论文标题
通过有限混合物的贝叶斯混合物的计数价值数据的空间聚类回归
Spatial Clustering Regression of Count Value Data via Bayesian Mixture of Finite Mixtures
论文作者
论文摘要
在环境科学，地球科学和公共卫生等领域调查响应变量与协变量之间的关系是一项重要的努力。基于有限混合模型的贝叶斯混合物，我们为计数值数据提供了一种新型的空间簇系数回归模型。所提出的方法检测泊松回归系数的空间均匀性。 Markov随机场约束有限混合物的混合物提供了带有地理邻域信息的回归系数簇数量的正则化估计器。作为副产品，当马尔可夫随机场可交换时，我们还提供了我们提出的方法的理论特性。通过使用多元对数伽马分布作为基础分布，开发了有效的马尔可夫链蒙特卡洛算法。进行了模拟研究以检查所提出方法的经验性能。此外，我们分析了佐治亚州的过早死亡数据，以说明我们方法的有效性。补充材料在\ url {https://github.com/pengzhaostat/mlg_mfm}上提供。
Investigating relationships between response variables and covariates in areas such as environmental science, geoscience, and public health is an important endeavor. Based on a Bayesian mixture of finite mixtures model, we present a novel spatially clustered coefficients regression model for count value data. The proposed method detects the spatial homogeneity of the Poisson regression coefficients. A Markov random field constrained mixture of finite mixtures prior provides a regularized estimator of the number of clusters of regression coefficients with geographical neighborhood information. As a by-product, we also provide the theoretical properties of our proposed method when the Markov random field is exchangeable. An efficient Markov chain Monte Carlo algorithm is developed by using the multivariate log gamma distribution as a base distribution. Simulation studies are carried out to examine the empirical performance of the proposed method. Additionally, we analyze Georgia's premature death data as an illustration of the effectiveness of our approach. The supplementary materials are provided on GitHub at \url{https://github.com/pengzhaostat/MLG_MFM}.
