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.
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.
Ery Arias-Castro is a professor in the Department of Mathematics and in the Hal¿c¿ölu 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.
Inhaltsangabe
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.
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.
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