Kauermann G., Küchenhoff H., Heumann C. Statistical Foundations, Reasoning and Inference: For Science and Data Science

Springer, 2021. — 361 p. — (Springer Series in Statistics). — ISBN 978-3-030-69826-3.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.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