Abstract
In spite of the interest in and appeal of convolution-based approaches for nonstationary spatial modeling, off-the-shelf software for model fitting does not as of yet exist. Convolution-based models are highly flexible yet notoriously difficult to fit, even with relatively small data sets. The general lack of pre-packaged options for model fitting makes it difficult to compare new methodology in nonstationary modeling with other existing methods, and as a result most new models are simply compared to stationary models. Using a convolution-based approach, we present 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 or mixture model, and second, by estimating the component parameters through a local likelihood approach. In order to make computations for a convolutionbased nonstationary spatial model readily available, this paper also presents and describes the convoSPAT package for R. The nonstationary model is fit to both a synthetic data set and a real data application involving annual precipitation to demonstrate the capabilities of the package.
Highlights
The Gaussian process is an extremely popular modeling approach in modern-day spatial and environmental statistics, due largely to the fact that the model is completely characterized by first- and second-order properties, and the second-order properties are straightforward to specify through widely used classes of valid covariance functions
We present a simplified version of the nonstationary spatial Gaussian process model introduced by Paciorek and Schervish (2006) in which the locally-varying geometric anisotropies are modeled using a “mixture component” approach, similar to the discrete mixture kernel convolution approach in Higdon (1998) but allowing the underlying correlation structure to be specified by the modeler
We have presented a nonstationary spatial Gaussian process model that is highly flexible yet amenable to computationally efficient inference, as shown through its implementation in the new convoSPAT package for R
Summary
The Gaussian process is an extremely popular modeling approach in modern-day spatial and environmental statistics, due largely to the fact that the model is completely characterized by first- and second-order properties, and the second-order properties are straightforward to specify through widely used classes of valid covariance functions. While software exists for several of these nonstationary approaches (see below), there are currently no pre-packaged options for fitting convolution-based nonstationary models To address this need, we present a simplified version of the nonstationary spatial Gaussian process model introduced by Paciorek and Schervish (2006) in which the locally-varying geometric anisotropies are modeled using a “mixture component” approach, similar to the discrete mixture kernel convolution approach in Higdon (1998) but allowing the underlying correlation structure to be specified by the modeler. There are several other (albeit non convolution-based) methods for nonstationary spatial modeling that do offer software, namely the basis function approach in the fields package (Nychka, Furrer, and Sain 2014) and the Gaussian Markov random field approach in the INLA package (Lindgren, Rue, and Lindstrom 2011; Ingebrigtsen, Lindgren, and Steinsland 2014; Fuglstad, Lindgren, Simpson, and Rue 2015; Lindgren and Rue 2015), both available for R.
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