometimes non-stationary Gaussian random fields are not necessary to model non- stationary spatial data. Expand
Spatio‐Temporal Smoothing and EM Estimation for Massive Remote‐Sensing Data Sets
The use of satellite measurements in climate studies promises many new scientific insights if those data can be efficiently exploited. Due to sparseness of daily data sets, there is a need to fillExpand