Principles of Statistical Analysis

Ery Arias-Castro is a professor in the Department of Mathematics and in the Halıcıoğlu Data Science Institute at the University of California, San Diego, where he specializes in theoretical statistics and machine learning. His education includes a bachelor's degree in mathematics and a master's degree in artificial intelligence, both from École Normale Supérieure de Cachan (now École Normale Supérieure Paris-Saclay) in France, as well as a Ph.D. in statistics from Stanford University in the United States.

'With the rapid development of data-driven decision making, statistical methods have become indispensable in countless domains of science, engineering, and management science, to name a few. Ery Arias-Castro's excellent text gives a self-contained and remarkably broad exposition of the current diversity of concepts and methods developed to tackle the challenges of data science. Simply put, everyone serious about understanding the theory behind data science should be exposed to the topics covered in this book.' Philippe Rigollet, Department of Mathematics, Massachusetts Institute of Technology

• Preface; Acknowledgments; Part I. Elements of Probability Theory: 1. Axioms of probability theory; 2. Discrete probability spaces; 3. Distributions on the real line; 4. Discrete distributions; 5. Continuous distributions; 6. Multivariate distributions; 7. Expectation and concentration; 8. Convergence of random variables; 9. Stochastic processes; Part II. Practical Considerations: 10. Sampling and simulation; 11. Data collection; Part III. Elements of Statistical Inference: 12. Models, estimators, and tests; 13. Properties of estimators and tests; 14. One proportion; 15. Multiple proportions; 16. One numerical sample; 17. Multiple numerical samples; 18. Multiple paired numerical samples; 19. Correlation analysis; 20. Multiple testing; 21. Regression analysis; 22. Foundational issues; References; Index.