Classical methods of statistics: with applications in fusion-oriented experimental plasma physics

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