Statistics—Coping with Uncertainty

This undergraduate textbook provides a novel introduction to the concepts of statistical inference. Approached from a fresh information-theoretic perspective, statistics is presented as a scientific discipline that offers concepts for handling uncertainty, which is a common thread throughout the book. This framing naturally leads readers to key ideas such as maximum likelihood estimation, statistical testing, regression, and model selection. Uncertainty can be explored through simulation-based approaches, which are given particular emphasis in the book and open the door to Bayesian inference, also discussed in the text. Beyond standard scenarios, the book extends classical methods to handle extreme and multivariate data as well as data that deviate from the independent and identically distributed assumption. By drawing parallels to methods from machine learning, the book demonstrates how modern statistical thinking complements and enriches machine learning methodologies. The book presents the versatility of statistical ideas, concepts, and questions in a form that is easy to understand and digest, without neglecting the methodological and mathematical foundations of statistics. Each chapter is complemented by exercises to support learning, and examples in the book are accompanied by computer code and additional material available online. The text is intended for a two-semester course in statistical inference and assumes prior knowledge of fundamental ideas of probability theory. Given its fresh approach, it will equally appeal to aspiring statisticians at the bachelor’s level and to computer scientists in the field of machine learning.