带有缺失数据的纵向隐马尔可夫因子模型的贝叶斯分析

发布时间：2018-05-29 15:27

本文选题：隐马尔可夫模型 + 因子分析模型　；参考：《应用数学》2017年02期

【摘要】：隐马尔可夫因子模型在刻画多元纵向数据的关联性和异质性具有重要作用.在实际应用中,观测数据往往呈现缺失数据.本文在纵向框架内,对缺失的数据提出了一个建模.使用一个多项模型去拟合缺失数据指标,并提出用一系列一维条件分布的联合分布来建模.每个一维条件分布不仅取决于当前变量的观测值,而且也糅合以前的观测值和丢失的信息.在贝叶斯框架内,马尔可夫链蒙特卡罗方法用于实现后验分析.带有Metropolis-Hastings算法的Gibbs采样器被用来从相关的满条件分布中抽取随机样本.后验推断基于这些模拟观测值进行展开.我们进行了模拟研究.实证结果表明,所提出的方法在模型是正确指定时是十分有效的,而且对模型偏移也具有一定的稳健性.
[Abstract]:Hidden Markov factor model plays an important role in describing the relevance and heterogeneity of multiple longitudinal data. In practical application, observation data often appear missing data. In this paper, a model of missing data is presented in the vertical frame. A multi-term model is used to fit the missing data index, and a series of joint distributions of one-dimensional conditional distributions are proposed to model the missing data. Each one-dimensional conditional distribution depends not only on the observed values of the current variables, but also on the combination of the previous observations and the missing information. In Bayesian framework, Markov chain Monte Carlo method is used to implement posterior analysis. The Gibbs sampler with Metropolis-Hastings algorithm is used to extract random samples from the related full conditional distribution. Posteriori extrapolation is based on these simulated observations. We conducted a simulation study. The empirical results show that the proposed method is very effective when the model is correctly specified and is robust to model migration.
【作者单位】：南京林业大学理学院;南京林业大学经济管理学院;
【基金】：国家自然科学基金(11471161) 南京市留学回国人员科技择优资助项目(013101001)
【分类号】：O211.62

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