ABSTRACT
Statistical models and methods are the basis for many parts of music data analysis. In this chapter we will lay the statistical foundations for the methods described in the next chapters. An overview is given over the most important notions and theorems in statistics, needed in this book. The notion of probability is introduced as well as random variables. We will define, characterize and represent stochastic distributions in general and give examples relevant for music data analysis. We will show how to estimate unknown parameters and how to test hypotheses on the distribution of variables. Typical statistical models for the relationship between different random variables will be introduced, and the estimation of their unknown parameters and the properties of predictions from such models will be discussed. We will introduce the most important statistical models for signal analysis, namely time series models and, finally, a first impression of dimension reduction methods will be given.
