基于狄利克雷过程的潜变量模型贝叶斯半参数分析

项目名称： 基于狄利克雷过程的潜变量模型贝叶斯半参数分析

项目编号： No.11471161

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 夏业茂

作者单位： 南京林业大学

项目金额： 70万元

中文摘要： 潜变量模型是一种用来体现潜变量相互关系和构建潜变量与观测变量关联的重要统计方法。通常的参数贝叶斯推断在分布偏离假定形式或数据含有异常值时有严重偏差。特别地，对于多级、多组别、嵌套式潜变量模型，单一参数模型很难界定不同水平分布间的关联性。本研究着力于潜变量模型贝叶斯半参数分析。相较于目前该领域的研究进展，本研究创新之处为：（一）基于多狄利克雷过程对多级、多组别和嵌套潜变量模型集中展开半参数贝叶斯分析；（二）系统地展开时空潜变量模型的贝叶斯半参数分析；（三）对带有定性数据的潜变量模型进行贝叶斯半参数分析；（四）集中考虑基于数据似然的贝叶斯半参数模型选择。为了贝叶斯分析，我们将基于诸如马尔可夫链蒙特卡罗算法和数据扩充技术等仿真方法来进行后验推断。模型拟合将通过模型的选择/比较、统计诊断和相关的假设检验程序来达到。更重要地，我们将在不同的应用环境中展示方法的有效性。

中文关键词： 潜变量模型；狄利克雷过程；贝叶斯半参数分析

英文摘要： Latent variable model (LVM) is an important statistical method for identifying the interrelationships among latent variables and building the relationships between latent constructs and observed variables. The statistical inferences based on the common parametric Bayesian approaches often suffer from serious biases when the underlying distrbutions deviate from the assumed forms or when data contain extrem values. In particular, a single parametric model is difficult to identify the dependence among the distributions at the different levels. In this study, we will develope Bayesian semiparametric analysis procedure for analyzing LVMs. Comparing to the existing developments of Bayesian semiparametric analysis for LVMs, the novelty of this study lies in the following four aspects: (i) we will intensively carry out semiparametric Bayesian analysis for multilevel, multigroup and nested LVMs based on the multi-Dirichlet processes; (ii) we will systematically develope Bayesian semiparametric analysis procedure for temporal-spatial LVMs; (iii) we will develope a Bayesian semiparametric analysis for LVMs with qualitative data; and (iv) we will focus on the Bayseian semiparametric model selection in terms of the likelihood of data. For Bayesian analysis, posterior inferences will be carried out through simulation-based methods such as Markov chains Monte Carlo algorithm and data-augmentation technique. Model fit will be assessed through model selections/comparison, statistical diagnosis and related hypothesis test procedures. More importantly, we will illustrate the effectiveness of the proposed methodology in the different application contexts.

英文关键词： latent variable models;Dirichlet process;Bayesian semiparametric analysis