A TEST-BED TO COMPARE ALTERNATIVE BAYESIAN REGRESSION FORMULATIONS AND AN APPLICATION OF CNC MILLING ROUGHNESS MINIMIZATION

以測試平臺檢驗與評估貝氏迴歸模型：以CNC製造木製圓盤表面粗糙度最小化為例

曾世賢(Shih-Hsien Tseng) ； 康煌易(Huang-Yi Kang) ； 陳曉瑩(Hsiao-Yin Chen)

《品質學報》 25卷4期 (2018/08) Pp. 241-257

https://doi.org/10.6220/joq.201808_25(4).0002

摘要

In this paper, we proposed Bayesian regression, four commonly used priors, and a test-bed methodology for evaluating empirical modeling techniques. This method was applied to evaluate and fine-tune several of the most popular Bayesian regression formulations. It provides a systematic analysis of the robustness of alternative Bayesian regression priors. Based on the result, we concluded that stochastic search variable selection (SSVS), which relies on a mixture of normal priors and Gibbs sampling, performed better than other priors, and handled regression problems such as bias, multicollinearity, and design moment better than other methods. To illustrate the proposed methods, we applied a tuned Bayesian regression formulation to minimize the surface roughness of a wooden plate.

關鍵字

Bayesian regression ； Bayesian priors ； Markov chain Monte Carlo ； furniture systems design

並列摘要

本研究提出以實驗設計法建構測試平台以檢驗貝氏迴歸中四類常用之先驗假設其建模技術優劣。本研究利用此測試平台評估和調整相對較熱門之貝氏迴歸公式中有關先驗之假設，並提供了貝氏迴歸先驗的穩健性的系統分析。根據研究結果本研究得出結論為隨機搜索變量選擇（stochastic search variable selection, SSVS）在吉氏抽樣的混合之下，處理貝氏迴歸的問題中面臨如模型偏誤，多重共線性和資料分布型態不均時，相對其他先驗假設法表現更為穩健。為說明本研究提出之方法，本研究以隨機搜索變量選擇方式探討家具廠製造木製圓盤最小化木板的表面粗糙度相關參數之設定。

並列關鍵字

貝氏迴歸 ； 貝氏先驗 ； 馬可夫鏈蒙地卡 ； 家具系統設計

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