Principles of Data Analysis

Abstract

What this book hopes to convey are ways of thinking (= principles) about data analysis problems, and how a small number of ideas are enough for a large number of applications. The material is organized into eight chapters: (1) Basic probability theory, what it is with the Bayesians versus the Frequentists, and a bit about why quantum mechanics is weird (Bell's theorem).(2) Binomial and Poisson distributions, and some toy problems introducing the key ideas of parameter fitting and model comparison.(3) The central limit theorem, and why it makes Gaussians ubiquitous, from counting statistics to share prices.(4) An interlude on Monte-Carlo algorithms.(5) Least squares, and related things like the chi^2 test and error propagation. [Including the old problem of fitting a straight line amid errors in both x and y.](6) Distribution function fitting and comparison, and why the Kolmogorov-Smirnov test and variants of it with even longer names are not really arcane. [Sample problem: invent your own KS-like statistic.](7) Entropy in information theory and in image reconstruction.(8) Thermodynamics and statistical physics reinterpreted as data analysis problems.As you see, we are talking about data analysis in its broadest, most general, sense.