Scalable Models, Fast Computation and Predictability for Spatio-temporal Ordinal Data

美国干旱监测机构将干旱的严重程度分为六个等级，从无干旱到异常干旱。这些测量是在美国所有地点进行的，每周更新一次。利用这些数据对未来的干旱做出准确预测，将有助于水资源管理者、农业生产者和社会其他关键部门对干旱风险进行规划。然而，由于拟合模型的计算限制，分析这类数据所需的统计方法可能不切实际。随着数据收集和存储的不断进步，像美国干旱监测这样的时空有序数据的规模和计算需求将继续增加。该项目将通过生产新的统计工具来解决这一挑战，这些工具能够以可控的计算成本分析和预测时空有序数据，从而支持美国的干旱研究和预测。主要目标是开发新的统计方法，以有效地拟合有序数据的贝叶斯分层时空模型。该模型将是可解释的，可扩展到大型数据集，并专门设计用于支持反映所有不确定性来源的概率预测。该方法将通过将随机效应的低秩投影到合适的基函数上来解决空间和时间依赖性，从而避免了与固定效应混淆的已知问题，有助于解释，并大大降低了拟合模型的计算成本。通过将数据视为面而不是点参考，避免了密集矩阵反演，从而降低了从后验采样的成本，这是现有方法的主要局限性。研究人员将开发这个模型，其目标并不总是处于其他时空研究工作的前沿——如何快速更新模型以纳入新出现的观测结果，而不必每次都重新拟合整个模型。该模型将用于研究美国的干旱，捕捉预测的不确定性如何及时传播，并记录这种不确定性何时以及如何超过做出有意义预测的能力。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The United States Drought Monitor measures the severity of drought as one of six ordered levels, ranging from no drought through exceptional drought. These measurements are taken at all US locations, and updated each week. Using these data to make accurate predictions of future drought would assist water resource managers, agriculture producers, and other crucial sectors of society plan for the risk of drought. However, statistical methods needed to analyze this type of data can be impractical due to computational limitations of fitting the model. With ongoing advances in data collection and storage, the size and computational demands of spatio-temporal ordinal data like the US Drought Monitor will continue to increase. This project will address the challenge by producing new statistical tools which enable the analysis and forecasting of spatio-temporal ordinal data at a controlled computational cost, and thereby support drought research and prediction for the US.The primary objective is to develop novel statistical methodology to efficiently fit a Bayesian hierarchical spatio-temporal model for ordinal data. The model will be interpretable, scalable to large data sets, and specifically designed to support probabilistic predictions reflecting all sources of uncertainty. The approach will address spatial and temporal dependence through low rank projections of random effects onto suitable basis functions, which avoids known problems of confounding with fixed effects, aids with interpretation, and substantially reduces the computational cost of fitting the model. By viewing the data as areal rather than point-referenced, the cost of sampling from the posterior is reduced by avoiding dense matrix inversion, a major limitation of existing methods. The investigators will develop this model with a goal not always at the forefront of other spatio-temporal research efforts --- how to update the model rapidly to incorporate newly emerging observations, without resorting to re-fitting the full model each time. The model will be deployed to study US drought, capturing how prediction uncertainty propagates forward in time, and documenting when and how this uncertainty overtakes the ability to make meaningful predictions.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.