Classical Methods of Statistics (eBook)

Trademark information 6
PREFACE 7
Contents 11
1 Elements of Probability Theory 14
1.1 Introduction 14
1.2 Probability Measures and Their Generalisation 19
1.3 Conditional Probablity Structures and Bayes’ Theorem 29
1.4 Random Variables and Probability Distributions 35
1.5 Parametric Families of Probability Distributions 43
1.6 Exponential Transformations 55
1.7 Central Limit Theorem 60
1.8 Asymptotic Error Propagation 61
1.9 Modes of Convergence 64
1.10 Conditional Expectation 68
2 Elements of Statistical Theory 73
2.1 Introduction 73
2.2 Statistical Inference 74
2.3 The k(1, 2, . . .)-Sample Problem 95
2.4 The General Linear Model 101
2.5 Introduction to Multivariate Analysis 111
3 Applied Linear Regression 124
3.1 Introduction 124
3.2 Estimation and Hypothesis Testing 126
3.3 Model Selection and Validation 139
3.4 Analysis under Non-Standard Assumptions 145
3.5 Generalisations of Linear Regression 161
4 Profile Analysis 172
4.1 Introduction: Fusion Context 172
4.2 Discrete Profile Representations 179
4.3 Continuous Profile Representations 181
4.4 Profile Dependence on Plasma Parameters 190
4.5 Estimation of Regression Coefficients 193
4.6 Model Testing 200
4.7 Confidence Bands and Regression 205
4.8 Summary and Conclusions 211
4.9 Appendix 213
5 Discriminant Analysis 215
5.1 Introduction 215
5.2 Theory 218
5.3 Practice 226
5.4 Summary and Discussion 254
6 Statistical Software 258
6.1 Overview 258
6.2 SAS 263
6.3 S–Plus 265
7 Annotated Plasma Physical Datasets 268
7.1 Introduction 268
7.2 Case I: Scalings of the Energy Confinement Time 269
7.3 Case II: Halo Currents at ASDEX Upgrade (AUG) 281
7.4 Case III: Density Limit (AUG) 283
7.5 Case IV: High-frequency MHD Oscillations (AUG) 287
7.6 Case V: Heat Flux Profiles at the Outer Divertor Plate ( AUG) 291
7.7 Case VI: Density Profiles of Neutral Particles ( AUG) 294
7.8 Case VII: Plasma Parameter Recovery from External Magnetic Measurements ( AUG) 298
Keywords 310
Stichworte 312
Mots Cles 314
Palabras Claves 316
References 340
Index 379