Spatial Bayesian Neural Networks
This work addresses the need for more flexible and accurate spatial-process models in fields like environmental science or geostatistics, though it appears incremental as it builds on existing Bayesian neural network frameworks.
The authors tackled the problem of poor characterization of spatial heterogeneity in conventional models by proposing spatial Bayesian neural networks (SBNNs), which incorporate spatial embeddings and parameters to better match target spatial processes, showing improved performance over conventional BNNs in matching finite-dimensional distributions.
interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest. Here, we propose a new, flexible class of spatial-process models, which we refer to as spatial Bayesian neural networks (SBNNs). An SBNN leverages the representational capacity of a Bayesian neural network; it is tailored to a spatial setting by incorporating a spatial ``embedding layer'' into the network and, possibly, spatially-varying network parameters. An SBNN is calibrated by matching its finite-dimensional distribution at locations on a fine gridding of space to that of a target process of interest. That process could be easy to simulate from or we may have many realisations from it. We propose several variants of SBNNs, most of which are able to match the finite-dimensional distribution of the target process at the selected grid better than conventional BNNs of similar complexity. We also show that an SBNN can be used to represent a variety of spatial processes often used in practice, such as Gaussian processes, lognormal processes, and max-stable processes. We briefly discuss the tools that could be used to make inference with SBNNs, and we conclude with a discussion of their advantages and limitations.