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中文题名:

 基于Stan的贝叶斯分析及其应用    

姓名:

 徐睿    

学生类型:

 学士    

学位名称:

 理学学士    

学校:

 中国人民大学    

院系:

 统计学院    

专业:

 统计学    

第一导师姓名:

 孟生旺    

完成日期:

 2015    

中文关键词:

 贝叶斯推断 HMC算法 Stan软件    

中文摘要:
贝叶斯分析方法越来越多地被运用于各个学科中,尤其是提出MCMC算法后。近年来,常用的贝叶斯分析软件有BUGS、JAGS等,虽然它们操作方便,在大部分问题上也可以获得很好的结果,但是总体推断效率不高,且无法处理一些复杂问题。为解决这些问题,学者们设计了Stan软件。 本文首先对Stan软件作了基本介绍,尤其是它的抽样方法、最优化推断和程序设计。Stan主要采取的抽样方法是HMC(Hamiltonian/ Hybrid Monte Carlo)算法的变体NUTS(No-U-Turn Sampler),它去除了设定步数参数的需要,采用递归算法。Stan提供牛顿法、 BFGS和L-BFGS三种不同的优化程序,其中默认优化程序是L-BFGS算法。对于程序设计,本文介绍了Stan的数据类型、模型构造和一般步骤。 R软件是Stan的一个接口,由于R软件目前已经成为普遍的统计分析工具,因而在第二部分,本文介绍了RStan包中的常用函数stan_model、sampling、stan和optimizing等,并辅以程序实例详细说明了使用方法及结果分析。然后本文对Stan与WinBUGS软件进行了对比说明,同时利用一个贝叶斯分层模型的例子,展现了两种软件操作与结果表达的差异。 最后,本文使用Stan对一个婴儿出生体重的实际例子做了研究,同时与传统的Logistic回归作了比较。 Bayesian Inference method is widely used in many subjects, especially after appearance of MCMC algorithm. BUGS and JAGS are common software to do Bayesian analysis in recent years. Although it’s not difficult to operate them and most questions can get good results by using them, they are not very efficient and face challenges for some complex questions. In order to solve these problems, scientists created Stan. In this paper, we introduce Stan software firstly, especially its sampling method, optimization and programming. Stan mainly uses NUTS, a variant of HMC algorithm. NUTS eliminates the need to set the number of steps and uses a recursive algorithm. Stan provides three different optimizers, Newton optimizer, BFGS and L-BFGS. L-BFGS is default algorithm. For programming, we introduce data type, model construction and primary steps of Stan. R is an interface of Stan. Since R has been a common software to do statistics analysis, we introduce some useful functions in RStan package, such as stan_model, sampling, stan and optimizing. At the same time, we use some examples to show their way of using and results. Then we compare Stan and WinBUGS and show the difference between these two software by a Bayesian hierarchy model. Finally, we make a research about infant birth weight by using Stan and compare its result with traditional logistic regression.
开放日期:

 2016-03-21    

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