Introduction to Statistics and Data Analysis for Physicists

There is a large number of excellent statistic books. Nevertheless, we think that it is justified to complement them by another textbook with the focus on modern applications in nuclear and particle physics. To this end we have included a large number of related examples and figures in the text. We emphasize less the mathematical foundations but appeal to the intuition of the reader. 

Data analysis in modern experiments is unthinkable without simulation techniques. We discuss in some detail how to apply Monte Carlo simulation to parameter estimation, deconvolution, goodness-of-fit tests. We sketch also modern developments like artificial neural nets, bootstrap methods, boosted decision trees and support vector machines. 

Likelihood is a central concept of statistical analysis and its foundation is the likelihood principle. We discuss this concept in more detail than usually done in textbooks and base the treatment of inference problems as far as possible on the likelihood function only, as is common in the majority of the nuclear and particle physics community. In this way point and interval estimation, error propagation, combining results, inference of discrete and continuous parameters are consistently treated. We apply Bayesian methods where the likelihood function is not sufficient to proceed to sensible results, for instance in handling systematic errors, deconvolution problems and in some cases when nuisance parameters have to be eliminated, but we avoid improper prior densities. Goodness-of-fit and significance tests, where no likelihood function exists, are based on standard frequentist methods.