A BAYESIAN ANALYSIS FOR ROBUST PARAMETER DESIGNS WITH ORDINAL RESPONSES

具有有序資料的穩健參數設計實驗之貝氏分析

俞一唐(I-Tang Yu)；杜維珍(Wei-Chen Tu)

高斯過程 ； 有序資料 ； 穩健參數設計 ； Gaussian process ； ordinal response ； robust parameter design

中國統計學報

54卷1期（2016 / 03 / 01）

26 - 42

英文

在本文中, 我們提供了一個貝氏方法來分析反應值為有序資料的穩健參數設計實驗。在模型建構方面, 不同於一般常用來分析有序資料的廣義線性模型,我們利用高斯過程來建模。而在最佳化的部分, 我們使用貝氏預測法來進行最佳因子設定的篩選。最後, 我們利用本文所提的方法分析了一筆實際的實驗資料, 從資料分析中我們發現當因子間具有複雜之交互作用時, 我們所提出的方法會比利用廣義線性模型更能得到一個可靠的結果。

In this work, we propose a Bayesian method to analyze robust parameter design experiments with ordinal responses. Instead of generalized linear models, we use a Gaussian process model on the latent variable representation of cumulative regression models. The optimization is then implemented based on the Bayesian predictive approach. The Bayesian Gaussian process model approach is illustrated by analyzing the foam experiment. From the analysis, we conclude that our approach can obtain a more reliable result than generalized-linear-model based approaches when complex interactions are present.

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