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List of Figures | p. xv |
List of Tables | p. xvii |
Preface | p. xix |
Introduction | p. 1 |
What Is a Model? | p. 1 |
What Is a Statistical Model? | p. 2 |
The Modeling Process | p. 3 |
Modeling Pitfalls | p. 4 |
Characteristics of Good Modelers | p. 5 |
The Future of Predictive Analytics | p. 7 |
Properties of Statistical Distributions | p. 9 |
Fundamental Distributions | p. 9 |
Uniform Distribution | p. 9 |
Details of the Normal (Gaussian) Distribution | p. 10 |
Lognormal Distribution | p. 19 |
¿ Distribution | p. 20 |
Chi-Squared Distribution | p. 22 |
Non-Central Chi-Squared Distribution | p. 25 |
Student's t-Distribution | p. 28 |
Multivariate t-Distribution | p. 29 |
F-Distribution | p. 31 |
Binomial Distribution | p. 31 |
Poisson Distribution | p. 32 |
Exponential Distribution | p. 32 |
Geometric Distribution | p. 33 |
Hypergeometric Distribution | p. 33 |
Negative Binomial Distribution | p. 34 |
Inverse Gaussian (IG) Distribution | p. 35 |
Normal Inverse Gaussian (NIG) Distribution | p. 36 |
Central Limit Theorem | p. 38 |
Estimate of Mean, Variance, Skewness, and Kurtosis from Sample Data | p. 40 |
Estimate of the Standard Deviation of the Sample Mean | p. 40 |
(Pseudo) Random Number Generators | p. 41 |
Mersenne Twister Pseudorandom Number Generator | p. 42 |
Box-Muller Transform for Generating a Normal Distribution | p. 42 |
Transformation of a Distribution Function | p. 43 |
Distribution of a Function of Random Variables | p. 43 |
Z = X + Y | p. 44 |
Z = XY | p. 44 |
(Z_{1},Z_{2},…,Z_{n}) = (X_{1},X_{2},…,X_{n}) Y | p. 44 |
Z = X/Y | p. 45 |
Z = max(X,Y) | p. 45 |
Z = min(X,Y) | p. 45 |
Moment Generating Function | p. 46 |
Moment Generating Function of Binomial Distribution | p. 46 |
Moment Generating Function of Normal Distribution | p. 47 |
Moment Generating Function of the ¿ Distribution | p. 47 |
Moment Generating Function of Chi-Square Distribution | p. 47 |
Moment Generating Function of the Poisson Distribution | p. 48 |
Cumulant Generating Function | p. 48 |
Characteristic Function | p. 50 |
Relationship between Cumulative Function and Characteristic Function | p. 51 |
Characteristic Function of Normal Distribution | p. 52 |
Characteristic Function of ¿ Distribution | p. 52 |
Chebyshev's Inequality | p. 53 |
Markov's Inequality | p. 54 |
Gram-Charlier Series | p. 54 |
Edgeworth Expansion | p. 55 |
Cornish-Fisher Expansion | p. 56 |
Lagrange Inversion Theorem | p. 56 |
Cornish-Fisher Expansion | p. 57 |
Copula Functions | p. 58 |
Gaussian Copula | p. 60 |
t-Copula | p. 61 |
Archimedean Copula | p. 62 |
Important Matrix Relationships | p. 63 |
Pseudo-Inverse of a Matrix | p. 63 |
A Lemma of Matrix Inversion | p. 64 |
Identity for a Matrix Determinant | p. 66 |
Inversion of Partitioned Matrix | p. 66 |
Determinant of Partitioned Matrix | p. 67 |
Matrix Sweep and Partial Correlation | p. 67 |
Singular Value Decomposition (SVD) | p. 69 |
Diagonalization of a Matrix | p. 71 |
Spectral Decomposition of a Positive Semi-Definite Matrix | p. 75 |
Normalization in Vector Space | p. 76 |
Conjugate Decomposition of a Symmetric Definite Matrix | p. 77 |
Cholesky Decomposition | p. 77 |
Cauchy-Schwartz Inequality . | p. 80 |
Relationship of Correlation among Three Variables | p. 81 |
Linear Modeling and Regression | p. 83 |
Properties of Maximum Likelihood Estimators | p. 84 |
Likelihood Ratio Test | p. 87 |
Wald Test | p. 87 |
Lagrange Multiplier Statistic | p. 88 |
Linear Regression | p. 88 |
Ordinary Least Squares (OLS) Regression | p. 89 |
Interpretation of the Coefficients of Linear Regression | p. 95 |
Regression on Weighted Data | p. 97 |
Incrementally Updating a Regression Model with Additional Data | p. 100 |
Partitioned Regression | p. 101 |
How Does the Regression Change When Adding One More Variable? | p. 101 |
Linearly Restricted Least Squares Regression | p. 103 |
Significance of the Correlation Coefficient | p. 105 |
Partial Correlation | p. 105 |
Ridge Regression | p. 105 |
Fisher's Linear Discriminant Analysis | p. 106 |
Principal Component Regression (PCR) | p. 109 |
Factor Analysis | p. 110 |
Partial Least Squares Regression (PLSR) | p. 111 |
Generalized Linear Model (GLM) | p. 113 |
Logistic Regression: Binary | p. 116 |
Logistic Regression: Multiple Nominal | p. 119 |
Logistic Regression: Proportional Multiple Ordinal | p. 121 |
Fisher Scoring Method for Logistic Regression . . | p. 123 |
Tobit Model: A Censored Regression Model | p. 125 |
Some Properties of the Normal Distribution | p. 125 |
Formulation of the Tobit Model | p. 126 |
Nonlinear Modeling | p. 129 |
Naive Bayesian Classifier | p. 129 |
Neural Network | p. 131 |
Back Propagation Neural Network | p. 131 |
Segmentation and Tree Models | p. 137 |
Segmentation | p. 137 |
Tree Models | p. 138 |
Sweeping to Find the Best Cutpoint | p. 140 |
Impurity Measure of a Population: Entropy and Gini Index | p. 143 |
Chi-Square Splitting Rule | p. 147 |
Implementation of Decision Trees | p. 148 |
Additive Models | p. 151 |
Boosted Tree | p. 153 |
Least Squares Regression Boosting Tree | p. 154 |
Binary Logistic Regression Boosting Tree | p. 155 |
Support Vector Machine (SVM) | p. 158 |
Wolfe Dual | p. 158 |
Linearly Separable Problem | p. 159 |
Linearly Inseparable Problem | p. 161 |
Constructing Higher-Dimensional Space and Kernel | p. 162 |
Model Output | p. 163 |
C-Support Vector Classification (C-SVC) for Classification | p. 164 |
¿-Support Vector Regression (¿-SVR) for Regression | p. 164 |
The Probability Estimate | p. 167 |
Fuzzy Logic System | p. 168 |
A Simple Fuzzy Logic System | p. 168 |
Clustering | p. 169 |
K Means, Fuzzy C Means | p. 170 |
Nearest Neighbor, K Nearest Neighbor (KNN | p. 171 |
Comments on Clustering Methods | p. 171 |
Time Series Analysis | p. 173 |
Fundamentals of Forecasting | p. 173 |
Box-Cox Transformation | p. 174 |
Smoothing Algorithms | p. 175 |
Convolution of Linear Filters | p. 176 |
Linear Difference Equation | p. 177 |
The Autocovariance Function and Autocorrelation Function | p. 178 |
The Partial Autocorrelation Function | p. 179 |
ARIMA Models | p. 181 |
MA(q) Process | p. 182 |
AR(p) Process | p. 184 |
ARMA(p, q) Process | p. 186 |
Survival Data Analysis | p. 187 |
Sampling Method | p. 190 |
Exponentially Weighted Moving Average (EWMA) and GARCH(1, 1) | p. 191 |
Exponentially Weighted Moving Average (EWMA) | p. 191 |
ARCH and GARCH Models | p. 192 |
Data Preparation and Variable Selection | p. 195 |
Data Quality and Exploration | p. 196 |
Variable Scaling and Transformation | p. 197 |
How to Bin Variables . | p. 197 |
Equal Interval | p. 198 |
Equal Population | p. 198 |
Tree Algorithms | p. 199 |
Interpolation in One and Two Dimensions | p. 199 |
Weight of Evidence (WOE) Transformation | p. 200 |
Variable Selection Overview | p. 204 |
Missing Data Imputation | p. 206 |
Stepwise Selection Methods | p. 207 |
Forward Selection in Linear Regression | p. 208 |
Forward Selection in Logistic Regression | p. 208 |
Mutual Information, KL Distance | p. 209 |
Detection of Multicollinearity | p. 210 |
Model Goodness Measures | p. 213 |
Training, Testing, Validation | p. 213 |
Continuous Dependent Variable | p. 215 |
Example: Linear Regression | p. 217 |
Binary Dependent Variable (Two-Group Classification) | p. 218 |
Kolmogorov-Smirnov (KS) Statistic | p. 218 |
Confusion Matrix | p. 220 |
Concordant and Discordant | p. 221 |
R^{2} for Logistic Regression | p. 223 |
AIC and SBC | p. 224 |
Hosmer-Lemeshow Goodness-of-Fit Test | p. 224 |
Example: Logistic Regression | p. 225 |
Population Stability Index Using Relative Entropy | p. 227 |
Optimization Methods | p. 231 |
Lagrange Multiplier | p. 232 |
Gradient Descent Method | p. 234 |
Newton-Raphson Method | p. 236 |
Conjugate Gradient Method | p. 238 |
Quasi-Newton Method | p. 240 |
Genetic Algorithms (GA) | p. 242 |
Simulated Annealing | p. 242 |
Linear Programming | p. 243 |
Nonlinear Programming (NLP) | p. 247 |
General Nonlinear Programming (GNLP) | p. 248 |
Lagrange Dual Problem | p. 249 |
Quadratic Programming (QP) | p. 250 |
Linear Complementarity Programming (LCP | p. 254 |
Sequential Quadratic Programming (SQP) | p. 256 |
Nonlinear Equations | p. 263 |
Expectation-Maximization (EM) Algorithm | p. 264 |
Optimal Design of Experiment | p. 268 |
Miscellaneous Topics | p. 271 |
Multidimensional Scaling | p. 271 |
Simulation | p. 274 |
Odds Normalization and Score Transformation | p. 278 |
Reject Inference | p. 280 |
Dempster-Shafer Theory of Evidence | p. 281 |
Some Properties in Set Theory | p. 281 |
Basic Probability Assignment, Belief Function, and Plausibility Function | p. 282 |
Dempster-Shafer's Rule of Combination | p. 285 |
Applications of Dempster-Shafer Theory of Evidence: Multiple Classifier Function | p. 287 |
Useful Mathematical Relations | p. 291 |
Information Inequality | p. 291 |
Relative Entropy | p. 291 |
Saddle-Point Method | p. 292 |
Stirling's Formula | p. 293 |
Convex Function and Jensen's Inequality | p. 294 |
DataMinerXL - Microsoft Excel Add-In for Building Predictive Models | p. 299 |
Overview | p. 299 |
Utility Functions | p. 299 |
Data Manipulation Functions | p. 300 |
Basic Statistical Functions | p. 300 |
Modeling Functions for All Models | p. 301 |
Weight of Evidence Transformation Functions | p. 301 |
Linear Regression Functions | p. 302 |
Partial Least Squares Regression Functions | p. 302 |
Logistic Regression Functions | p. 303 |
Time Series Analysis Functions | p. 303 |
Naive Bayes Classifier Functions | p. 303 |
Tree-Based Model Functions | p. 304 |
Clustering and Segmentation Functions | p. 304 |
Neural Network Functions | p. 304 |
Support Vector Machine Functions | p. 304 |
Optimization Functions | p. 305 |
Matrix Operation Functions | p. 305 |
Numerical Integration Functions | p. 306 |
Excel Built-in Statistical Distribution Functions | p. 306 |
Bibliography | p. 309 |
Index | p. 313 |
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