两阶段的贝叶斯模型选择与筛选试验分析  

Two-stage Bayesian model choice and analysis of screening experiments

作　　者：汪建均[1] 马义中[1] 汪新[2] 

机构地区：[1]南京理工大学经济管理学院,南京210094 [2]云南财经大学统计与数学学院,昆明650221

出　　处：《系统工程理论与实践》2011年第8期1447-1453,共7页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(70931002)

摘　　要：针对非正态响应的部分因子试验设计,当筛选试验所涉及的因子数目较大时,提出了一种两阶段的贝叶斯模型选择方法.首先,运用蒙特卡洛(MCMC)方法模拟广义线性模型各参数的后验分布,并根据各参数大于零或小于零的后验概率考察各变量的显著性,得到初始的当前模型与候选模型;其次,利用贝叶斯模型评估准则DIC对当前模型与候选模型进行逐步迭代优化,筛选出显著性因子,得到了具有最佳短期预测性能的模型;最后,实际的工业案例说明此方法能够有效处理非正态响应部分因子试验中显著性因子筛选问题.As for fractional factorial experiment design with non-normal responses,a method of two-stage Bayesian model choice was proposed in the paper when the number of the factors in screening experiments is large.Firstly,the MCMC method was used to simulate dynamically the Markov Chain of every parameter＇s posterior distribution in generalized linear models,and the significant level of the factors was identified according to the Bayesian posterior probability of every parameter which is more than or less than zero, then initial current model and candidate models were obtained by the significant level of these factors. Secondly,the significant factors were identified to establish a model with best short-term predictions by means of the Bayesian model assessment criterion based on the deviance information criterion（DIC）, which was used to stepwise optimize the output from the current model and candidate models.Finally,a practical industrial example reveals that the proposed method can identify effectively significant factors in fractional factorial experiment design with non-normal responses.

关 键 词：广义线性模型 非正态响应 部分因子试验设计 贝叶斯分析 

分 类 号：F273.2[经济管理—企业管理]