In order to learn the complex features of large spatio-temporal data, models with a large number of parameters are often required. However, inference is often infeasible due to the computational and memory costs of maximum likelihood estimation (MLE). The class of marginally parameterized (MP) models is introduced, where estimation can be performed efficiently with a sequence of marginal likelihood functions with stepwise maximum likelihood estimation (SMLE). The conditions under which the stepwise estimators are consistent are provided, and it is shown that this class of models includes the diagonal vector autoregressive moving average model. It is demonstrated that the parameters of this model can be obtained at least three orders of magnitude faster with SMLE compared to MLE, with only a small loss in statistical efficiency. A MP model is applied to a spatio-temporal global climate data set consisting of over five million data points, and it is demonstrated how estimation can be achieved in less than one hour on a laptop with a dual core at 2.9 Ghz.

中文翻译：

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边际参数化时空模型和逐步最大似然估计

为了学习大型时空数据的复杂特征，通常需要具有大量参数的模型。然而，由于最大似然估计 (MLE) 的计算和内存成本，推理通常是不可行的。引入了边际参数化 (MP) 模型类，其中可以使用具有逐步最大似然估计 (SMLE) 的边际似然函数序列有效地执行估计。给出了逐步估计量一致的条件，表明该类模型包括对角向量自回归移动平均模型。结果表明，与 MLE 相比，使用 SMLE 可以获得该模型的参数至少快三个数量级，并且统计效率损失很小。