Principles of Statistical Analysis

Erscheinungsjahr 2022
ISBN: 978-1-108-74744-8
Verlag: Cambridge University Press

Buch, Englisch, 400 Seiten, Paperback, Format (B × H): 152 mm x 229 mm, Gewicht: 589 g

Reihe: Institute of Mathematical Statistics Textbooks

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.

Autoren/Hrsg.

Arias-Castro, Ery

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Informationstheorie, Kodierungstheorie
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken Automatische Datenerfassung, Datenanalyse
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Forschungsmethodik, Wissenschaftliche Ausstattung
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen

Inhaltsverzeichnis

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.

Über Autor(innen)

Arias-Castro, Ery
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 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.