Principles of statistical analysis : learning from randomized experiments
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Bibliographic Information
Principles of statistical analysis : learning from randomized experiments
（Institute of Mathematical Statistics textbooks, 15）
Cambridge University Press, 2022
- : pbk
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Note
Includes bibliographical references (p. 371-383) and index
Description and Table of Contents
Description
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.
Table 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.
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