Название: Statistical Methods for Data Analysis: With Applications in Particle Physics, Third Edition
Автор: Luca Lista
Издательство: Springer
Год: 2023
Страниц: 358
Язык: английский
Формат: pdf (true)
Размер: 32.8 MB

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.

Machine Learning is a rapidly developing field of Computer Science. It provides classes of algorithms that automatically learn from data to make predictions that are useful in many applications, in both science and society at large. Progress in computing technologies allows to implement complex and advanced Machine Learning algorithms that are currently used in a vast number of fields, such as image recognition, written text and speech recognition, human language translation, e-mail spam detection, self-driving car, social media, customized advertisements, and more, including of course applications for particle physics. In several problems, such as classifying images or playing board games, Machine Learning algorithms already outperform humans.

Unlike more traditional computing algorithms, Machine Learning methods define data models that are not hard-coded into an explicit software program, and the computer learns the structure of the model from data itself. In general, Machine Learning algorithms implement very generic and possibly complex parametric models. After a learning phase, Machine Learning algorithms provide outputs that addresses the desired problem.

Many of the limitations of more traditional algorithms have been recently overcome thanks to modifications of the network models and the training algorithms. Recent software algorithms are now able to manage several hidden layers and a relatively large numbers of nodes per layer, with up-to-date computing technologies, for cases that were intractable with traditional algorithms. Those techniques are called Deep Learning, in the sense that they allow to use deeper network structures in terms of the number of hidden layers. The possibility to manage complex network architectures allows to define more advanced classes of models that can manage a richer variety of input data with many more features compared to traditional neural networks. In this way, deep neural networks can address more complex problems and perform new tasks. For this reason, Deep Learning has recently become popular for advanced applications such as the capability to identify faces in an image, or human speech in sound recording, and has widely expanded the fields of applicability of Machine Learning.

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.