Essentials of Statistical Inference: (Series Number 16 Cambridge Series in Statistical and Probabilistic Mathematics)

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.

Table of Contents:
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.

About the Author :
G. A. Young is Professor of Statistics at Imperial College London. R. L. Smith is Mark L. Reed Distinguished Professor of Statistics at the University of North Carolina, Chapel Hill.

Review :
'This is a delightful book! It gives a well-written exposure to inference issues in statistics, very suitable for a first-year graduate course … The authors present the material in a very good pedagogical manner. The examples are excellent, and the exercises are very instructive … very much up to date and includes recent developments in the field.' MAA Reviews 'This is a solid book, ideal for advanced classes in the mathematical justification for statistical inference.' Journal of Recreational Mathematics 'I wish that I had had such a textbook during my student days … this new book presents the core ideas of statistical inference in the unifying framework of decision theory and includes a fruitful discussion of the different foundational standpoints (Bayesian, Fisherian and frequentist) … [it is] sufficiently precise to satisfy a mathematician and yet omitting too much technical detail that could hide the core of the ideas. Carefully selected examples from a rainbow of application areas such as baseball, coal-mining disasters or gene expression data make it even more enjoyable to read … this book is a very nice graduate level textbook.' Journal of the Royal Statistical Society '[This] book gives a clear and comprehensive account of the basic elements of statistical theory. It should make a good text for an advanced course on statistical inference … Students will find it informative and challenging.' ISI Short Book Reviews 'Essentials of Statistical Inference is a book worth having.' Jane L. Harvill, Journal of the American Statistical Association 'The book is comprehensively written without dwelling in unnecessary details.' Iris Pigeot, Biometrics '… gives a clear and comprehensive account of the basic elements of statistical theory … a good text for an advanced course on statistical inference.' Publication of the International Statistical Institute '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