Statistical models for spatial processes play a central role in statistical
analyses of spatial data. Yet, it is the simple, 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 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 a single SBNN can be used to represent a
variety of spatial processes often used in practice, such as Gaussian processes
and lognormal 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.

我们提出了一种新的灵活类的空间过程模型，称为空间贝叶斯神经网络（SBNNs），它通过将空间嵌入层和可能的空间变化的网络参数结合到贝叶斯神经网络中，能更好地匹配目标过程的有限维分布。