Principles of Statistical Analysis
Learning from Randomized Experiments

This concise course in data analysis and inference for the mathematically literate builds on survey sampling and designed experiments.

Ery Arias-Castro (Author)

9781108747448, Cambridge University Press

Paperback / softback, published 25 August 2022

400 pages
22.8 x 15.2 x 2.1 cm, 0.53 kg

'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

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.

Subject Areas: Machine learning [UYQM], Data capture & analysis [UNC], Mathematical & statistical software [UFM], Probability & statistics [PBT], Research methods: general [GPS], Information theory [GPF]