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Statistical Methods for Data Analysis in Particle Physics 1st ed. 2016 [Pehme köide]

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  • Formaat: Paperback / softback, 172 pages, kõrgus x laius: 235x155 mm, kaal: 302 g, 59 Illustrations, color; 4 Illustrations, black and white; XIX, 172 p. 63 illus., 59 illus. in color., 1 Paperback / softback
  • Sari: Lecture Notes in Physics 909
  • Ilmumisaeg: 05-Aug-2015
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319201751
  • ISBN-13: 9783319201757
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Statistical Methods for Data Analysis in Particle Physics 1st ed. 2016Suurem pilt
  • Formaat: Paperback / softback, 172 pages, kõrgus x laius: 235x155 mm, kaal: 302 g, 59 Illustrations, color; 4 Illustrations, black and white; XIX, 172 p. 63 illus., 59 illus. in color., 1 Paperback / softback
  • Sari: Lecture Notes in Physics 909
  • Ilmumisaeg: 05-Aug-2015
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319201751
  • ISBN-13: 9783319201757
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319201757.html
Märksõnad:
This concise set of course-based notes provides the reader with the main concepts and tools to perform statistical analysis of experimental data, in particular in the field of high-energy physics (HEP). First, an introduction to probability theory and basic statistics is given, mainly as reminder from advanced undergraduate studies, yet also in view to clearly distinguish the Frequentist versus Bayesian approaches and interpretations in subsequent applications. More advanced concepts and applications are gradually introduced, culminating in the chapter on upper limits as many applications in HEP concern hypothesis testing, where often the main goal is to provide better and better limits so as to be able to distinguish eventually between competing hypotheses or to rule out some of them altogether. Many worked examples will help newcomers to the field and graduate students to understand the pitfalls in applying theoretical concepts to actual data.

Arvustused

This book is an excellent introduction to statistical methods for data analysis in general, not only in particle physics. The contents are well structured, concise and easily understandable. Particular effort was made in illustrating distinct characters of frequency and Bayesian approaches. I highly recommend this book to anyone who is interested in pursuing data analysis in all fields. (Zhen Mei, zbMATH 1333.81007, 2016)

1 Probability Theory
1(20)
1.1 The Concept of Probability
1(1)
1.2 Classical Probability
2(2)
1.3 Issues with the Generalization to the Continuum
4(2)
1.3.1 The Bertrand's Paradox
5(1)
1.4 Axiomatic Probability Definition
6(1)
1.5 Probability Distributions
6(1)
1.6 Conditional Probability and Independent Events
7(1)
1.7 Law of Total Probability
8(1)
1.8 Average, Variance and Covariance
9(3)
1.9 Variables Transformations
12(1)
1.10 The Bernoulli Process
13(1)
1.11 The Binomial Process
14(4)
1.11.1 Binomial Distribution and Efficiency Estimate
15(3)
1.12 The Law of Large Numbers
18(3)
References
19(2)
2 Probability Distribution functions
21(32)
2.1 Definition of Probability Distribution Function
21(1)
2.2 Average and Variance in the Continuous Case
22(1)
2.3 Cumulative Distribution
23(1)
2.4 Continuous Variables Transformation
24(1)
2.5 Uniform Distribution
24(2)
2.6 Gaussian Distribution
26(1)
2.7 Log-Normal Distribution
27(1)
2.8 Exponential Distribution
28(3)
2.9 Poisson Distribution
31(3)
2.10 Other Distributions Useful in Physics
34(4)
2.10.1 Argus Function
34(1)
2.10.2 Crystal Ball Function
35(2)
2.10.3 Landau Distribution
37(1)
2.11 Central Limit Theorem
38(2)
2.12 Convolution of Probability Distribution Functions
40(1)
2.13 Probability Distribution Functions in More than One Dimension
41(5)
2.13.1 Marginal Distributions
41(4)
2.13.2 Conditional Distributions
45(1)
2.14 Gaussian Distributions in Two or More Dimensions
46(7)
References
51(2)
3 Bayesian Approach to Probability
53(16)
3.1 Bayes' Theorem
53(5)
3.2 Bayesian Probability Definition
58(2)
3.3 Bayesian Probability and Likelihood Functions
60(2)
3.3.1 Repeated Use of Bayes' Theorem and Learning Process
61(1)
3.4 Bayesian Inference
62(3)
3.5 Bayes Factors
65(1)
3.6 Arbitrariness of the Prior Choice
66(1)
3.7 Jeffreys' Prior
67(1)
3.8 Error Propagation with Bayesian Probability
68(1)
References
68(1)
4 Random Numbers and Monte Carlo Methods
69(12)
4.1 Pseudorandom Numbers
69(1)
4.2 Pseudorandom Generators Properties
69(2)
4.3 Uniform Random Number Generators
71(1)
4.3.1 Remapping Uniform Random Numbers
72(1)
4.4 Non Uniform Random Number Generators
72(4)
4.4.1 Gaussian Generators Using the Central Limit Theorem
73(1)
4.4.2 Non-uniform Distribution From Inversion of the Cumulative Distribution
73(2)
4.4.3 Gaussian Numbers Generation
75(1)
4.5 Monte Carlo Sampling
76(3)
4.5.1 Hit-or-Miss Monte Carlo
76(2)
4.5.2 Importance Sampling
78(1)
4.6 Numerical Integration with Monte Carlo Methods
79(2)
References
80(1)
5 Parameter Estimate
81(32)
5.1 Measurements and Their Uncertainties
82(2)
5.2 Nuisance Parameters and Systematic Uncertainties
84(1)
5.3 Estimators
84(1)
5.4 Properties of Estimators
85(2)
5.4.1 Consistency
85(1)
5.4.2 Bias
86(1)
5.4.3 Minimum Variance Bound and Efficiency
86(1)
5.4.4 Robust Estimators
87(1)
5.5 Maximum-Likelihood Method
87(4)
5.5.1 Likelihood Function
88(1)
5.5.2 Extended Likelihood Function
89(2)
5.5.3 Gaussian Likelihood Functions
91(1)
5.6 Errors with the Maximum-Likelihood Method
91(4)
5.6.1 Properties of Maximum-Likelihood Estimators
94(1)
5.7 Minimum χ2 and Least-Squares Methods
95(4)
5.7.1 Linear Regression
97(1)
5.7.2 Goodness of Fit
98(1)
5.8 Error Propagation
99(2)
5.8.1 Simple Cases of Error Propagation
100(1)
5.9 Issues with Treatment of Asymmetric Errors
101(3)
5.10 Binned Samples
104(2)
5.10.1 Minimum-χ2 Method for Binned Histograms
105(1)
5.10.2 Binned Poissonian Fits
105(1)
5.11 Combining Measurements
106(7)
5.11.1 Weighted Average
107(1)
5.11.2 χ2 in n Dimensions
108(1)
5.11.3 The Best Linear Unbiased Estimator
108(3)
References
111(2)
6 Confidence Intervals
113(10)
6.1 Neyman's Confidence Intervals
113(3)
6.1.1 Construction of the Confidence Belt
113(2)
6.1.2 Inversion of the Confidence Belt
115(1)
6.2 Binomial Intervals
116(1)
6.3 The "Flip-Flopping" Problem
117(2)
6.4 The Unified Feldman--Cousins Approach
119(4)
References
121(2)
7 Hypothesis Tests
123(14)
7.1 Introduction to Hypothesis Tests
123(3)
7.2 Fisher's Linear Discriminant
126(2)
7.3 The Neyman--Pearson Lemma
128(1)
7.4 Likelihood Ratio Discriminant
129(1)
7.5 Kolmogorov--Smirnov Test
129(2)
7.6 Wilks' Theorem
131(2)
7.7 Likelihood Ratio in the Search for a New Signal
133(4)
References
135(2)
8 Upper Limits
137
8.1 Searches for New Phenomena: Discovery and Upper Limits
137(1)
8.2 Claiming a Discovery
138(3)
8.2.1 The p-Value
138(1)
8.2.2 Significance
139(1)
8.2.3 Significance and Discovery
140(1)
8.3 Excluding a Signal Hypothesis
141(1)
8.4 Significance and Parameter Estimates Using Likelihood Ratio
141(2)
8.4.1 Significance Evaluation with Toy Monte Carlo
142(1)
8.5 Definitions of Upper Limits
143(1)
8.6 Poissonian Counting Experiments
143(1)
8.6.1 Simplified Significance Evaluation for Counting Experiments
144(1)
8.7 Bayesian Approach
144(3)
8.7.1 Bayesian Upper Limits for Poissonian Counting
145(1)
8.7.2 Limitations of the Bayesian Approach
146(1)
8.8 Frequentist Upper Limits
147(6)
8.8.1 The Counting Experiment Case
148(1)
8.8.2 Upper Limits from Neyman's Confidence Intervals
149(1)
8.8.3 Frequentist Upper Limits on Discrete Variables
149(2)
8.8.4 Feldman--Cousins Upper Limits for Counting Experiments
151(2)
8.9 Can Frequentist and Bayesian Upper Limits Be "Unified"?
153(1)
8.10 Modified Frequentist Approach: The CLs Method
154(3)
8.11 Incorporating Nuisance Parameters and Systematic Uncertainties
157(2)
8.11.1 Nuisance Parameters with the Bayesian Approach
157(1)
8.11.2 Hybrid Treatment of Nuisance Parameters
158(1)
8.12 Upper Limits Using the Profile Likelihood
159(1)
8.13 Variations of Profile-Likelihood Test Statistics
160(9)
8.13.1 Test Statistic for Positive Signal Strength
161(1)
8.13.2 Test Statistics for Discovery
161(1)
8.13.3 Test Statistics for Upper Limits
161(1)
8.13.4 Higgs Test Statistic
162(1)
8.13.5 Asymptotic Approximations
162(7)
8.14 The Look-Elsewhere Effect
169
8.14.1 Trial Factors
170(1)
References
171