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.

Göran Kauermann is a Professor and holds the Chair of Statistics at the LMU Munich, Germany. He is an internationally recognized expert and the author of numerous publications in the field of applied statistics, including areas of machine learning. He has been the Chair of the German Data Science Society and an Elected Panel Member for statistics and econometrics at the German Research Foundation (DFG) and was the Chair of the German Consortium in Statistics (DAGStat) and Spokesperson of the (Elite) master's program Data Science at LMU Munich. His research interests include quantification of uncertainty, statistical modelling, and network data analysis. He is a co-author of a book on Statistical Foundations, Reasoning and Inference.

Giacomo De Nicola is a Postdoctoral Research Fellow at the Harvard T.H. Chan School of Public Health, Boston, MA, USA. His research focuses on designing, implementing and leveraging modern statistical tools to address real-world problems, with a focus on applications in the socio-economic sciences and public health, including social network modeling, models for monitoring epidemics, and methods for quantifying the impact of crises.

Cornelius Fritz is an Assistant Professor at the School for Computer Science and Statistics at Trinity College Dublin, Ireland. He uses statistics to learn from network data to answer questions posed within the social sciences in uncertain and changing environments and develops novel data analysis techniques by combining statistical and machine learning with substantive theory to bridge the gap between the real and model world.

David Rügamer is an Associate Professor at the LMU Munich, Germany, heading the Munich Uncertainty Quantification AI Lab. He is also an Ellis Member, Associated Fellow of the Konrad Zuse School of Excellence in Reliable AI (relAI), and a Principal Investigator of the Munich Center for Machine Learning (MCML). His current research involves the development of uncertainty quantification for deep learning approaches (using e.g. a Bayesian paradigm), the unification of concepts from statistics and deep learning, and studying overparametrization in neural networks.