Statistical Foundations, Reasoning and Inference

This textbook provides a comprehensive introduction to statistical principles, concepts and methods that are essential in modern statistics and data science. The topics covered include likelihood-based inference, Bayesian statistics, regression, statistical tests and the quantification of uncertainty. Moreover, the book addresses statistical ideas that are useful in modern data analytics, including bootstrapping, modeling of multivariate distributions, missing data analysis, causality as well as principles of experimental design. The textbook includes sufficient material for a two-semester course and is intended for master's students in data science, statistics and computer science with a rudimentary grasp of probability theory. It will also be useful for data science practitioners who want to strengthen their statistics skills.

Introduces statistics and data science students to classical and modern statistical concepts Features detailed derivations and explanations of complex statistical methods Includes statistical tools for applied data science, e.g. for missing data or causality

Autorentext
Göran Kauermann is a Professor of Statistics at the Department of Statistics and Chair of the Elite Master's Program in Data Science at the LMU Munich, Germany. He is a recognized expert in applied statistics. He previously served as Editor-in-Chief of AStA Advances in Statistical Analysis, a journal of the German Statistical Society.

Helmut Küchenhoff is a Professor of Statistics at the Department of Statistics and Head of the Statistical Consulting Unit (StaBLab) at the LMU Munich, Germany. He has extensive experience in working on practical statistical projects in science and industry. His teaching focuses on practical work, where students engage in practical projects with real-world problems.

Christian Heumann is a Professor at the Department of Statistics, LMU Munich, Germany, where he teaches students in both the Bachelor's and Master's programs. His research interests include statistical modeling, computational statistics and methods for missing data, also in connection with causal inference. Recently, he has begun exploring statistical methods in natural language processing.

Inhalt

Introduction.- Background in Probability.- Parametric Statistical Models.- Maximum Likelihood Inference.- Bayesian Statistics.- Statistical Decisions.- Regression.- Bootstrapping.- Model Selection and Model Averaging.- Multivariate and Extreme Value Distributions.- Missing and Deficient Data.- Experiments and Causality.