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

PrefaceThis book aims to provide a concise but comprehensive account of the essential elements ofstatistical inference and theory. It is designed to be used as a text for courses on statisticaltheory for students of mathematics or statistics at the advanced undergraduate or Masterslevel (UK) or the first-year graduate level (US), or as a reference for researchers in otherfields seeking a concise treatment of the key concepts of and approaches to statisticalinference. It is intended to give a contemporary and accessible account of procedures usedto draw formal inference from data.The book focusses on a clear presentation of the main concepts and results underlyingdifferent frameworks of inference, with particular emphasis on the contrasts amongfrequentist, Fisherian and Bayesian approaches. It provides a description of basic materialon these main approaches to inference, as well as more advanced material on recentdevelopments in statistical theory, including higher-order likelihood inference, bootstrapmethods, conditional inference and predictive inference. It places particular emphasis oncontemporary computational ideas, such as applied in bootstrap methodology and Markovchain Monte Carlo techniques of Bayesian inference. Throughout, the text concentrateson concepts, rather than mathematical detail, but every effort has been made to presentthe key theoretical results in as precise and rigorous a manner as possible, consistent withthe overall mathematical level of the book. The book contains numerous extended examplesof application of contrasting inference techniques to real data, as well as selectedhistorical commentaries. Each chapter concludes with an accessible set of problems andexercises.Prerequisites for the book are calculus, linear algebra and some knowledge of basicprobability (including ideas such as conditional probability, transformations of densitiesetc., though not measure theory). Some previous familiarity with the objectives of andmain approaches to statistical inference is helpful, but not essential. Key mathematical andprobabilistic ideas are reviewed in the text where appropriate. 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. G. A. Young, R. L. Smith. Title From Publisher's Bibliographic System (viewed On 01 Jun 2016). Mode Of Access: World Wide Web. 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. "Written in an informal style, this concise text provides both basic material on the main approaches to inference, as well as more advanced material on modern developments in statistical theory, including: contemporary 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." "Based to a large extent on lectures given at the University of Cambridge over a number of years, the material has been polished by student feedback. 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."--BOOK JACKET 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. Aimed at advanced undergraduates and graduate students in mathematics and related disciplines, this engaging textbook gives 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

concise Account Of Main Approaches; First Textbook To Synthesize Modern Computation With Basic Theory.