Spatio-temporal count data relating to a set of non-overlapping areal units are prevalent in many fields, including epidemiology and social science. The spatial autocorrelation inherent in these data is typically modelled by a set of random effects that are assigned a conditional autoregressive prior distribution, which is a special case of a Gaussian Markov random field. The autocorrelation structure implied by this model depends on a binary neighbourhood matrix, where two random effects are assumed to be partially autocorrelated if their areal units share a common border, and are conditionally independent otherwise. This paper proposes a novel graph-based optimisation algorithm for estimating either a static or a temporally varying neighbourhood matrix for the data that better represents its spatial correlation structure, by viewing the areal units as the vertices of a graph and the neighbour relations as the set of edges. The improved estimation performance of our methodology compared to the commonly used border sharing rule is evidenced by simulation, before the method is applied to a new respiratory disease surveillance study in Scotland between 2011 and 2017.

与一组非重叠区域单位相关的时空计数数据在许多领域都很普遍，包括流行病学和社会科学。这些数据中固有的空间自相关通常由一组随机效应建模，这些随机效应被分配了条件自回归先验分布，这是高斯马尔可夫随机场的一个特例。该模型隐含的自相关结构取决于二元邻域矩阵，其中如果两个随机效应的面积单位共享一个公共边界，则假定它们是部分自相关的，否则条件独立。本文提出了一种新的基于图的优化算法，用于估计数据的静态或随时间变化的邻域矩阵，以更好地表示其空间相关结构，通过将面积单位视为图的顶点，将相邻关系视为边的集合。在将该方法应用于 2011 年至 2017 年间在苏格兰进行的一项新的呼吸系统疾病监测研究之前，我们的方法与常用的边界共享规则相比，其估计性能得到了改进。