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：空间错位数据可通过贝叶斯融合模型实现整合，该模型假设所有观测值背后存在一个空间连续的随机高斯场过程。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，若数据存在偏好采样——即观测点位置与潜在空间过程不独立——则忽略此类依赖结构的模型推断结果可能失效。本文提出一种考虑偏好采样的贝叶斯空间模型，用于融合点数据和面数据。该模型结合了贝叶斯融合规范与随机依赖采样及潜在空间过程的建模方案。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。基于模拟数据在多种现实场景和采样策略下评估模型性能，并将该模型应用于美国空气污染预测。