We address in this paper a new approach for fitting spatiotemporal models with application in disease mapping using the interaction types 1,2,3, and 4. When we account for the spatiotemporal interactions in disease-mapping models, inference becomes more useful in revealing unknown patterns in the data. However, when the number of locations and/or the number of time points is large, the inference gets computationally challenging due to the high number of required constraints necessary for inference, and this holds for various inference architectures including Markov chain Monte Carlo (MCMC) and Integrated Nested Laplace Approximations (INLA). We re-formulate INLA approach based on dense matrices to fit the intrinsic spatiotemporal models with the four interaction types and account for the sum-to-zero constraints, and discuss how the new approach can be implemented in a high-performance computing framework. The computing time using the new approach does not depend on the number of constraints and can reach a 40-fold faster speed compared to INLA in realistic scenarios. This approach is verified by a simulation study and a real data application, and it is implemented in the R package INLAPLUS and the Python header function: inla1234().

中文翻译：

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交互类型 1、2、3 和 4 的近似贝叶斯推断及其在疾病映射中的应用

我们在本文中讨论了一种使用交互类型 1、2、3 和 4 来拟合时空模型与疾病映射应用的新方法。当我们考虑疾病映射模型中的时空交互时，推理在揭示未知数方面变得更加有用数据中的模式。然而，当位置的数量和/或时间点的数量很大时，由于推理所需的大量约束条件，推理在计算上变得具有挑战性，这适用于包括马尔可夫链蒙特卡罗 (MCMC) 在内的各种推理架构和集成嵌套拉普拉斯近似 (INLA)。我们基于密集矩阵重新制定 INLA 方法，以拟合具有四种交互类型的内在时空模型，并考虑总和为零的约束，并讨论如何在高性能计算框架中实施新方法。使用新方法的计算时间不依赖于约束的数量，在实际场景中可以达到比 INLA 快 40 倍的速度。该方法通过仿真研究和真实数据应用验证，在R包INLAPLUS和Python头函数inla1234()中实现。