Introduction to Probability and Inference

Probability is a fundamental concept in physics because the outcome of experiments is determined by random processes. Different approaches to probability are introduced: classical probability, frequentist and Bayesian approaches, that are more extensively discussed in dedicated chapters. The problem to generalize classical probability to the continuum is discussed, and the axiomatic approach to probability due to Kolmogorov is introduced. The general problem of inference is introduced, with the two main interpretations under the frequentist and the Bayesian approaches. Parameters of interest and nuisance parameters, required to treat systematic uncertainties, are defined.