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This concise course in principled data analysis for the mathematically literate uses survey sampling and designed experiments as a foundation for statistical inference. Covering essentials for advanced undergraduates and selected topics typically taught at the graduate level, its 700 problems - many computational - build understanding and skills.
List of contents
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.
About the author
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.
Summary
This concise course in principled data analysis for the mathematically literate uses survey sampling and designed experiments as a foundation for statistical inference. Covering essentials for advanced undergraduates and selected topics typically taught at the graduate level, its 700 problems – many computational – build understanding and skills.
