Cover -- Title Page -- Copyright -- Contents -- Series Preface -- Preface -- Acknowledgments -- Nomenclature -- Symbols -- Part I Introduction -- Chapter 1 Introductory Concepts -- 1.1 Illustrative Example-Traditional Linear Least-Squares Regression -- 1.2 How Models Are Used -- 1.3 Nonlinear Regression -- 1.4 Variable Types -- 1.5 Simulation -- 1.6 Issues -- 1.7 Takeaway -- Exercises -- Chapter 2 Model Types -- 2.1 Model Terminology -- 2.2 A Classification of Mathematical Model Types -- 2.3 Steady-State and Dynamic Models -- 2.4 Pseudo-First Principles-Appropriated First Principles -- 2.5 Pseudo-First Principles-Pseudo-Components -- 2.6 Empirical Models with Theoretical Grounding -- 2.7 Empirical Models with No Theoretical Grounding -- 2.8 Partitioned Models -- 2.9 Empirical or Phenomenological? -- 2.10 Ensemble Models -- 2.11 Simulators -- 2.12 Stochastic and Probabilistic Models -- 2.13 Linearity -- 2.14 Discrete or Continuous -- 2.15 Constraints -- 2.16 Model Design (Architecture, Functionality, Structure) -- 2.17 Takeaway -- Exercises -- Part II Preparation for Underlying Skills -- Chapter 3 Propagation of Uncertainty -- 3.1 Introduction -- 3.2 Sources of Error and Uncertainty -- 3.3 Significant Digits -- 3.4 Rounding Off -- 3.5 Estimating Uncertainty on Values -- 3.6 Propagation of Uncertainty-Overview-Two Types, Two Ways Each -- 3.7 Which to Report? Maximum or Probable Uncertainty -- 3.8 Bootstrapping -- 3.9 Bias and Precision -- 3.10 Takeaway -- Exercises -- Chapter 4 Essential Probability and Statistics -- 4.1 Variation and Its Role in Topics -- 4.2 Histogram and Its PDF and CDF Views -- 4.3 Constructing a Data-Based View of PDF and CDF -- 4.4 Parameters that Characterize the Distribution -- 4.5 Some Representative Distributions -- 4.6 Confidence Interval -- 4.7 Central Limit Theorem -- 4.8 Hypothesis and Testing.

4.9 Type I and Type II Errors, Alpha and Beta -- 4.10 Essential Statistics for This Text -- 4.11 Takeaway -- Exercises -- Chapter 5 Simulation -- 5.1 Introduction -- 5.2 Three Sources of Deviation: Measurement, Inputs, Coefficients -- 5.3 Two Types of Perturbations: Noise (Independent) and Drifts (Persistence) -- 5.4 Two Types of Influence: Additive and Scaled with Level -- 5.5 Using the Inverse CDF to Generate n and u from UID(0, 1) -- 5.6 Takeaway -- Exercises -- Chapter 6 Steady and Transient State Detection -- 6.1 Introduction -- 6.2 Method -- 6.3 Applications -- 6.4 Takeaway -- Exercises -- Part III Regression, Validation, Design -- Chapter 7 Regression Target - Objective Function -- 7.1 Introduction -- 7.2 Experimental and Measurement Uncertainty-Static and Continuous Valued -- 7.3 Likelihood -- 7.4 Maximum Likelihood -- 7.5 Estimating x and y Values -- 7.6 Vertical SSD-A Limiting Consideration of Variability Only in the Response Measurement -- 7.7 r-Square as a Measure of Fit -- 7.8 Normal, Total, or Perpendicular SSD -- 7.9 Akaho's Method -- 7.10 Using a Model Inverse for Regression -- 7.11 Choosing the Dependent Variable -- 7.12 Model Prediction with Dynamic Models -- 7.13 Model Prediction with Classification Models -- 7.14 Model Prediction with Rank Models -- 7.15 Probabilistic Models -- 7.16 Stochastic Models -- 7.17 Takeaway -- Exercises -- Chapter 8 Constraints -- 8.1 Introduction -- 8.2 Constraint Types -- 8.3 Expressing Hard Constraints in the Optimization Statement -- 8.4 Expressing Soft Constraints in the Optimization Statement -- 8.5 Equality Constraints -- 8.6 Takeaway -- Exercises -- Chapter 9 The Distortion of Linearizing Transforms -- 9.1 Linearizing Coefficient Expression in Nonlinear Functions -- 9.2 The Associated Distortion -- 9.3 Sequential Coefficient Evaluation -- 9.4 Takeaway -- Exercises.

Chapter 10 Optimization Algorithms -- 10.1 Introduction -- 10.2 Optimization Concepts -- 10.3 Gradient-Based Optimization -- 10.4 Direct Search Optimizers -- 10.5 Takeaway -- Chapter 11 Multiple Optima -- 11.1 Introduction -- 11.2 Quantifying the Probability of Finding the Global Best -- 11.3 Approaches to Find the Global Optimum -- 11.4 Best-of-N Rule for Regression Starts -- 11.5 Interpreting the CDF -- 11.6 Takeaway -- Chapter 12 Regression Convergence Criteria -- 12.1 Introduction -- 12.2 Convergence versus Stopping -- 12.3 Traditional Criteria for Claiming Convergence -- 12.4 Combining DV Influence on OF -- 12.5 Use Relative Impact as Convergence Criterion -- 12.6 Steady-State Convergence Criterion -- 12.7 Neural Network Validation -- 12.8 Takeaway -- Exercises -- Chapter 13 Model Design - Desired and Undesired Model Characteristics and Effects -- 13.1 Introduction -- 13.2 Redundant Coefficients -- 13.3 Coefficient Correlation -- 13.4 Asymptotic and Uncertainty Effects When Model is Inverted -- 13.5 Irrelevant Coefficients -- 13.6 Poles and Sign Flips w.r.t. the DV -- 13.7 Too Many Adjustable Coefficients or Too Many Regressors -- 13.8 Irrelevant Model Coefficients -- 13.9 Scale-Up or Scale-Down Transition to New Phenomena -- 13.10 Takeaway -- Exercises -- Chapter 14 Data Pre- and Post-processing -- 14.1 Introduction -- 14.2 Pre-processing Techniques -- 14.3 Post-processing -- 14.4 Takeaway -- Exercises -- Chapter 15 Incremental Model Adjustment -- 15.1 Introduction -- 15.2 Choosing the Adjustable Coefficient in Phenomenological Models -- 15.3 Simple Approach -- 15.4 An Alternate Approach -- 15.5 Other Approaches -- 15.6 Takeaway -- Exercises -- Chapter 16 Model and Experimental Validation -- 16.1 Introduction -- 16.2 Logic-Based Validation Criteria -- 16.3 Data-Based Validation Criteria and Statistical Tests -- 16.4 Model Discrimination.

16.5 Procedure Summary -- 16.6 Alternate Validation Approaches -- 16.7 Takeaway -- Exercises -- Chapter 17 Model Prediction Uncertainty -- 17.1 Introduction -- 17.2 Bootstrapping -- 17.3 Takeaway -- Chapter 18 Design of Experiments for Model Development and Validation -- 18.1 Concept-Plan and Data -- 18.2 Sufficiently Small Experimental Uncertainty-Methodology -- 18.3 Screening Designs-A Good Plan for an Alternate Purpose -- 18.4 Experimental Design-A Plan for Validation and Discrimination -- 18.5 EHS&LP -- 18.6 Visual Examples of Undesired Designs -- 18.7 Example for an Experimental Plan -- 18.8 Takeaway -- Exercises -- Chapter 19 Utility versus Perfection -- 19.1 Competing and Conflicting Measures of Excellence -- 19.2 Attributes for Model Utility Evaluation -- 19.3 Takeaway -- Exercises -- Chapter 20 Troubleshooting -- 20.1 Introduction -- 20.2 Bimodal and Multimodal Residuals -- 20.3 Trends in the Residuals -- 20.4 Parameter Correlation -- 20.5 Convergence Criterion-Too Tight, Too Loose -- 20.6 Overfitting (Memorization) -- 20.7 Solution Procedure Encounters Execution Errors -- 20.8 Not a Sharp CDF (OF) -- 20.9 Outliers -- 20.10 Average Residual Not Zero -- 20.11 Irrelevant Model Coefficients -- 20.12 Data Work-Up after the Trials -- 20.13 Too Many rs! -- 20.14 Propagation of Uncertainty Does Not Match Residuals -- 20.15 Multiple Optima -- 20.16 Very Slow Progress -- 20.17 All Residuals are Zero -- 20.18 Takeaway -- Exercises -- Part IV Case Studies and Data -- Chapter 21 Case Studies -- 21.1 Valve Characterization -- 21.2 CO2 Orifice Calibration -- 21.3 Enrollment Trend -- 21.4 Algae Response to Sunlight Intensity -- 21.5 Batch Reaction Kinetics -- Appendix A: VBA Primer: Brief on VBA Programming - Excel in Office 2013 -- Appendix B: Leapfrogging Optimizer Code for Steady-State Models -- Appendix C: Bootstrapping with Static Model.

References and Further Reading -- Index -- EULA.