High-dimensional and spatial data analysis by Bayesian inference

项目摘要：鉴于(1)均值回归(普通最小二乘回归)等标准回归模型在经济学、遗传学、生态学和环境等领域得到了广泛的应用，并引起了大量文献的关注，(2)贝叶斯推理是近几十年来流行的方法之一，但针对这些领域的问题，对超出均值的回归模型的贝叶斯推断的研究相对较少。本项目的目的是：开发超出均值的贝叶斯自回归新方法，提出用于高维数据分析的新的单指数模型，探索超出均值的有效空间回归，比较上述回归模型的贝叶斯推断的不同算法。

Project summary: Whereas (1) standard regression models such as mean regression (ordinary least-squares regression) have been widely applied in many fields such as economics, genetics, ecology and environment and attracted huge amount of attention in literature, and (2) Bayesian inference is one of popular methods recent decades, there is relatively little work on Bayesian inference of regression models beyond mean for problems in those fields.This project aims to: develop novel methods of Bayesian autoregressive beyond mean, propose new single-index models for high-dimensional data analysis, explore effective spatial regression beyond mean, compare different algorithms for Bayesian inference of regression models above.