Principles of Statistical Analysis: Learning from Randomized Experiments

Ery Arias-Castro

400 pages, parution le 29/04/2022

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Résumé

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 compact course is written for the mathematically literate reader who wants to learn to analyze data in a principled fashion. The language of mathematics enables clear exposition that can go quite deep, quite quickly, and naturally supports an axiomatic and inductive approach to data analysis. Starting with a good grounding in probability, the reader moves to statistical inference via topics of great practical importance - simulation and sampling, as well as experimental design and data collection - that are typically displaced from introductory accounts. The core of the book then covers both standard methods and such advanced topics as multiple testing, meta-analysis, and causal inference.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.Ery Arias-Castro is a professor in the Department of Mathematics and in the Halicioglu 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 Ecole Normale Superieure de Cachan (now Ecole Normale Superieure Paris-Saclay) in France, as well as a Ph.D. in statistics from Stanford University in the United States.

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Ery Arias-Castro
Parution	29/04/2022
Nb. de pages	400
EAN13	9781108747448

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Principles of Statistical Analysis: Learning from Randomized Experiments

Résumé

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