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.

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.