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Concise account of main approaches; first textbook to synthesize modern computation with basic theory.This engaging textbook introduces the key ideas behind drawing formal inferences from data. Aimed at advanced undergraduates and graduate students in mathematics and related disciplines, it is a concise account of the main approaches to inference, with particular emphasis on the contrasts between them. It is the first textbook to synthesize contemporary material on computational topics with basic mathematical theory. Numerous extended examples apply formal inference techniques to real data, while historical commentary sketches the development of the subject. Each chapter ends with a set of accessible problems.This engaging textbook introduces the key ideas behind drawing formal inferences from data. Aimed at advanced undergraduates and graduate students in mathematics and related disciplines, it is a concise account of the main approaches to inference, with particular emphasis on the contrasts between them. It is the first textbook to synthesize contemporary material on computational topics with basic mathematical theory. Numerous extended examples apply formal inference techniques to real data, while historical commentary sketches the development of the subject. Each chapter ends with a set of accessible problems.This 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 basic mathematical theory as well as more advanced material, including such contemporary topics as Bayesian computation, higher-order likelihood theory, predictive inference, bootstrap methods, and conditional inference.Preface; Introduction; 1. Decision theory; 2. Bayesian methods; 3. Hypothesis testing; 4. Special models; 5. Sufficiency and completeness; 6. Two-

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