利用M-H算法求解Logistic回归模型参数的贝叶斯估计
发布时间：2018-08-06 17:25
【摘要】：文章以航天飞机在不同温度下发射密封圈的失效数据为例,采用随机游动与变量变换M-H算法获得Logistic回归模型参数的后验分布样本并进行贝叶斯分析。同时,进行蒙特卡洛模拟,通过样本轨迹图、直方图、自相关系数图等考查M-H算法的抽样表现,并讨论每种抽样方法的优缺点与提高措施。结果表明:先验分布的选取直接影响贝叶斯估计效果,有先验信息的M-H算法估计的标准差比无先验信息的M-H算法要精确,但随着样本容量增大,趋势在减少,适当的建议分布与变量变换可大大提高M-H算法的抽样效率。
[Abstract]:In this paper, taking the failure data of the space shuttle's launching sealing ring at different temperatures as an example, the posterior distribution samples of the parameters of the Logistic regression model are obtained by using the M-H algorithm of random walk and variable transformation, and the Bayesian analysis is carried out. At the same time, Monte Carlo simulation is carried out. The sampling performance of M-H algorithm is examined by sample locus, histogram and autocorrelation coefficient diagram, and the advantages and disadvantages of each sampling method and the improvement measures are discussed. The results show that the selection of prior distribution directly affects the effect of Bayesian estimation. The standard deviation of M-H algorithm with prior information is more accurate than that of M-H algorithm without prior information, but the trend decreases with the increase of sample size. The sampling efficiency of M-H algorithm can be greatly improved by appropriate recommended distribution and variable transformation.
【作者单位】： 天水师范学院数学与统计学院;
【基金】：国家自然科学基金资助项目(61104045) 天水师范学院中青年教师科研资助项目(TSA1506)
【分类号】：O212.8
本文编号：2168451
[Abstract]:In this paper, taking the failure data of the space shuttle's launching sealing ring at different temperatures as an example, the posterior distribution samples of the parameters of the Logistic regression model are obtained by using the M-H algorithm of random walk and variable transformation, and the Bayesian analysis is carried out. At the same time, Monte Carlo simulation is carried out. The sampling performance of M-H algorithm is examined by sample locus, histogram and autocorrelation coefficient diagram, and the advantages and disadvantages of each sampling method and the improvement measures are discussed. The results show that the selection of prior distribution directly affects the effect of Bayesian estimation. The standard deviation of M-H algorithm with prior information is more accurate than that of M-H algorithm without prior information, but the trend decreases with the increase of sample size. The sampling efficiency of M-H algorithm can be greatly improved by appropriate recommended distribution and variable transformation.
【作者单位】： 天水师范学院数学与统计学院;
【基金】：国家自然科学基金资助项目(61104045) 天水师范学院中青年教师科研资助项目(TSA1506)
【分类号】：O212.8
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