Fundamentals of Statistical Inference

This book serves as a concise and reader-friendly, yet rigorous and thought-provoking introduction to the field of statistical inference. As opposed to classical books on mathematical statistics, where there is a strong emphasis on proofs, this book focuses on developing statistical thinking, intuitive understandings of the subject, and specific applications of statistical inference in data science. As a corollary, though also covered, proofs will not be of paramount importance in the book. Their main role will be to provide the intuition and rationale behind the corresponding methods. The focus is on methods of statistical inference and their scope and limitations for real-world applications. On the other hand, statistical inference is not simply a toolbox that contains ready-made answers to all data-related questions. Almost always, as in solving engineering problems, statistical inference and analysis of new data require adjustment of existing tools or even developing completely new methods. To enable readers to modify existing methods and develop new ones, the book not only explains how the standard methods work, but also why, when, and under what assumptions. All chapters include end-of-chapter problems, with solutions provided at the end of the book. One of the goals of the book is to serve as an introductory text on statistical inference that can be used for teaching a semester-long course. The book is suitable for future and junior data scientists, data analysts, and industry researchers, as well as graduate and upper undergraduate students in computing and mathematical sciences, and master's and Ph.D. students in non-mathematical sciences and engineering. While familiarity with probability is assumed, readers need no prior knowledge of statistics.