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Improved inference for areal unit count data using graph-based optimisation

机译：使用基于图形的优化改进了区域单位计数数据的推理

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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.
机译：与一组非重叠区域单位有关的时空计数数据在许多领域中普遍存在，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，该随机效应被分配了一个条件自回归的先前分布，这是高斯马尔可夫随机字段的特殊情况。该模型隐含的自相关结构取决于二进制邻矩阵，其中假设两个随机效果如果其区域单位共享公共边界，则会被局部自相关，并且有条件地独立于其他方案。本文提出了一种基于曲线图的优化算法，用于估计静态或时间上变化的邻域矩阵，其通过将区域单位视为图形和邻居关系的顶点来估计更好代表其空间相关结构的数据边缘。在2011年至2017年间苏格兰的新呼吸道疾病监测研究之前，模拟已经证明了与常用的边境共享规则相比的方法的改进估计性能。

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