贝叶斯离散分位数回归模型：理论，方法及应用

项目名称： 贝叶斯离散分位数回归模型：理论，方法及应用

项目编号： No.11261048

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 虞克明

作者单位： 石河子大学

项目金额： 51万元

中文摘要： 实践中许多随机变量取离散值。以这些变量为因变量的重要回归分析包括Logistic回归，有序回归等。此外,隐马尔可夫模型（HMM）的隐变量的状态空间是离散的。分位数回归或依据因变量分位数的回归已经成为常用的分析工具。贝叶斯统计和以Lasso为基础的变量选择方法是当今的热门课题。近年来贝叶斯推断因变量为连续的分位数回归有很多应用和文章发表。但很少有研究离散分位数回归和HMM分位数回归。用贝叶斯方法推断这些分位数回归几乎是空白，但是它极其重要和具有广阔的应用前景。我们将利用近年在发展贝叶斯推断连续依赖性变量分位数回归的经验优势来发展贝叶斯推断离散分位数和HMM分位数回归，研究后验估计的一致性和渐近正态性,先验选择，参数贝叶斯和非参数贝叶斯，变量选择。研发方法有离散模型连续化，MCMC算法和正倒向隐藏状态更新算法等。应用包括新疆人口数据分析，少数民族就业困难分析,城市机动车导致空气污染状况分析等。

中文关键词： 回归分析；分位数回归；极值回归；离散型数据分析；贝叶斯推断

英文摘要： Many random variables in practice take discrete values or count outcomes. Regression analysis based on this type of dependent variables include Logistic regression, ordinal regression, and multinomial regression and Poisson regression and so on. Also, the state space of the hidden variables in the famous Hidden Markov models (HMMs) is discrete. Quantile regression for continuous dependent variable is a standard regression analysis tool and is becoming increasing popular nowadays. Bayesian statistics and Lasso-based variable selection have been hot topics and popular in numerous fields in which statistics is applied in last two decades. Bayesian inference quantile regression has attracted a lot of attention in literature recent ten years. However, there is little research on discrete quantile regression and quantile HMM regression and there is even no research on Bayesian inference these discrete quantile regressing models and HMM quantile regression, but highly expected. Based on our experience of developing Bayesain inference continuous-type of quantile regression models, it's highly timing for us to explore Bayesian inference these discrete quantile regression models and variable selection. In the project, we will make a comprehensive study and deep investigation of Bayesian inference discrete quantile regr

英文关键词： regression analysis；quantile regrerssion；extreme value distribution；discrte data analysis；Bayesain inference