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

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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.