Statistical Foundations, Reasoning and Inference: For Science and Data Science

This textbook covers statistical principles, concepts, and methods for modern data science and analytics, including likelihood-based inference, Bayesian statistics, regression, statistical tests, and uncertainty quantification. It is designed for masters students in data science, statistics, and computer science with a basic understanding of probability theory and is useful for data science practitioners who want to strengthen their statistics skills.

Format: Hardback
Length: 356 pages
Publication date: 01 October 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook offers an in-depth exploration of statistical principles, concepts, and methodologies, which are crucial in modern statistics and data science. It encompasses a wide range of topics, including likelihood-based inference, Bayesian statistics, regression analysis, statistical tests, and the quantification of uncertainty. Furthermore, the book delves into statistical concepts that are essential for contemporary data analytics, such as bootstrapping, modeling of multivariate distributions, missing data analysis, causality analysis, and experimental design principles. The textbook provides ample material for a two-semester course and is designed for master's students in data science, statistics, and computer science who possess a foundational understanding of probability theory. It is also valuable for data science practitioners seeking to enhance their statistical expertise.

The textbook is organized into nine chapters, each dedicated to a specific topic. The first chapter provides an introduction to statistical principles and concepts, including probability theory, random variables, and distributions. It also introduces the basic ideas of hypothesis testing and statistical inference.

Chapter 2 explores likelihood-based inference, which involves using probability distributions to make predictions about unknown quantities. It covers topics such as maximum likelihood estimation, Bayesian inference, and decision theory. Chapter 3 discusses Bayesian statistics, which is an approach that combines probability theory with prior knowledge to make inferences about unknown quantities. It covers topics such as Bayesian inference, Markov chain Monte Carlo methods, and hierarchical modeling.

Chapter 4 covers regression analysis, which is a method for modeling the relationship between a dependent variable and one or more independent variables. It includes topics such as linear regression, multiple linear regression, and nonlinear regression. Chapter 5 explores statistical tests, which are used to determine whether there is a significant difference between groups or between variables. It covers topics such as t-tests, chi-square tests, and ANOVA.

Chapter 6 discusses the quantification of uncertainty, which is an important aspect of statistical analysis. It covers topics such as confidence intervals, hypothesis testing, and Bayesian uncertainty quantification. Chapter 7 explores bootstrapping, which is a method for estimating the uncertainty of statistical estimates. It covers topics such as resampling techniques, bootstrap confidence intervals, and bootstrap percentiles.

Chapter 8 discusses modeling of multivariate distributions, which is a method for describing the distribution of multiple variables. It covers topics such as Gaussian distributions, multinomial distributions, and Poisson distributions. Chapter 9 covers missing data analysis, which is a method for handling data that is missing or incomplete. It covers topics such as imputation, multiple imputation, and Bayesian methods for handling missing data.

In conclusion, this textbook provides a comprehensive introduction to statistical principles, concepts, and methods that are essential in modern statistics and data science. It covers a wide range of topics and is designed for master's students in data science, statistics, and computer science who possess a foundational understanding of probability theory. The book is also valuable for data science practitioners seeking to enhance their statistical expertise.

Weight: 720g
Dimension: 163 x 242 x 28 (mm)
ISBN-13: 9783030698263
Edition number: 1st ed. 2021