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 2 to 4, depending on the sizes of the data sets.

翻译：本文研究Knorr-Held IV型时空模型。此类模型通常采用本征马尔可夫随机场，并施加约束条件以实现可识别性。INLA是处理此类模型的有效推断工具，通过克里金条件化方法处理约束。当空间和/或时间点数量较大时，由于涉及的约束数量众多，拟合此类模型的计算成本会显著增加。我们提出一种新方法HyMiK，将约束分为两组：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。该新方法易于在现有INLA实现基础上应用。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肺炎确诊病例真实数据集上运行模型。在所有案例中，新方法与传统方法的结果高度一致，同时计算速度显著提升——根据数据集规模不同，加速比可达2至4倍。