An integro‐difference equation can be represented as a hierarchical spatiotemporal dynamic model using appropriate parameterizations. The dynamics of the process defined by an integro‐difference equation depends on the choice of a bivariate kernel distribution, where more flexible shapes generally result in more flexible models. Under a Bayesian modelling framework, we consider the use of the stable family of distributions for the kernel, as they are infinitely divisible and offer a variety of tail behaviours, orientations and skewness. Many of the attributes of the bivariate stable distribution are controlled by a measure, which we model using a flexible Bernstein polynomial basis prior. The method is the first attempt to incorporate non‐Gaussian kernels in a two‐dimensional integro‐difference equation model and will be shown to improve prediction over the Gaussian kernel model for a data set of Pacific sea surface temperatures.

中文翻译：

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使用具有双变量稳定核的整数差分方程的时空建模

可以使用适当的参数化将积分差方程表示为分层时空动力学模型。积分差方程定义的过程动力学取决于双变量核分布的选择，在这种分布中，形状更灵活通常会导致模型更灵活。在贝叶斯建模框架下，我们考虑对内核使用稳定的分布族，因为它们是无限可分割的，并提供各种尾部行为，方向和偏度。双变量稳定分布的许多属性都由一种度量控制，我们先使用了灵活的伯恩斯坦多项式基础对其进行了建模。