基于GLM的贝叶斯变量与模型选择

摘要

针对非正态响应的部分因子试验,当筛选试验所涉及的因子数目较大时,提出了基于广义线性模型( generalized linear models,GLM)的贝叶斯变量与模型选择方法.首先,针对模型参数的不确定性,选择了经验贝叶斯先验.其次,在广义线性模型的线性预测器中对每个变量设置了二元变量指示器,并建立起变量指示器与模型指示器之间的转换关系.然后,利用变量指示器与模型指示器的后验概率来识别显著性因子与选择最佳模型.最后,以实际的工业案例说明此方法能够有效地识别非正态响应部分因子试验的显著性因子.%As for fractional factorial experiments with non-normal responses, a Bayesian variable and model selection approach based on generalized linear models (GLM) was proposed in the paper when the number of factors in screening experiments is large. Firstly, an empirical Bayesian prior was selected to consider the uncertainty of parameters in GLM. Secondly, we set a binary variable indicator for each variable in the linear predicates of GLM, and established a transformational relation between the variable indicators and the model indicators. Thirdly, we could identify significant factors and select the best model by the posterior probabilities of the variable indicators and the model indicators. Finally, a practical industrial example reveals that the proposed method can effectively identify significant factors in the fractional factorial experiment with non-normal responses.