Essentials of Statistical Inference

This textbook presents the concepts and results underlying the Bayesian, frequentist, and Fisherian approaches to statistical inference.

G. A. Young (Author), R. L. Smith (Author)

9780521839716, Cambridge University Press

Hardback, published 25 July 2005

236 pages, 92 exercises
25.4 x 17.8 x 1.4 cm, 0.63 kg

'The text presents the main concepts and results underlying different frameworks of inference, with particular emphasis on the contrasts among frequentist, Fisherian, and Bayesian approaches. It provides a depiction of basic material on these main approaches to inference, as well as more advanced material on recent developments in statistical theory, including higher-order likelihood inference, bootstrap methods, conditional inference, and predictive inference.' Zentralblatt MATH

Aimed at advanced undergraduate and graduate students in mathematics and related disciplines, this book presents the concepts and results underlying the Bayesian, frequentist and Fisherian approaches, with particular emphasis on the contrasts between them. Computational ideas are explained, as well as basic mathematical theory. Written in a lucid and informal style, this concise text provides both basic material on the main approaches to inference, as well as more advanced material on developments in statistical theory, including: material on Bayesian computation, such as MCMC, higher-order likelihood theory, predictive inference, bootstrap methods and conditional inference. It contains numerous extended examples of the application of formal inference techniques to real data, as well as historical commentary on the development of the subject. Throughout, the text concentrates on concepts, rather than mathematical detail, while maintaining appropriate levels of formality. Each chapter ends with a set of accessible problems.

1. Introduction
2. Decision theory
3. Bayesian methods
4. Hypothesis testing
5. Special models
6. Sufficiency and completeness
7. Two-sided tests and conditional inference
8. Likelihood theory
9. Higher-order theory
10. Predictive inference
11. Bootstrap methods.

Subject Areas: Probability & statistics [PBT]