{"product_id":"decision-theory-9780471496571","title":"Decision Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eDecision theory provides a formal framework for making logical choices in the face of uncertainty. Given a set of alternatives, a set of consequences, and a correspondence between those sets, decision theory offers conceptually simple procedures for choice. This book presents an overview of the fundamental concepts and outcomes of rational decision making under uncertainty, highlighting the implications for statistical practice.\u003cbr\u003e \u003cbr\u003e \u003cbr\u003e The authors have developed a series of self contained chapters focusing on bridging the gaps between the different fields that have contributed to rational decision making and presenting ideas in a unified framework and notation while respecting and highlighting the different and sometimes conflicting perspectives.\u003cbr\u003e \u003cbr\u003e \u003cbr\u003e This book:\u003cbr\u003e \u003cbr\u003e * Provides a rich collection of techniques and procedures.\u003cbr\u003e * Discusses the foundational aspects and modern day practice.\u003cbr\u003e * Links foundations to practical applications in biostatistics, computer \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“Also anyone interested in learning more about decision theoretic experimental design (a topic of growing interest for example in sequential clinical trials) will find a useful overview and a good starting point for further investigations.”  (\u003ci\u003eStat Papers\u003c\/i\u003e, 2011)\u003c\/p\u003e   \"Decision theory is fundamental to all scientific disciplines., including biostatistics, computer science, economics and engineering. Anyone interested in the whys and wherefores of statistical science will find much to enjoy in this book.\" (Mathematical Reviews, 2011)\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface.\u003cbr\u003e \u003cbr\u003e Acknowledgments.\u003cbr\u003e \u003cbr\u003e 1 Introduction.\u003cbr\u003e \u003cbr\u003e 1.1 Controversies.\u003cbr\u003e \u003cbr\u003e 1.2 A guided tour of decision theory.\u003cbr\u003e \u003cbr\u003e Part One: Foundations.\u003cbr\u003e \u003cbr\u003e 2 Coherence.\u003cbr\u003e \u003cbr\u003e 2.1 The \"Dutch Book\" theorem.\u003cbr\u003e \u003cbr\u003e 2.2 Temporal coherence.\u003cbr\u003e \u003cbr\u003e 2.3 Scoring rules and the axioms of probabilities.\u003cbr\u003e \u003cbr\u003e 2.4 Exercises.\u003cbr\u003e \u003cbr\u003e 3 Utility.\u003cbr\u003e \u003cbr\u003e 3.1 St. Petersburg paradox.\u003cbr\u003e \u003cbr\u003e 3.2 Expected utility theory and the theory of means.\u003cbr\u003e \u003cbr\u003e 3.3 The expected utility principle.\u003cbr\u003e \u003cbr\u003e 3.4 The von Neumann-Morgenstern representation theorem.\u003cbr\u003e \u003cbr\u003e 3.5 Allais' criticism.\u003cbr\u003e \u003cbr\u003e 3.6 Extensions.\u003cbr\u003e \u003cbr\u003e 3.7 Exercises.\u003cbr\u003e \u003cbr\u003e 4 Utility in action.\u003cbr\u003e \u003cbr\u003e 4.1 The \"standard gamble\".\u003cbr\u003e \u003cbr\u003e 4.2 Utility of money.\u003cbr\u003e \u003cbr\u003e 4.3 Utility functions for medical decisions.\u003cbr\u003e \u003cbr\u003e 4.4 Exercises.\u003cbr\u003e \u003cbr\u003e 5 Ramsey and Savage.\u003cbr\u003e \u003cbr\u003e 5.1 Ramsey's theory.\u003cbr\u003e \u003cbr\u003e 5.2 Savage's theory.\u003cbr\u003e \u003cbr\u003e 5.3 Allais revisited.\u003cbr\u003e \u003cbr\u003e 5.4 Ellsberg paradox.\u003cbr\u003e \u003cbr\u003e 5.5 Exercises.\u003cbr\u003e \u003cbr\u003e 6 State independence.\u003cbr\u003e \u003cbr\u003e 6.1 Horse lotteries.\u003cbr\u003e \u003cbr\u003e 6.2 State-dependent utilities.\u003cbr\u003e \u003cbr\u003e 6.3 State-independent utilities.\u003cbr\u003e \u003cbr\u003e 6.4 Anscombe-Aumann representation theorem.\u003cbr\u003e \u003cbr\u003e 6.5 Exercises.\u003cbr\u003e \u003cbr\u003e Part Two Statistical Decision Theory.\u003cbr\u003e \u003cbr\u003e 7 Decision functions.\u003cbr\u003e \u003cbr\u003e 7.1 Basic concepts.\u003cbr\u003e \u003cbr\u003e 7.2 Data-based decisions.\u003cbr\u003e \u003cbr\u003e 7.3 The travel insurance example.\u003cbr\u003e \u003cbr\u003e 7.4 Randomized decision rules.\u003cbr\u003e \u003cbr\u003e 7.5 Classification and hypothesis tests.\u003cbr\u003e \u003cbr\u003e 7.6 Estimation.\u003cbr\u003e \u003cbr\u003e 7.7 Minimax-Bayes connections.\u003cbr\u003e \u003cbr\u003e 7.8 Exercises.\u003cbr\u003e \u003cbr\u003e 8 Admissibility.\u003cbr\u003e \u003cbr\u003e 8.1 Admissibility and completeness.\u003cbr\u003e \u003cbr\u003e 8.2 Admissibility and minimax.\u003cbr\u003e \u003cbr\u003e 8.3 Admissibility and Bayes.\u003cbr\u003e \u003cbr\u003e 8.4 Complete classes.\u003cbr\u003e \u003cbr\u003e 8.5 Using the same ± level across studies with different sample sizes is inadmissible.\u003cbr\u003e \u003cbr\u003e 8.6 Exercises.\u003cbr\u003e \u003cbr\u003e 9 Shrinkage.\u003cbr\u003e \u003cbr\u003e 9.1 The Stein effect.\u003cbr\u003e \u003cbr\u003e 9.2 Geometric and empirical Bayes heuristics.\u003cbr\u003e \u003cbr\u003e 9.3 General shrinkage functions.\u003cbr\u003e \u003cbr\u003e 9.4 Shrinkage with different likelihood and losses.\u003cbr\u003e \u003cbr\u003e 9.5 Exercises.\u003cbr\u003e \u003cbr\u003e 10 Scoring rules.\u003cbr\u003e \u003cbr\u003e \u003cbr\u003e 10.1 Betting and forecasting.\u003cbr\u003e \u003cbr\u003e 10.2 Scoring rules.\u003cbr\u003e \u003cbr\u003e 10.3 Local scoring rules.\u003cbr\u003e \u003cbr\u003e 10.4 Calibration and refinement.\u003cbr\u003e \u003cbr\u003e 10.5 Exercises.\u003cbr\u003e \u003cbr\u003e 11 Choosing models.\u003cbr\u003e \u003cbr\u003e 11.1 The \"true model\" perspective.\u003cbr\u003e \u003cbr\u003e 11.2 Model elaborations.\u003cbr\u003e \u003cbr\u003e 11.3 Exercises.\u003cbr\u003e \u003cbr\u003e Part Three Optimal Design.\u003cbr\u003e \u003cbr\u003e 12 Dynamic programming.\u003cbr\u003e \u003cbr\u003e 12.1 History.\u003cbr\u003e \u003cbr\u003e 12.2 The travel insurance example revisited.\u003cbr\u003e \u003cbr\u003e 12.3 Dynamic programming.\u003cbr\u003e \u003cbr\u003e 12.4 Trading off immediate gains and information.\u003cbr\u003e \u003cbr\u003e 12.5 Sequential clinical trials.\u003cbr\u003e \u003cbr\u003e 12.6 Variable selection in multiple regression.\u003cbr\u003e \u003cbr\u003e 12.7 Computing.\u003cbr\u003e \u003cbr\u003e 12.8 Exercises.\u003cbr\u003e \u003cbr\u003e 13 Changes in utility as information.\u003cbr\u003e \u003cbr\u003e 13.1 Measuring the value of information.\u003cbr\u003e \u003cbr\u003e 13.2 Examples.\u003cbr\u003e \u003cbr\u003e 13.3 Lindley information.\u003cbr\u003e \u003cbr\u003e 13.4 Minimax and the value of information.\u003cbr\u003e \u003cbr\u003e 13.5 Exercises.\u003cbr\u003e \u003cbr\u003e 14 Sample size.\u003cbr\u003e \u003cbr\u003e 14.1 Decision-theoretic approaches to sample size.\u003cbr\u003e \u003cbr\u003e 14.2 Computing.\u003cbr\u003e \u003cbr\u003e 14.3 Examples.\u003cbr\u003e \u003cbr\u003e 14.4 Exercises.\u003cbr\u003e \u003cbr\u003e 15 Stopping.\u003cbr\u003e \u003cbr\u003e 15.1 Historical note.\u003cbr\u003e \u003cbr\u003e 15.2 A motivating example.\u003cbr\u003e \u003cbr\u003e 15.3 Bayesian optimal stopping.\u003cbr\u003e \u003cbr\u003e 15.4 Examples.\u003cbr\u003e \u003cbr\u003e 15.5 Sequential sampling to reduce uncertainty.\u003cbr\u003e \u003cbr\u003e 15.6 The stopping rule principle.\u003cbr\u003e \u003cbr\u003e 15.7 Exercises.\u003cbr\u003e \u003cbr\u003e Appendix.\u003cbr\u003e \u003cbr\u003e A.1 Notation.\u003cbr\u003e \u003cbr\u003e A.2 Relations.\u003cbr\u003e \u003cbr\u003e A.3 Probability (density) functions of some distributions.\u003cbr\u003e \u003cbr\u003e A.4 Conjugate updating.\u003cbr\u003e \u003cbr\u003e References.\u003cbr\u003e \u003cbr\u003e Index.","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402616086871,"sku":"9780471496571","price":71.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471496571.jpg?v=1730480988","url":"https:\/\/bookcurl.com\/products\/decision-theory-9780471496571","provider":"Book Curl","version":"1.0","type":"link"}