Accurate predictions of pollutant concentrations at new locations are often of interest in air pollution studies on fine particulate matters (PM2.5), in which data is usually not measured at all study locations. PM2.5 is also a mixture of many different chemical components. Principal component analysis (PCA) can be incorporated to obtain lower-dimensional representative scores of such multi-pollutant data. Spatial prediction can then be used to estimate these scores at new locations. Recently developed predictive PCA modifies the traditional PCA algorithm to obtain scores with spatial structures that can be well predicted at unmeasured locations. However, these approaches require complete data, whereas multi-pollutant data tends to have complex missing patterns in practice. We propose probabilistic versions of predictive PCA which allow for flexible model-based imputation that can account for spatial information and subsequently improve the overall predictive performance.

中文翻译：

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缺失观测的空间错位和高维空气污染数据的概率预测主成分分析

在细颗粒物 (PM2.5) 的空气污染研究中，新地点污染物浓度的准确预测通常很重要，其中通常不会在所有研究地点测量数据。PM2.5 也是许多不同化学成分的混合物。可以结合主成分分析 (PCA) 来获得此类多污染物数据的低维代表性分数。然后可以使用空间预测来估计新位置的这些分数。最近开发的预测 PCA 修改了传统的 PCA 算法，以获得可以在未测量位置很好地预测的空间结构的分数。然而，这些方法需要完整的数据，而多污染物数据在实践中往往具有复杂的缺失模式。