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

时空序数数据的可扩展模型、快速计算和可预测性

• 批准号: 2151881
• 负责人: Robert Erhardt
• 金额: $ 21万
• 依托单位: Wake Forest University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2151881&HistoricalAwards=false
• 关键词: Scalable; Models; Fast; Computation; Predictability

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.

美国干旱监测机构衡量干旱的严重程度是六个有序级别之一，范围从无干旱到异常干旱。这些测量在美国所有地点进行，并每周更新。利用这些数据对未来干旱做出准确预测，将有助于水资源管理者、农业生产者和社会其他关键部门计划应对干旱风险。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是不切实际的。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顺序数据的大小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应对这一挑战，这些工具能够以受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，以有效地适应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，并专门为支持反映所有不确定性来源的概率预测而设计。该方法将通过将随机效应低阶投影到合适的基函数上来解决空间和时间相关性，这避免了已知的与固定效应相混淆的问题，有助于解释，并大大降低了模型拟合的计算成本。通过将数据视为面状数据而不是点参考数据，避免了现有方法的主要局限性--密集矩阵求逆，从而降低了从后方采样的成本。研究人员开发这一模型的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数据，而不是每次都求助于重新拟合完整的模型。该模型将用于研究美国干旱，捕捉预测不确定性如何随时间向前传播，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NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。