用于离散空间随机场的有向图模型混合
Mixture of Directed Graphical Models for Discrete Spatial Random Fields
AI总结：
研究针对空间相关区域单元离散值建模的挑战，提出有向图模型混合（MDGMs）框架。其组件由有向无环图表示，计算快，非MRF近似。通过兼容性概念创建DAG集，在模拟和数据 分析中与MRF等比较，提供有效后验推断且计算更快更有原则。
摘要：
当前对与空间相关的区域单元的离散值结果进行建模的方法面临计算和理论挑战，特别是在贝叶斯环境中需要完全后验推断时。作为替代方案，我们为此数据设置提出了一种新颖的统计建模框架，即有向图模型混合（MDGMs）。混合的组件，即有向图模型，可以由有向无环图（DAG）表示，并且计算评估速度快。表示混合组件的DAG被选择为对应于区域单元假设的空间邻接/依赖结构的无向图表示，这是离散空间过程（如马尔可夫随机场（MRF））传统建模方法规范的基础。值得注意的是，MDGM不是作为MRF的近似提出的，而是作为一种替代方案，它提供有效的后验推断，同时在计算上比精确的MRF推断更快，并且比实践中常用的伪似然近似（aMRF）更有原则。我们引入兼容性概念，以展示无向图如何用作区域单元之间依赖关系的模板，以创建DAG集，作为一个集合，保留模板无向图中表示的依赖关系。最后，我们在一系列模拟以及对作为“青少年健康与发展背景研究”一部分收集的生态计量学数据的分析中，将突出的MDGM类与MRF和高维设置中使用的流行贝叶斯MRF模型近似进行了比较。
英文摘要：
Current approaches for modeling discrete-valued outcomes associated with spatially-dependent areal units incur computational and theoretical challenges, especially in the Bayesian setting when full posterior inference is desired. As an alternative, we propose a novel statistical modeling framework for this data setting, namely a mixture of directed graphical models (MDGMs). The components of the mixture, directed graphical models, can be represented by directed acyclic graphs (DAGs) and are computationally quick to evaluate. The DAGs representing the mixture components are selected to correspond to an undirected graphical representation of an assumed spatial contiguity/dependence structure of the areal units, which underlies the specification of traditional modeling approaches for discrete spatial processes such as Markov random fields (MRFs). Notably, the MDGM is not proposed as an approximation to an MRF, but rather as an alternative that provides valid posterior inference while being computationally faster than exact MRF inference and more principled than the pseudo-likelihood approximation (aMRF) commonly used in practice. We introduce the concept of compatibility to show how an undirected graph can be used as a template for the dependencies between areal units to create sets of DAGs which, as a collection, preserve the dependencies represented in the template undirected graph. Lastly, we compare highlighted classes of MDGMs to MRFs and a popular Bayesian MRF model approximation used in high-dimensional settings in a series of simulations and an analysis of ecometrics data collected as part of the Adolescent Health and Development in Context Study.
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