| Description |
1 online resource (358 p.) |
| Series |
Lecture Notes in Physics ; v.1010 |
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Lecture notes in physics ; 1010.
|
| Contents |
2.12 The Law of Large Numbers -- 2.13 Law of Large Numbers and Frequentist Probability -- References -- 3 Probability Density Functions -- 3.1 Introduction -- 3.2 Definition of Probability Density Function -- 3.3 Statistical Indicators in the Continuous Case -- 3.4 Cumulative Distribution -- 3.5 Continuous Transformations of Variables -- 3.6 Marginal Distributions -- 3.7 Uniform Distribution -- 3.8 Gaussian Distribution -- 3.9 [chi]2 Distribution -- 3.10 Log Normal Distribution -- 3.11 Exponential Distribution -- 3.12 Gamma Distribution -- 3.13 Beta Distribution -- 3.14 Breit-Wigner Distribution |
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Intro -- Preface -- Contents -- List of Figures -- List of Tables -- List of Examples -- 1 Introduction to Probability and Inference -- 1.1 Why Probability Matters to a Physicist -- 1.2 Random Processes and Probability -- 1.3 Different Approaches to Probability -- 1.4 Classical Probability -- 1.5 Problems with the Generalization to the Continuum -- 1.6 The Bertrand's Paradox -- 1.7 Axiomatic Probability Definition -- 1.8 Conditional Probability -- 1.9 Independent Events -- 1.10 Law of Total Probability -- 1.11 Inference -- 1.12 Measurements and Their Uncertainties |
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1.13 Statistical and Systematic Uncertainties -- 1.14 Frequentist vs Bayesian Inference -- References -- 2 Discrete Probability Distributions -- 2.1 Introduction -- 2.2 Joint and Marginal Probability Distributions -- 2.3 Conditional Distributions and Chain Rule -- 2.4 Independent Random Variables -- 2.5 Statistical Indicators: Average, Variance, and Covariance -- 2.6 Statistical Indicators for Finite Samples -- 2.7 Transformations of Variables -- 2.8 The Bernoulli Distribution -- 2.9 The Binomial Distribution -- 2.10 The Multinomial Distribution -- 2.11 The Poisson Distribution |
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3.15 Relativistic Breit-Wigner Distribution -- 3.16 Argus Distribution -- 3.17 Crystal Ball Function -- 3.18 Landau Distribution -- 3.19 Mixture of PDFs -- 3.20 Central Limit Theorem -- 3.21 Probability Distributions in Multiple Dimension -- 3.22 Independent Variables -- 3.23 Covariance, Correlation, and Independence -- 3.24 Conditional Distributions -- 3.25 Gaussian Distributions in Two or More Dimensions -- References -- 4 Random Numbers and Monte Carlo Methods -- 4.1 Pseudorandom Numbers -- 4.2 Properties of Pseudorandom Generators -- 4.3 Uniform Random Number Generators |
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4.4 Inversion of the Cumulative Distribution -- 4.5 Random Numbers Following a Finite Discrete Distribution -- 4.6 Gaussian Generator Using the Central Limit Theorem -- 4.7 Gaussian Generator with the Box-Muller Method -- 4.8 Hit-or-Miss Monte Carlo -- 4.9 Importance Sampling -- 4.10 Numerical Integration with Monte Carlo Methods -- 4.11 Markov Chain Monte Carlo -- References -- 5 Bayesian Probability and Inference -- 5.1 Introduction -- 5.2 Bayes' Theorem -- 5.3 Bayesian Probability Definition -- 5.4 Decomposing the Denominator in Bayes' Formula |
| Summary |
This third edition expands on the original material. Large portions of the text have been reviewed and clarified. More emphasis is devoted to machine learning including more modern concepts and examples. This book provides the reader with the main concepts and tools needed to perform statistical analyses of experimental data, in particular in the field of high-energy physics (HEP). It starts with an introduction to probability theory and basic statistics, mainly intended as a refresher from readers advanced undergraduate studies, but also to help them clearly distinguish between the Frequentist and Bayesian approaches and interpretations in subsequent applications. Following, the author discusses Monte Carlo methods with emphasis on techniques like Markov Chain Monte Carlo, and the combination of measurements, introducing the best linear unbiased estimator. More advanced concepts and applications are gradually presented, including unfolding and regularization procedures, culminating in the chapter devoted to discoveries and upper limits. The reader learns through many applications in HEP where the hypothesis testing plays a major role and calculations of look-elsewhere effect are also presented. Many worked-out examples help newcomers to the field and graduate students alike understand the pitfalls involved in applying theoretical concepts to actual data |
| Notes |
5.5 Bayesian Probability Density and Likelihood Functions |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed May 4, 2023) |
| Subject |
Particles (Nuclear physics) -- Statistical methods
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Particles (Nuclear physics) -- Data processing
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Machine learning.
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Machine learning
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Particles (Nuclear physics) -- Data processing
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Particles (Nuclear physics) -- Statistical methods
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| Form |
Electronic book
|
| ISBN |
9783031199349 |
|
3031199340 |
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