层次贝叶斯模型中隐性变量分布的非参数估计及在RNA-seq数据中的应用

With the recent advent of new technologies such as image detecting, gene sequencing, social media, hierarchical Bayes models have been used more and more widely in the analysis of large datasets. Our proposed project plans to study two-level hierarchical Bayes models, and investigate nonparametric methods of estimating the distributions of latent variables. Nonparametric approaches relay on less prior knowledge of the model, enjoy more flexible forms through data-driven strategies, hence can be applied to more data types than otherwise. We will use spline, kernel and other smoothing techniques to approximate the density functions of latent variables, give rules of choosing the weights as well as the number of base functions, and provide theoretical derivations on the large sample properties of the nonparametric estimates. The new developed method will be compared with previous ones such as empirical Bayes, mixture distribution, Dirichlet process etc. As an important application, hierarchical Bayes model could be used to analyze high-throughput sequencing data, for example, to detect differentially expressed genes from RNA-seq data. We expect that through simulation study and real-data analysis, nonparametric estimation of hierarchical Bayes model will show its advantages compared with previous methods by higher testing power and more precise FDR control. Hence, our proposed research project will have significant theoretically and implementation contribution.

近年随着图像识别、基因测序、社交网络等新技术的革新，对大量数据分析的需要也更加迫切，层次贝叶斯模型因此得到了越来越广泛的应用。本项目拟针对两个层次的层次贝叶斯模型，研究用非参数方法来估计隐性变量的分布。非参数方法依赖于更少的先验知识、提供更加灵活的形式、能够适应更多的数据类型。我们拟使用样条函数、核函数等光滑技术逼近隐性变量的密度函数，将深入研究基函数的个数选择和权重估计问题，证明非参数估计的一致性和其它大样本性质，同时给出计算上高效、可靠的算法。估计的结果将与已有的经验贝叶斯、混合分布、Dirichlet Process等方法作比较。作为一个重要的应用，层次贝叶斯模型可以用来分析高通量测序数据，例如检测RNA-seq数据中的异表达基因，通过仿真实验和真实实验数据的分析来验证用非参数方法估计隐性变量分布的优越性，诸如更高的检测效能和更精确地FDR控制。因此本项目的研究将有重要的理论意义。

近年随着图像识别、基因测序、社交网络等新技术的革新，对大量数据分析的需要也更加迫切，层次贝叶斯模型因此得到了越来越广泛的应用。本项目针对两个层次的层次贝叶斯模型，研究用非参数方法来估计隐性变量的分布。非参数方法依赖于更少的先验知识、提供更加灵活的形式、能够适应更多的数据类型。我们使用样条函数、核函数等光滑技术逼近隐性变量的密度函数，深入研究了基函数的个数选择和权重估计问题，证明了非参数估计的一致性和其它大样本性质，同时给出计算上高效、可靠的算法。估计的结果与已有的经验贝叶斯、混合分布、Dirichlet Process等方法作比较。作为一个重要的应用，层次贝叶斯模型可以用来分析高通量测序数据，例如检测RNA-seq数据中的异表达基因，通过仿真实验和真实实验数据的分析来验证了用非参数方法估计隐性变量分布的优越性，诸如更高的检测效能和更精确地FDR控制。因此本项目的研究将有重要的理论意义。