Principles of Statistical Analysis: Learning from Randomized Experiments

ISBN-13: 9781108747448 / Angielski / Miękka / 2022 / 400 str.

San Diego) Ery Arias-Castro (University of California

Opis

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.

Recenzje

'This text is highly recommended for undergraduate students wanting to grasp the key ideas of modern data analysis. Arias-Castro achieves something that is rare in the art of teaching statistical science - he uses mathematical language in an intelligible and highly helpful way, without surrendering key intuitions of statistics to formalism and proof. In this way, the reader can get through an impressive amount of material without, however, ever getting into muddy waters.' Richard Nickl, Statistical Laboratory, Cambridge University

Spis treści

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.