Essentials of Statistical Inference
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Short description/annotationConcise account of main approaches; first textbook to synthesize modern computation with basic theory.Main descriptionThis engaging textbook presents the concepts and results underlying the Bayesian, frequentist and Fisherian approaches to statistical inference, with particular emphasis on the contrasts between them. Aimed at advanced undergraduates and graduate students in mathematics and related disciplines, it covers in a concise treatment both basic mathematical theory and more advanced material, including such contemporary topics as Bayesian computation, higher...
Short description/annotation
Concise account of main approaches; first textbook to synthesize modern computation with basic theory.
Main description
This engaging textbook presents the concepts and results underlying the Bayesian, frequentist and Fisherian approaches to statistical inference, with particular emphasis on the contrasts between them. Aimed at advanced undergraduates and graduate students in mathematics and related disciplines, it covers in a concise treatment both basic mathematical theory and more advanced material, including such contemporary topics as Bayesian computation, 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. Some prior knowledge of probability is assumed, while some previous knowledge of the objectives and main approaches to statistical inference would be helpful but is not essential.
Table of contents:
Preface; Introduction; 1. Decision theory; 2. Bayesian methods; 3. Hypothesis testing; 4. Special models; 5. Sufficiency and completeness; 6. Two-sided tests and conditional inference; 7. Likelihood theory; 8. Higher-order theory; 9. Predictive inference; 10. Bootstrap methods; References; Index.
Concise account of main approaches; first textbook to synthesize modern computation with basic theory.
Main description
This engaging textbook presents the concepts and results underlying the Bayesian, frequentist and Fisherian approaches to statistical inference, with particular emphasis on the contrasts between them. Aimed at advanced undergraduates and graduate students in mathematics and related disciplines, it covers in a concise treatment both basic mathematical theory and more advanced material, including such contemporary topics as Bayesian computation, 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. Some prior knowledge of probability is assumed, while some previous knowledge of the objectives and main approaches to statistical inference would be helpful but is not essential.
Table of contents:
Preface; Introduction; 1. Decision theory; 2. Bayesian methods; 3. Hypothesis testing; 4. Special models; 5. Sufficiency and completeness; 6. Two-sided tests and conditional inference; 7. Likelihood theory; 8. Higher-order theory; 9. Predictive inference; 10. Bootstrap methods; References; Index.
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