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ОбложкаBevan A. Statistical data analysis for the physical sciences. - Cambridge: Cambridge University Press, 2013. - xi, 220 p.: ill. - Ref.: p.216-217. - Ind.: p.218-220. - ISBN 978-1-107-67034-1
Шифр: (И/В3-В54) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
 
  Preface ..................................................... ix

1  Introduction ................................................. 1
   1.1  Measuring g, the coefficient of acceleration due to 
        gravity ................................................. 1
   1.2  Verification of Ohm's law ............................... 5
   1.3  Measuring the half-life of an isotope ................... 7
   1.4  Summary ................................................ 10
2  Sets ........................................................ 12
   2.1  Relationships between sets ............................. 13
   2.2  Summary ................................................ 17
   Exercises ................................................... 18
3  Probability ................................................. 20
   3.1  Elementary rales ....................................... 21
   3.2  Bayesian probability ................................... 21
   3.3  Classic approach ....................................... 24
   3.4  Frequentist probability ................................ 25
   3.5  Probability density functions .......................... 26
   3.6  Likelihood ............................................. 27
   3.7  Case studies ........................................... 27
   3.8  Summary ................................................ 32
   Exercises ................................................... 33
4  Visualising and quantifying the properties of data .......... 35
   4.1  Visual representation of data .......................... 35
   4.2  Mode, median, mean ..................................... 37
   4.3  Quantifying the spread of data ......................... 39
   4.4  Presenting a measurement ............................... 41
   4.5  Skew ................................................... 43
   4.6  Measurements of more than one observable ............... 44
   4.7  Case study ............................................. 52
   4.8  Summary ................................................ 53
   Exercises ................................................... 53
5  Useful distributions ........................................ 56
   5.1  Expectation values of probability density functions .... 57
   5.2  Binomial distribution .................................. 57
   5.3  Poisson distribution ................................... 62
   5.4  Gaussian distribution .................................. 65
   5.5  x2 distribution ........................................ 67
   5.6  Computational issues ................................... 68
   5.7  Summary ................................................ 70
   Exercises ................................................... 70
6  Uncertainty and errors ...................................... 72
   6.1  The nature of errors ................................... 72
   6.2  Combination of errors .................................. 75
   6.3  Binomial error ......................................... 79
   6.4  Averaging results ...................................... 81
   6.5  Systematic errors and systematic bias .................. 82
   6.6  Blind analysis technique ............................... 84
   6.7  Case studies ........................................... 85
   6.8  Summary ................................................ 90
   Exercises ................................................... 91
7  Confidence intervals ........................................ 93
   7.1  Two-sided intervals .................................... 93
   7.2  Upper and lower limit calculations ..................... 94
   7.3  Limits for a Gaussian distribution ..................... 96
   7.4  Limits for a Poisson distribution ...................... 98
   7.5  Limits for a binomial distribution .................... 100
   7.6  Unified approach to analysis of small signals ......... 101
   7.7  Monte Carlo method .................................... 105
   7.8  Case studies .......................................... 106
   7.9  Summary ............................................... 111
   Exercises .................................................. 112
8  Hypothesis testing ......................................... 114
   8.1  Formulating a hypothesis .............................. 114
   8.2  Testing if the hypothesis agrees with data ............ 115
   8.3  Testing if the hypothesis disagrees with data ......... 117
   8.4  Hypothesis comparison ................................. 117
   8.5  Testing the compatibility of results .................. 119
   8.6  Establishing evidence for, or observing a new effect .. 120
   8.7  Case studies .......................................... 124
   8.8  Summary ............................................... 125
   Exercises .................................................. 126
9  Fitting .................................................... 128
   9.1  Optimisation .......................................... 128
   9.2  The least squares or χ2 fit ........................... 131
   9.3  Linear least-squares fit .............................. 134
   9.4  Maximum-likelihood fit ................................ 136
   9.5  Combination of results ................................ 140
   9.6  Template fitting ...................................... 142
   9.7  Case studies .......................................... 142
   9.8  Summary ............................................... 150
   Exercises .................................................. 151
10 Multivariate analysis ...................................... 153
   10.1 Cutting on variables .................................. 154
   10.2 Bayesian classifier ................................... 157
   10.3 Fisher discriminant ................................... 158
   10.4 Artificial neural networks ............................ 162
   10.5 Decision trees ........................................ 169
   10.6 Choosing an MVA technique ............................. 171
   10.7 Case studies .......................................... 174
   10.8 Summary ............................................... 177

   Exercises .................................................. 178
   Appendix A  Glossary ....................................... 181
   Appendix В  Probability density functions .................. 186
   Appendix С  Numerical integration methods .................. 198
   Appendix D  Solutions ...................................... 201
   Appendix E  Reference tables ............................... 207
   References ................................................. 216
   Index ...................................................... 218

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