两类统计模型中方差和协方差分量的Bayes估计

【作者】 闫同新；

【导师】 王志忠；

【作者基本信息】 中南大学 ， 概率论与数理统计， 2007， 硕士

【摘要】 回归模型中的方差和协方差分量的估计在工业、化学、生物和行为科学等领域中有广泛应用,本文中的两类统计模型分别为非线性模型和混合整数线性模型。通过采用Bayes方法,从无先验信息和有逆Gamma先验信息出发,研究了这两类统计模型中的方差和协方差分量的估计。本文中所研究的非线性模型中方差和协方差分量的Bayes估计包含相关系数ρ,而其他学者提出的线性模型中方差和协方差分量的Bayes估计只是本文的特殊情况。通过实例说明了Bayes方法是可行的,并且有逆Gamma先验信息要比无先验信息得出的结果要好。对混合整数线性模型的研究。始于GPS定位测量(XuPeiliang,2006),这个问题在统计学中还没有研究。GPS定位测量中研究的只是基线向量β∈R~t和双差整周模糊度θ∈Z~m,没有考虑方差和协方差分量。从统计学的角度来看,方差和协方差分量的估计与其他未知参数的估计同样重要,从而本文所研究的另一个问题是混合整数线性模型中方差因子的Bayes估计,并通过卫星在不同的历元时所得到的实际数据得出混合整数线性模型中方差因子的Bayes估计。同样,结果表明有逆Gamma先验信息要比无先验信息得出的结果要好。更多还原

【Abstract】 In the regression model, the estimation of variance and covariance components is wider applied in the industrial, chemical, biological, behavioral sciences, and other fields. In this paper, the two kinds of statistical models are the nonlinear model and the mixed-integer linear model. The estimations of variance and covariance components which come from non-informative prior and inverted gamma prior are researched with the Bayesian approach in the two kinds of statistical models.In this paper, the Bayesian estimation of the variance and covariance components include the correlation coefficientρin the nonlinear model, but the Bayesian estimation of the variance and covariance components in the linear model is provided by other scholars just only a special situation. By an example , the feasibility of the Bayesian approach is demonstrated, and the result of inverted gamma prior is better than non-informative prior.The research of the mixed-integer linear model began with the GPS measurement (Xu peiliang, 2006), this issue is not studied in the statistics. The baseline vectorβ∈R~l and the difference-two whole ambiguityθ∈Z~m are studied in the GPS measurement, in which the variance and covariance components are not considered. From the view of statistics, the estimation of variance and covariance components is the same important as other estimations of unknown parameters. So another issue of research in this paper is the Bayesian estimation of variance in the mixed-integer linear model by satellites. Similarly, the result indicates that the result of inverted gamma prior is better than non-informative prior.更多还原