Statistical Inference

Abstract

This first chapter will briefly review basic statistical concepts, ways of thinking, and ideas that will reoccur throughout the book, as well as some general principles and mathematical techniques for handling these. In this sense it will lay out some of the ground on which statistical methods developed in later chapters rest. It is assumed that the reader is basically familiar with core concepts in probability theory and statistics, such as expectancy values, probability distributions like the binomial or Gaussian, Bayes’ rule, or analysis of variance. The presentation given in this chapter is quite condensed and mainly serves to summarize and organize key facts and concepts required later, as well as to put special emphasis on some topics. Although this chapter is self-contained, if the reader did not pass through an introductory statistics course so far, it may be advisable to consult introductory chapters in a basic statistics textbook first (very readable introductions are provided, for instance, by Hays 1994, or Wackerly et al. 2007; Kass et al. 2014, in particular, give a highly recommended introduction specifically targeted to a neuroscience readership). More generally, it is remarked here that the intention of the first six chapters was more to extract and summarize essential points and concepts from the literature referred to.