论文标题
使用马尔可夫随机场约束产品分区模型在空间面板数据中识别潜在组
Identifying latent groups in spatial panel data using a Markov random field constrained product partition model
论文作者
论文摘要
了解空间位置的异质性是一个重要的问题，在经济学和环境科学等许多应用中已广泛研究。在本文中，我们关注用于空间面板数据分析的回归模型，其中随着时间的流逝在各个空间位置收集重复测量。我们提出了一类新型的非参数先验，将马尔可夫随机场（MRF）与产品分区模型（PPM）结合在一起，并表明，由MRF-PPM称为的先验能够在空间位置之间识别潜在的群体结构，同时有效利用空间依赖信息。我们为拟议的先验得出了封闭形式的条件分布，并引入了一种计算有效贝叶斯推论的边际可能性的新方法。我们进一步研究了拟议的MRF-PPM之前的理论特性，并显示后验分布的聚类一致性结果。我们通过广泛的仿真研究和对美国降水数据和加利福尼亚州中位家庭收入数据研究的广泛模拟研究和应用来证明我们方法的出色经验性能。
Understanding the heterogeneity over spatial locations is an important problem that has been widely studied in many applications such as economics and environmental science. In this paper, we focus on regression models for spatial panel data analysis, where repeated measurements are collected over time at various spatial locations. We propose a novel class of nonparametric priors that combines Markov random field (MRF) with the product partition model (PPM), and show that the resulting prior, called by MRF-PPM, is capable of identifying the latent group structure among the spatial locations while efficiently utilizing the spatial dependence information. We derive a closed-form conditional distribution for the proposed prior and introduce a new way to compute the marginal likelihood that renders efficient Bayesian inference. We further study the theoretical properties of the proposed MRF-PPM prior and show a clustering consistency result for the posterior distribution. We demonstrate the excellent empirical performance of our method via extensive simulation studies and applications to a US precipitation data and a California median household income data study.
