4.4 Article

Robust Bayesian hierarchical modeling and inference using scale mixtures of normal distributions

Journal

IISE TRANSACTIONS
Volume 54, Issue 7, Pages 659-671

Publisher

TAYLOR & FRANCIS INC
DOI: 10.1080/24725854.2021.1912440

Keywords

Bayesian analysis; laser cladding repair; process modeling; variable selection; seemingly unrelated regression

Funding

  1. National Natural Science Foundation of China [72072089, 71931006, 71702072, 71811540414]
  2. Internal Research Awards (INTRA) program from the UTSA Vice President for Research, Economic Development, and Knowledge Enterprise at the University of Texas at San Antonio
  3. National Research Foundation of Korea (NRF) - Korean government [NRF-2017R1A2B4004169]

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The article introduces a robust Bayesian seemingly unrelated regression model to analyze multiple-feature systems while addressing issues like high correlation, non-normality, and variable selection. Through simulation experiments and application to a laser cladding repair process, the proposed method is demonstrated to outperform its classic counterpart in literature.
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.

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