Foreword |
|
xiii | |
Symbols |
|
xix | |
Author Bios |
|
xxi | |
|
|
1 | (96) |
|
1 What to Expect in This Book? |
|
|
3 | (4) |
|
2 Calculus and Linear Algebra Essentials |
|
|
7 | (48) |
|
2.1 Scalars, Vectors, and Matrices |
|
|
7 | (3) |
|
|
10 | (6) |
|
|
10 | (3) |
|
|
13 | (3) |
|
|
16 | (9) |
|
|
18 | (1) |
|
2.3.2 Composition of functions |
|
|
19 | (1) |
|
2.3.3 Inverse functions and solving equations |
|
|
19 | (2) |
|
2.3.4 Multivariate functions |
|
|
21 | (1) |
|
2.3.5 Linear transformations, matrix inverses, and matrix decompositions |
|
|
22 | (3) |
|
|
25 | (6) |
|
2.4.1 Multivariate derivatives |
|
|
28 | (1) |
|
|
29 | (2) |
|
|
31 | (5) |
|
2.5.1 Second derivative test, saddle points, and inflection points |
|
|
33 | (1) |
|
2.5.2 Newton-Raphson algorithm for finding optima |
|
|
34 | (2) |
|
|
36 | (7) |
|
|
38 | (1) |
|
2.6.2 Practical integration rules |
|
|
39 | (1) |
|
|
40 | (2) |
|
2.6.4 Interchange integration and differentiation |
|
|
42 | (1) |
|
2.7 Differential Equations |
|
|
43 | (6) |
|
2.7.1 Equilibrium solutions of differential equations |
|
|
45 | (1) |
|
2.7.2 First-order equations with separable variables |
|
|
46 | (3) |
|
2.8 Complex Numbers and Functions |
|
|
49 | (2) |
|
|
51 | (4) |
|
|
55 | (42) |
|
3.1 Probability of Events |
|
|
55 | (10) |
|
|
56 | (1) |
|
3.1.2 Laplace's definition of probability |
|
|
57 | (3) |
|
3.1.3 General definition of probability |
|
|
60 | (3) |
|
|
63 | (2) |
|
|
65 | (22) |
|
3.2.1 Definition of random variables |
|
|
65 | (1) |
|
3.2.2 Distribution functions |
|
|
66 | (2) |
|
3.2.3 Moments of a random variable |
|
|
68 | (3) |
|
3.2.4 Some standard probability distributions |
|
|
71 | (3) |
|
3.2.5 Joint and marginal distribution functions |
|
|
74 | (2) |
|
3.2.6 Independent random variables |
|
|
76 | (3) |
|
3.2.7 Conditional distributions |
|
|
79 | (2) |
|
3.2.8 Random variables related to the normal |
|
|
81 | (3) |
|
3.2.9 Multivariate normal distribution |
|
|
84 | (1) |
|
3.2.10 Exponential family of distributions |
|
|
85 | (2) |
|
3.3 Pseudo Random Number Generation |
|
|
87 | (2) |
|
|
89 | (1) |
|
|
90 | (1) |
|
|
90 | (7) |
|
II Numerics and Error Propagation |
|
|
97 | (30) |
|
4 Introduction to Numerical Methods |
|
|
99 | (16) |
|
|
99 | (7) |
|
4.1.1 Fixed point iteration |
|
|
100 | (2) |
|
|
102 | (4) |
|
4.2 Numerical Methods for Solving Differential Equations |
|
|
106 | (4) |
|
4.2.1 Euler's iterative method |
|
|
106 | (1) |
|
4.2.2 Runge-Kutta iterative method |
|
|
107 | (3) |
|
4.3 Differential Algebraic Equations |
|
|
110 | (1) |
|
|
111 | (1) |
|
|
112 | (1) |
|
|
112 | (3) |
|
5 Laws on Propagation of Error |
|
|
115 | (12) |
|
5.1 Absolute and Relative Error of Measurement |
|
|
115 | (2) |
|
|
117 | (1) |
|
5.3 Functions that Depend on One Variable |
|
|
118 | (2) |
|
5.3.1 First-order approximation |
|
|
118 | (1) |
|
5.3.2 Second-order approximation |
|
|
119 | (1) |
|
5.4 Functions that Depend on Two Variables |
|
|
120 | (3) |
|
5.4.1 Covariance and correlation |
|
|
121 | (1) |
|
5.4.2 First-order approximation |
|
|
122 | (1) |
|
5.4.3 Second-order approximation |
|
|
122 | (1) |
|
|
123 | (1) |
|
|
123 | (1) |
|
|
123 | (4) |
|
III Various Types of Models and Their Estimation |
|
|
127 | (156) |
|
6 Measurement Models for a Chemical Quantity |
|
|
129 | (52) |
|
|
130 | (3) |
|
|
133 | (2) |
|
6.3 Constructing Confidence Intervals |
|
|
135 | (8) |
|
6.3.1 Confidence interval from the central limit theorem |
|
|
135 | (5) |
|
6.3.2 Confidence interval from the bootstrap |
|
|
140 | (1) |
|
6.3.3 Confidence interval from the normal distribution |
|
|
141 | (2) |
|
6.4 Testing Chemical Hypotheses related to Measurement Models |
|
|
143 | (4) |
|
6.4.1 Testing for the presence of bias |
|
|
143 | (1) |
|
6.4.2 Testing for equality of two means |
|
|
144 | (2) |
|
6.4.3 Testing for equality of variance |
|
|
146 | (1) |
|
6.5 General Inference Paradigm |
|
|
147 | (23) |
|
6.5.1 Maximum likelihood estimation (MLE) |
|
|
147 | (2) |
|
6.5.2 Consistency of the MLE |
|
|
149 | (3) |
|
6.5.3 Efficiency of the MLE |
|
|
152 | (3) |
|
6.5.4 Confidence intervals using the MLE |
|
|
155 | (1) |
|
6.5.5 Testing hypotheses with the MLE |
|
|
156 | (5) |
|
6.5.6 Testing multiple parameters with likelihood ratio test |
|
|
161 | (2) |
|
|
163 | (7) |
|
|
170 | (1) |
|
|
171 | (1) |
|
|
172 | (9) |
|
|
181 | (28) |
|
|
182 | (1) |
|
7.2 Estimation and Prediction |
|
|
182 | (4) |
|
7.2.1 Parameter estimation |
|
|
183 | (3) |
|
|
186 | (1) |
|
|
186 | (5) |
|
7.3.1 Diagnostics for high leverage points |
|
|
186 | (1) |
|
7.3.2 Diagnostics for outlying observations |
|
|
187 | (1) |
|
7.3.3 Diagnostics for influential observations |
|
|
188 | (1) |
|
7.3.4 Diagnostics for linear dependency among predictors |
|
|
189 | (2) |
|
|
191 | (7) |
|
7.4.1 Marginal testing of parameters |
|
|
192 | (1) |
|
7.4.2 Testing a subset of parameters |
|
|
193 | (1) |
|
|
193 | (2) |
|
7.4.4 SCAD penalized regression |
|
|
195 | (3) |
|
7.5 Specific Linear Models |
|
|
198 | (3) |
|
7.5.1 Simple linear regression |
|
|
198 | (1) |
|
7.5.2 Polynomial regression |
|
|
199 | (2) |
|
|
201 | (2) |
|
|
203 | (1) |
|
|
203 | (6) |
|
|
209 | (36) |
|
8.1 Some Non-linear Functions Modeling Chemical Processes |
|
|
210 | (1) |
|
8.2 Non-linear Regression |
|
|
211 | (8) |
|
8.2.1 Non-linear least squares parameter estimation |
|
|
211 | (4) |
|
8.2.2 Estimating a function of the parameters |
|
|
215 | (2) |
|
8.2.3 Using the bootstrap |
|
|
217 | (2) |
|
|
219 | (3) |
|
8.3.1 Inverse linear regression |
|
|
219 | (2) |
|
8.3.2 Inverse non-linear regression |
|
|
221 | (1) |
|
8.4 Generalized Linear Models |
|
|
222 | (10) |
|
8.4.1 Estimation of a generalized linear model |
|
|
223 | (3) |
|
8.4.2 Binary dose-response models |
|
|
226 | (4) |
|
|
230 | (2) |
|
8.5 Semi-parametric Models |
|
|
232 | (6) |
|
|
238 | (2) |
|
|
240 | (1) |
|
|
240 | (5) |
|
9 Chemodynamics and Stoichiometry |
|
|
245 | (20) |
|
9.1 Stoichiometry of Systems of Reactions |
|
|
246 | (3) |
|
9.2 Stochastic Models for Particle Dynamics |
|
|
249 | (3) |
|
9.2.1 Gillespie algorithm for simulating reactions |
|
|
250 | (1) |
|
9.2.2 Euler-Maruyama approximation |
|
|
251 | (1) |
|
9.3 Estimating Reaction Rates |
|
|
252 | (3) |
|
9.4 Mean-Field Approximation of Reaction System |
|
|
255 | (5) |
|
9.4.1 Chemical reaction system as ODE |
|
|
255 | (1) |
|
9.4.2 Estimating reaction rates |
|
|
256 | (4) |
|
|
260 | (5) |
|
10 Multivariate Exploration |
|
|
265 | (18) |
|
|
266 | (1) |
|
10.2 Matrix Decomposition |
|
|
267 | (3) |
|
|
267 | (1) |
|
10.2.2 Eigen decomposition |
|
|
268 | (2) |
|
10.2.3 Singular value decomposition |
|
|
270 | (1) |
|
10.3 Principal Components Analysis |
|
|
270 | (3) |
|
10.4 Regression Using a Subspace |
|
|
273 | (3) |
|
10.4.1 Principal components regression |
|
|
273 | (1) |
|
10.4.2 Partial least squares regression |
|
|
274 | (1) |
|
10.4.3 Determining the number of components by cross-validation |
|
|
275 | (1) |
|
|
276 | (2) |
|
|
278 | (1) |
|
|
278 | (5) |
|
IV Analysis of Designed Experiments |
|
|
283 | (68) |
|
11 Analysis of Data from Designed Experiments |
|
|
285 | (42) |
|
11.1 Concepts of Factorial Designs |
|
|
285 | (7) |
|
11.1.1 Two-level one-factor design |
|
|
286 | (1) |
|
11.1.2 Two-level two-factor design |
|
|
286 | (3) |
|
11.1.3 Two-level k-factor designs |
|
|
289 | (1) |
|
11.1.4 Two-level k-factor fractional designs |
|
|
290 | (2) |
|
11.2 Analysis of Variance |
|
|
292 | (11) |
|
11.2.1 One-way analysis of variance |
|
|
292 | (5) |
|
11.2.2 Two-way analysis of variance |
|
|
297 | (4) |
|
|
301 | (2) |
|
11.3 Analysis of the Response Surface |
|
|
303 | (2) |
|
11.4 Mixed Effects Models |
|
|
305 | (11) |
|
11.4.1 Linear random effects models |
|
|
306 | (3) |
|
11.4.2 Linear mixed effects models |
|
|
309 | (3) |
|
11.4.3 Nonlinear mixed effects models |
|
|
312 | (4) |
|
|
316 | (3) |
|
|
319 | (1) |
|
|
320 | (7) |
|
12 Robust Analysis of Models |
|
|
327 | (24) |
|
12.1 Outlying Data Points |
|
|
328 | (3) |
|
12.1.1 A classical test for detecting an outlier |
|
|
328 | (1) |
|
12.1.2 The effect of an outlier on the estimated curve |
|
|
329 | (2) |
|
|
331 | (6) |
|
12.2.1 Robust estimation a location parameter |
|
|
331 | (3) |
|
12.2.2 Robust estimation of scale |
|
|
334 | (3) |
|
12.3 Robust Linear Regression |
|
|
337 | (5) |
|
12.3.1 Robust one-way analysis of variance |
|
|
340 | (1) |
|
12.3.2 Robust two-way analysis of variance |
|
|
341 | (1) |
|
12.4 Robust Nonlinear Regression |
|
|
342 | (2) |
|
12.5 Dealing with Heterogeneity |
|
|
344 | (1) |
|
12.6 Appendix: Scale Tau Estimator |
|
|
345 | (1) |
|
|
345 | (1) |
|
|
346 | (1) |
|
|
346 | (5) |
|
|
351 | (14) |
|
A Basics of R Computing Environment |
|
|
353 | (1) |
|
|
353 | (3) |
|
A.1.1 Installing packages |
|
|
354 | (1) |
|
|
355 | (1) |
|
|
356 | (1) |
|
|
356 | (4) |
|
A.2.1 Functions on scalars |
|
|
356 | (1) |
|
A.2.2 Functions on vectors |
|
|
356 | (1) |
|
A.2.3 Functions on matrices of data frames |
|
|
356 | (1) |
|
A.2.4 Some statistical functions in R |
|
|
357 | (1) |
|
A.2.5 Writing your own functions and source code |
|
|
357 | (1) |
|
|
358 | (1) |
|
A.2.7 For and while loops |
|
|
358 | (1) |
|
|
359 | (1) |
|
A.2.9 Functions for plotting |
|
|
359 | (1) |
|
|
360 | (1) |
|
|
361 | (4) |
|
|
361 | (4) |
Bibliography |
|
365 | (8) |
Index |
|
373 | |