Robust Bayesian hierarchical modeling and inference using scale mixtures of normal distributions
提出一种稳健贝叶斯看似不相关回归模型，同时处理多响应系统中的高相关性、非正态性和变量选择问题，并通过马尔可夫链蒙特卡洛算法进行推断，在激光熔覆修复过程中表现优于传统方法。
Empirical models that relate multiple quality features to a set of design variables play a vital role in many industrial process optimization methods. Many of the current modeling methods employ a single-response normal model to analyze industrial processes without taking into consideration the high correlations and the non-normality among the response variables. Also, the problem of variable selection has also not yet been fully investigated within this modeling framework. Failure to account for these issues may result in a misleading prediction model, and therefore, poor process design. In this article, we propose a robust Bayesian seemingly unrelated regression model to simultaneously analyze multiple-feature systems while accounting for the high correlation, non-normality, and variable selection issues. Additionally, we propose a Markov chain Monte Carlo sampling algorithm to generate posterior samples from the full joint posterior distribution to obtain the robust Bayesian estimates. Simulation experiments are executed to investigate the performance of the proposed Bayesian method, which is also illustrated by application to a laser cladding repair process. The analysis results show that the proposed modeling technique compares favorably with its classic counterpart in the literature.