论文标题
空间贝叶斯分层建模与集成的嵌套拉普拉斯近似
Spatial Bayesian Hierarchical Modelling with Integrated Nested Laplace Approximation
论文作者
论文摘要
我们考虑在空间点模式和Areal数据的上下文中对空间依赖进行建模的潜在高斯字段，提供了两个不同的应用程序。指定了不均匀的对数高斯的Cox过程模型来描述希腊发生的地震序列，并诉诸于随机的部分微分方程。 Besag-York-Mollie模型适用于意大利北部Covid-19感染的疾病图。这些模型都属于带有潜在高斯田地的贝叶斯分层模型的类别，其后部没有以封闭形式获得。因此，使用集成的嵌套拉普拉斯近似进行推理，该近似值提供了准确且相对较快的分析近似值。
We consider latent Gaussian fields for modelling spatial dependence in the context of both spatial point patterns and areal data, providing two different applications. The inhomogeneous Log-Gaussian Cox Process model is specified to describe a seismic sequence occurred in Greece, resorting to the Stochastic Partial Differential Equations. The Besag-York-Mollie model is fitted for disease mapping of the Covid-19 infection in the North of Italy. These models both belong to the class of Bayesian hierarchical models with latent Gaussian fields whose posterior is not available in closed form. Therefore, the inference is performed with the Integrated Nested Laplace Approximation, which provides accurate and relatively fast analytical approximations to the posterior quantities of interest.
