In this paper we study the type IV Knorr Held space time models. Such models typically apply intrinsic Markov random fields and constraints are imposed for identifiability. INLA is an efficient inference tool for such models where constraints are dealt with through a conditioning by kriging approach. When the number of spatial and/or temporal time points become large, it becomes computationally expensive to fit such models, partly due to the number of constraints involved. We propose a new approach, HyMiK, dividing constraints into two separate sets where one part is treated through a mixed effect approach while the other one is approached by the standard conditioning by kriging method, resulting in a more efficient procedure for dealing with constraints. The new approach is easy to apply based on existing implementations of INLA. We run the model on simulated data, on a real data set containing dengue fever cases in Brazil and another real data set of confirmed positive test cases of Covid-19 in the counties of Norway. For all cases we get very similar results when comparing the new approach with the tradition one while at the same time obtaining a significant increase in computational speed, varying on a factor from 3 to 23, depending on the sizes of the data sets.

翻译：本文研究了Knorr-Held IV型时空模型。该类模型通常采用内在马尔可夫随机场，并通过施加约束条件实现模型可识别性。INLA是该类模型的有效推断工具，通过克里金条件化方法处理约束条件。当空间和/或时间观测点数量增大时，受约束数量影响，模型拟合的计算成本显著增加。我们提出了一种新方法HyMiK，将约束条件划分为两组：一组通过混合效应方法处理，另一组采用标准克里金条件化方法，从而形成更高效的约束处理流程。该方法易于基于现有INLA实现进行部署。我们在模拟数据、巴西登革热病例真实数据集以及挪威各县新冠确诊病例真实数据集上运行模型。所有实验结果表明，与传统方法相比，新方法在获得非常相似结果的同时，计算速度获得了显著提升——根据数据集规模的不同，加速比达到3至23倍。