Bayesian Inference for Multivariate Hierarchical Regression Models

本项目将发展贝叶斯方法来分析多元回归模型。每个测量值的分布可以是离散的，也可以是连续的，测量值之间的依赖关系通过高斯联结的相关矩阵得到。通过识别相关矩阵中的零元素或其逆元素以及对回归参数进行变量选择，实现了模型的简约性。研究结果将应用于解决金融、健康管理和营销方面的问题。在所有这些领域中，经常对每个人或一个时间段进行多次观测，模型需要纳入依赖性和不确定性的措施。

This project will develop Bayesian methodology for analysing multivariate regression models. The distribution of each measurement can be discrete or continuous, with the dependence between measurements obtained through the correlation matrix of a Gaussian copula. Model parsimony is obtained by identifying zero elements in the correlation matrix or its inverse and by variable selection on the regression parameters. The results will be applied to solve problems in finance, health management and marketing. In all these fields multiple observations are often taken per individual or time period and the models need to incorporate measures of dependence and uncertainty.