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Discussion of “ Aspects of Bias, Prediction Variance and Mean Square Error”

Discussion of “ Aspects of Bias, Prediction Variance and Mean Square Error”. Geoff Vining Virginia Tech. Construction and Evaluation of Response Surface Designs Incorporating Bias from Model Misspecification. Appreciate that the Authors Are Exxtending FDS Plots to Include Bias

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Discussion of “ Aspects of Bias, Prediction Variance and Mean Square Error”

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  1. Discussion of “Aspects of Bias, Prediction Variance and Mean Square Error” Geoff Vining Virginia Tech

  2. Construction and Evaluation of Response Surface Designs Incorporating Bias from Model Misspecification • Appreciate that the Authors Are Exxtending FDS Plots to Include Bias • Very Natural and Welcomed Extension • Reflections from a Very Quick Reading!

  3. Construction and Evaluation of Response Surface Designs Incorporating Bias from Model Misspecification • Looks Like the Authors Are Treating the Lack-of-Fit Coefficients as Random • Very Problematic • Actually, They Are Fixed but Unknown • Suggest a More Thorough Literature Review

  4. Construction and Evaluation of Response Surface Designs Incorporating Bias from Model Misspecification • Box and Draper (1959, 1963) • Lambda – Optimality (1980s) • Trace L – Optimality (1980s) • Vining and Myers (Technometrics, 1991) • Extends VDGs to Include Bias • Defines the Lack-of-Fit in Terms of Power • Avoids the Need for Looking at Individual Coefficients

  5. Prediction Based Model Selection for Reliability • Takes a Generalized Linear Models Approach to Reliability • Not Focused on “Time to Failure” • Focus on Probability of Failure • Binary Response • Probit Models • “Region of Interest” • “True Value” Comes from the “Full Model”

  6. Prediction Based Model Selection for Reliability • Issues: • General There Are Multiple Regions of Interest • “In any generalized linear model, … , the estimate from the full model converges in probability to the true model.” • If, and only if, the full model is,in fact, the full model!! • “All models are wrong; some models are useful.” • More closely related to Mallows Cp. • Number of Models to Evaluate

  7. Prediction Based Model Selection for Reliability • Comments • Interesting Approach • Serious Approach to Model Selection for Reliability • Some Concern about Reliance on the Full Model • Focus on Probability of Failure Seems Limiting • Perhaps Appropriate • Seems to ignore the physics of failure.

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