Statistical Methods for Data Analysis in Particle Physics

Description

This concise set of course-based notes 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). First, the book provides 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. More advanced concepts and applications are gradually introduced, culminating in the chapter on both discoveries and upper limits, as many applications in HEP concern hypothesis testing, where the main goal is often to provide better and better limits so as to eventually be able to distinguish between competing hypotheses, or to rule out some of them altogether. Many worked-out examples will help newcomers to the field and graduate students alike understand the pitfalls involved in applying theoretical concepts to actual data. This new second edition significantly expands on the original material, with more background content (e.g. the Markov Chain Monte Carlo method, best linear unbiased estimator), applications (unfolding and regularization procedures, control regions and simultaneous fits, machine learning concepts) and examples (e.g. look-elsewhere effect calculation). Front Matter ....Pages i-xvi Probability Theory (Luca Lista)....Pages 1-23 Probability Distribution Functions (Luca Lista)....Pages 25-58 Bayesian Approach to Probability (Luca Lista)....Pages 59-80 Random Numbers and Monte Carlo Methods (Luca Lista)....Pages 81-95 Parameter Estimate (Luca Lista)....Pages 97-127 Combining Measurements (Luca Lista)....Pages 129-141 Confidence Intervals (Luca Lista)....Pages 143-154 Convolution and Unfolding (Luca Lista)....Pages 155-174 Hypothesis Tests (Luca Lista)....Pages 175-204 Discoveries and Upper Limits (Luca Lista)....Pages 205-249 Back Matter ....Pages 251-257