Spatially misaligned data can be fused by using a Bayesian melding model that assumes that underlying all observations there is a spatially continuous Gaussian random field process. This model can be used, for example, to predict air pollution levels by combining point data from monitoring stations and areal data from satellite imagery. However, if the data presents preferential sampling, that is, if the observed point locations are not independent of the underlying spatial process, the inference obtained from models that ignore such a dependence structure might not be valid. In this paper, we present a Bayesian spatial model for the fusion of point and areal data that takes into account preferential sampling. The model combines the Bayesian melding specification and a model for the stochastically dependent sampling and underlying spatial processes. Fast Bayesian inference is performed using the integrated nested Laplace approximation (INLA) and the stochastic partial differential equation (SPDE) approaches. The performance of the model is assessed using simulated data in a range of scenarios and sampling strategies that can appear in real settings. The model is also applied to predict air pollution in the USA.

翻译：空间错位数据可以通过贝叶斯融合模型进行融合，该模型假设所有观测值背后存在一个空间连续的高斯随机场过程。例如，该模型可通过结合监测站的点数据和卫星影像的面数据来预测空气污染水平。然而，如果数据存在优先采样，即观测点位置与潜在空间过程并非独立，那么忽略这种依赖结构的模型推断可能无效。本文提出了一种考虑优先采样的点数据与面数据融合的贝叶斯空间模型。该模型结合了贝叶斯融合规范以及随机依赖采样与潜在空间过程的模型。通过集成嵌套拉普拉斯近似（INLA）和随机偏微分方程（SPDE）方法实现快速贝叶斯推断。基于多种场景和实际中可能出现的采样策略下的模拟数据评估了模型性能，并将该模型应用于美国空气污染预测。