Often, in environmental data collection, data arise from two sources: numerical models and monitoring networks. The first source provides predictions at the level of grid cells, while the second source gives measurements at points. The first is characterized by full spatial coverage of the region of interest, high temporal resolution, no missing data but consequential calibration concerns. The second tends to be sparsely collected in space with coarser temporal resolution, often with missing data but, where recorded, provides, essentially, the true value. Accommodating the spatial misalignment between the two types of data is of fundamental importance for both improved predictions of exposure as well as for evaluation and calibration of the numerical model. In this article we propose a simple, fully model-based strategy to downscale the output from numerical models to point level. The static spatial model, specified within a Bayesian framework, regresses the observed data on the numerical model output using spatially-varying coefficients which are specified through a correlated spatial Gaussian process.As an example, we apply our method to ozone concentration data for the eastern U.S. and compare it to Bayesian melding (Fuentes and Raftery 2005) and ordinary kriging (Cressie 1993; Chilès and Delfiner 1999). Our results show that our method outperforms Bayesian melding in terms of computing speed and it is superior to both Bayesian melding and ordinary kriging in terms of predictive performance; predictions obtained with our method are better calibrated and predictive intervals have empirical coverage closer to the nominal values. Moreover, our model can be easily extended to accommodate for the temporal dimension. In this regard, we consider several spatio-temporal versions of the static model. We compare them using out-of-sample predictions of ozone concentration for the eastern U.S. for the period May 1-October 15, 2001. For the best choice, we present a summary of the analysis. Supplemental material, including color versions of Figures 4, 5, 6, 7, and 8, and MCMC diagnostic plots, are available online.

中文翻译：

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用于数值模型输出的时空缩减器。

通常，在环境数据收集中，数据来自两个来源：数值模型和监测网络。第一个源提供网格单元级别的预测，而第二个源提供点的测量。第一个特点是感兴趣区域的全空间覆盖、高时间分辨率、没有丢失数据但有相应的校准问题。第二种往往是在空间中以较粗糙的时间分辨率稀疏地收集，通常缺少数据，但在记录的地方，本质上提供了真实值。适应两种类型数据之间的空间错位对于改进曝光预测以及数值模型的评估和校准都至关重要。在这篇文章中，我们提出了一个简单的，完全基于模型的策略将输出从数值模型缩小到点级别。在贝叶斯框架内指定的静态空间模型使用通过相关空间高斯过程指定的空间变化系数对数值模型输出的观测数据进行回归。例如，我们将我们的方法应用于东部的臭氧浓度数据US 并将其与贝叶斯融合（Fuentes 和 Raftery 2005）和普通克里金法（Cressie 1993；Chilès 和 Delfiner 1999）进行比较。我们的结果表明，我们的方法在计算速度方面优于贝叶斯融合，并且在预测性能方面优于贝叶斯融合和普通克里金法；使用我们的方法获得的预测得到更好的校准，预测区间的经验覆盖更接近标称值。此外，我们的模型可以轻松扩展以适应时间维度。在这方面，我们考虑了静态模型的几个时空版本。我们使用 2001 年 5 月 1 日至 10 月 15 日期间美国东部臭氧浓度的样本外预测对它们进行了比较。对于最佳选择，我们提供了分析摘要。补充材料，包括图 4、5、6、7 和 8 的彩色版本以及 MCMC 诊断图，可在线获取。