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Abstract:
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Recent Bayesian modeling of univariate spatial data has considered mixed effect models, where a residual stationary Gaussian spatial effect is assumed. Arguably, we might prefer the flexibility of a nonstationary, non-Gaussian specification. In a nonparametric setting, this can be accommodated by a spatial Dirichlet process (Gelfand, Kottas, and MacEachern 2005). However, a limitation of this class of processes is that the latent factor driving surface selection is defined globally. In this work, we propose a class of random distributions, which enables us to model the effect of the latent factor locally and is an extension of the class of finite-dimensional Dirichlet priors (Iswharan and Zarepour 2000). In a spatial setting, it is characterized as a mixture of Gaussian random fields with spatially varying weights. We detail model fitting and inference and compare with the SDP.
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