Numerical Response – Linear Regression Models5.1.1 General Formulation of Linear Regression Model5.1.2 Significance and Interpretation of Regression Coefficients5.1.3 Other Types of Predictors in Linear Models5.2 Estimation and Inferences of Model Parameters for Linear Regression5.2.1 Least Squares Estimation5.2.2 Maximum Likelihood Estimation5.2.3 Variable Selection in Linear Regression5.2.4 Hypothesis Testing5.3 Categorical Response – Logistic Regression Model5.3.1 General Formulation of Logistic Regression Model5.3.2 Significance and Interpretation of Model Coefficients5.3.3 Maximum Likelihood Estimation for Logistic RegressionBibliographic NotesExercisesChapter 6: Linear Mixed Effects Model6.1 Model Structure6.2 Parameter Estimation for LME Model6.2.1 Maximum Likelihood Estimation Method6.2.2 Distribution-Free Estimation Methods6.3 Hypothesis Testing6.3.1 Testing for Fixed Effects6.3.2 Testing for Variance–Covariance ParametersBibliographic NotesExercises11 Part 2 Random Effects Approaches for Diagnosis and PrognosisChapter 7: Diagnosis of Variation Source Using PCA7.1 Linking Variation Sources to PCA7.2 Diagnosis of Single Variation Source7.3 Diagnosis of Multiple Variation Sources7.4 Data Driven Method for Diagnosing Variation SourcesBibliographic NotesExercisesChapter 8: Diagnosis of Variation Sources Through Random Effects Estimation8.1 Estimation of Variance Components8.2 Properties of Variation Source Estimators8.3 Performance Comparison of Variance Component EstimatorsBibliographic NotesExercisesChapter 9: Analysis of System Diagnosability9.1 Diagnosability of Linear Mixed Effects Model9.2 Minimal Diagnosable Class9.3 Measurement System Evaluation Based on System DiagnosabilityBibliographic NotesExercisesAppendixChapter 10: Prognosis Through Mixed Effects Models for Longitudinal Data10.1 Mixed Effects Model for Longitudinal Data10.2 Random Effects Estimation and Prediction for an Individual Unit10.3 Estimation of Time-to-Failure Distribution10.4 Mixed Effects Model with Mixture Prior Distribution10.4.1 Mixture Distribution10.4.2 Mixed Effects Model with Mixture Prior for Longitudinal Data10.5 Recursive Estimation of Random Effects Using Kalman Filter10.5.1 Introduction to the Kalman Filter10.5.2 Random Effects Estimation Using the Kalman FilterBiographical NotesExercisesAppendixChapter 11: Prognosis Using Gaussian Process Model11.1 Introduction to Gaussian Process Model11.2 GP Parameter Estimation and GP Based Prediction11.3 Pairwise Gaussian Process Model11.3.1 Introduction to Multi-output Gaussian Process11.3.2 Pairwise GP Modeling Through Convolution Process11.4 Multiple Output Gaussian Process for Multiple Signals11.4.1 Model Structure11.4.2 Model Parameter Estimation and Prediction11.4.3 Time-to-Failure Distribution Based on GP PredictionsBibliographical NotesExercisesChapter 12: Prognosis Through Mixed Effects Models for Time-to-Event Data12.1 Models for Time-to-Event Data Without Covariates12.1.1 Parametric Models for Time-to-Event Data12.1.2 Non-parametric Models for Time-to-Event Data12.2 Survival Regression Models12.2.1 Cox PH Model with Fixed Covariates12.2.2 Cox PH Model with Time Varying Covariates12.2.3 Assessing Goodness of Fit12.3 Joint Modeling of Time-to-Event Data and Longitudinal Data12.3.1 Structure of Joint Model and Parameter Estimation12.3.2 Online Event Prediction for a New Unit12.4 Cox PH Model with Frailty Term for Recurrent EventsBibliographical NotesExercisesAppendix
12 Appendix: Basics of Vectors, Matrices, and Linear Vector Space
13 References
14 Index
Guide
1 Cover
5 Table of Contents
6 Preface
8 Acronyms
11 Appendix: Basics of Vectors, Matrices, and Linear Vector Space
12 References
13 Index
Pages
1 i
2 ii
3 iii
4 iv
5 v
6 vi
7 vii
8 viii
9 ix
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