"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…mehr
"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"--Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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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