## Statistical Methods for Data Analysis in Particle PhysicsThis 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. |

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### Contents

1 | |

2 Probability Distribution Functions | 20 |

3 Bayesian Approach to Probability | 53 |

4 Random Numbers and Monte Carlo Methods | 69 |

5 Parameter Estimate | 81 |

6 Confidence Intervals | 112 |

7 Hypothesis Tests | 123 |

8 Upper Limits | 137 |

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### Common terms and phrases

2lnL algorithms approximation assuming asymmetric errors asymptotic Bayes Bayes factor Bayesian approach Bayesian probability binomial binomial distribution combination computed conditional probability confidence belt confidence interval considered corresponding data sample defined detector determine different values discussed in Sect distributed according equal evaluated Example expected background exponential distribution Feldman–Cousins frequentist approach Gaussian distribution Gaussian PDF given ıÂ large number likelihood function likelihood ratio maximum-likelihood estimate muon Neyman normalization nuisance parameters number of events number of observed nX iD1 obtained outcomes p-value P.AjB parameter Â parameter of interest particle PDF model Physics Poisson distribution Poissonian posterior probability prior PDF prior probability problem profile likelihood pseudorandom random extractions random number random variable result shown in Fig signal strength signal yield significance standard deviation test statistic theorem transformation two-dimensional uncertainty uniform uniformly distributed unknown parameters upper limit variance zero