%{search_type} search results

• Preface. Acknowledgments.
• 1 Introduction. 1.1 Controversies. 1.2 A guided tour of decision theory. Part One: Foundations.
• 2 Coherence. 2.1 The "Dutch Book" theorem. 2.2 Temporal coherence. 2.3 Scoring rules and the axioms of probabilities. 2.4 Exercises.
• 3 Utility. 3.1 St. Petersburg paradox. 3.2 Expected utility theory and the theory of means. 3.3 The expected utility principle. 3.4 The von Neumann-Morgenstern representation theorem. 3.5 Allais' criticism. 3.6 Extensions. 3.7 Exercises.
• 4 Utility in action. 4.1 The "standard gamble". 4.2 Utility of money. 4.3 Utility functions for medical decisions. 4.4 Exercises.
• 5 Ramsey and Savage. 5.1 Ramsey's theory. 5.2 Savage's theory. 5.3 Allais revisited. 5.4 Ellsberg paradox. 5.5 Exercises.
• 6 State independence. 6.1 Horse lotteries. 6.2 State-dependent utilities. 6.3 State-independent utilities. 6.4 Anscombe-Aumann representation theorem. 6.5 Exercises. Part Two Statistical Decision Theory.
• 7 Decision functions. 7.1 Basic concepts. 7.2 Data-based decisions. 7.3 The travel insurance example. 7.4 Randomized decision rules. 7.5 Classification and hypothesis tests. 7.6 Estimation. 7.7 Minimax-Bayes connections. 7.8 Exercises.
• 8 Admissibility. 8.1 Admissibility and completeness. 8.2 Admissibility and minimax. 8.3 Admissibility and Bayes. 8.4 Complete classes. 8.5 Using the same alpha level across studies with different sample sizes is inadmissible. 8.6 Exercises.
• 9 Shrinkage. 9.1 The Stein effect. 9.2 Geometric and empirical Bayes heuristics. 9.3 General shrinkage functions. 9.4 Shrinkage with different likelihood and losses. 9.5 Exercises.
• 10 Scoring rules. 10.1 Betting and forecasting. 10.2 Scoring rules. 10.3 Local scoring rules. 10.4 Calibration and refinement. 10.5 Exercises.
• 11 Choosing models. 11.1 The "true model" perspective. 11.2 Model elaborations. 11.3 Exercises. Part Three Optimal Design.
• 12 Dynamic programming. 12.1 History. 12.2 The travel insurance example revisited. 12.3 Dynamic programming. 12.4 Trading off immediate gains and information. 12.5 Sequential clinical trials. 12.6 Variable selection in multiple regression. 12.7 Computing. 12.8 Exercises.
• 13 Changes in utility as information. 13.1 Measuring the value of information. 13.2 Examples. 13.3 Lindley information. 13.4 Minimax and the value of information. 13.5 Exercises.
• 14 Sample size. 14.1 Decision-theoretic approaches to sample size. 14.2 Computing. 14.3 Examples. 14.4 Exercises.
• 15 Stopping. 15.1 Historical note. 15.2 A motivating example. 15.3 Bayesian optimal stopping. 15.4 Examples. 15.5 Sequential sampling to reduce uncertainty. 15.6 The stopping rule principle. 15.7 Exercises. Appendix. A.1 Notation. A.2 Relations. A.3 Probability (density) functions of some distributions. A.4 Conjugate updating. References. Index.
• (source: Nielsen Book Data)

Decision 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. 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. This book: Provides a rich collection of techniques and procedures. Discusses the foundational aspects and modern day practice. Links foundations to practical applications in biostatistics, computer science, engineering and economics. Presents different perspectives and controversies to encourage readers to form their own opinion of decision making and statistics. 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.
(source: Nielsen Book Data)

• Introduction
• PART I: Deterministic Models
• Multi-Stage Decision Problems
• Networks
• Further Applications
• Convexity
• PART II: Stochastic Models
• General Principles
• Optimal Stopping
• Special Problems
• PART III: Markov Decision Processes
• General Theory
• Minimising Average Costs
• Statistical Decision.
• (source: Nielsen Book Data)

Decision Theory An Introduction to Dynamic Programming and Sequential Decisions John Bather University of Sussex, UK Mathematical induction, and its use in solving optimization problems, is a topic of great interest with many applications. It enables us to study multistage decision problems by proceeding backwards in time, using a method called dynamic programming. All the techniques needed to solve the various problems are explained, and the author's fluent style will leave the reader with an avid interest in the subject. Tailored to the needs of students of optimization and decision theory Written in a lucid style with numerous examples and applications Coverage of deterministic models: maximizing utilities, directed networks, shortest paths, critical path analysis, scheduling and convexity Coverage of stochastic models: stochastic dynamic programming, optimal stopping problems and other special topics Coverage of advanced topics: Markov decision processes, minimizing expected costs, policy improvements and problems with unknown statistical parameters Contains exercises at the end of each chapter, with hints in an appendix Aimed primarily at students of mathematics and statistics, the lucid text will also appeal to engineering and science students and those working in the areas of optimization and operations research.
(source: Nielsen Book Data)

• 1. Introduction
• 2. News Value
• 3. Self-signalling
• 4. Randomization
• 5. Harmony
• 6. Conclusion
• Appendix A: Non-binary News Value
• Appendix B: Randomization and Accuracy
• Appendix C: Jeffrey-Bolker Representation Theorem.
• (source: Nielsen Book Data)

Evidential Decision Theory is a radical theory of rational decision-making. It recommends that instead of thinking about what your decisions *cause*, you should think about what they *reveal*. This Element explains in simple terms why thinking in this way makes a big difference, and argues that doing so makes for *better* decisions. An appendix gives an intuitive explanation of the measure-theoretic foundations of Evidential Decision Theory.
(source: Nielsen Book Data)

• Statistical models.- Tests in models with monotonicity properties.- Statistical decision theory.- Comparison of models, reduction by sufficiency.- Invariant statistical decision models.- Large sample approximations of models and decisions.- Estimation.- Testing.- Selection.
• (source: Nielsen Book Data)

This monograph is written for advanced graduate students, Ph.D. students, and researchers in mathematical statistics and decision theory. All major topics are introduced on a fairly elementary level and then developed gradually to higher levels. The book is self-contained as it provides full proofs, worked-out examples, and problems. It can be used as a basis for graduate courses, seminars, Ph.D. programs, self-studies, and as a reference book. The authors present a rigorous account of the concepts and a broad treatment of the major results of classical finite sample size decision theory and modern asymptotic decision theory. Highlights are systematic applications to the fields of parameter estimation, testing hypotheses, and selection of populations. With its broad coverage of decision theory that includes results from other more specialized books as well as new material, this book is one of a kind and fills the gap between standard graduate texts in mathematical statistics and advanced monographs on modern asymptotic theory. One goal is to present a bridge from the classical results of mathematical statistics and decision theory to the modern asymptotic decision theory founded by LeCam. The striking clearness and powerful applicability of LeCam's theory is demonstrated with its applications to estimation, testing, and selection on an intermediate level that is accessible to graduate students. Another goal is to present a broad coverage of both the frequentist and the Bayes approach in decision theory. Relations between the Bayes and minimax concepts are studied, and fundamental asymptotic results of modern Bayes statistical theory are included. The third goal is to present, for the first time in a book, a well-rounded theory of optimal selections for parametric families.
(source: Nielsen Book Data)

• 1. Introduction
• 2. News Value
• 3. Self-signalling
• 4. Randomization
• 5. Harmony
• 6. Conclusion
• Appendix A: Non-binary News Value
• Appendix B: Randomization and Accuracy
• Appendix C: Jeffrey-Bolker Representation Theorem.
• (source: Nielsen Book Data)

Evidential Decision Theory is a radical theory of rational decision-making. It recommends that instead of thinking about what your decisions *cause*, you should think about what they *reveal*. This Element explains in simple terms why thinking in this way makes a big difference, and argues that doing so makes for *better* decisions. An appendix gives an intuitive explanation of the measure-theoretic foundations of Evidential Decision Theory.
(source: Nielsen Book Data)

Decision-theoretic ideas can structure the process of inference together with the decision-making that inference supports. Statistical decision theory is the sub-discipline of statistics which explores and develops this structure. Typically, discusion of decision theory within one discipline does not recognise that other disciplines may have considered the same or similar problems. This text, Volume 9 in the prestigious Kendall's Library of Statistics, provides an overview of the main ideas and concepts of statistical decision theory and sets it within the broader concept of decision theory, decision analysis and decision support as they are practised in many disciplines beyond statistics - including artificial intelligence, economics, operational research, philosophy and psychology.
(source: Nielsen Book Data)

• Preface.- 1.Introduction.- 2.Estimating the Mean.- 3.Estimating the Variance.- 4.The Bayesian Paradigm.- 5.Data from other Distributions.- 6.Classification.- 7.Small-area Estimation.- 8.Study Design.- Index.
• (source: Nielsen Book Data)

• Machine generated contents note: 1. Introduction
• 1.1. Role of Statistics
• 1.2. Preliminaries
• 1.3. Estimation
• 1.4. Assessing an Estimator
• 1.5. Confidence Intervals
• 1.6. Hypothesis Testing
• 1.7. Loss Function
• 1.8. Problems, Exercises and Suggested Reading
• References
• 2. Estimating the Mean
• 2.1. Estimation with an Asymmetric Loss
• 2.2. Numerical Optimisation
• 2.3. Plausible Loss Functions
• 2.4. Other Classes of Loss Functions
• 2.4.1. LINEX Loss
• 2.5. Comparing Two Means
• 2.6. Problems, Exercises and Suggested Reading
• References
• 3. Estimating the Variance
• 3.1. Unbiased and Efficient Estimation
• 3.2. Loss Functions for Variance Estimators
• 3.3. Variance Versus a Constant
• 3.3.1. Decision with Utilities
• 3.3.2. Multiplicative Loss
• 3.4. Estimating the Variance Ratio
• 3.5. Problems, Exercises and Suggested Reading
• References
• 4. Bayesian Paradigm
• 4.1. Bayes Theorem
• 4.2. Comparing Two Normal Random Samples
• 4.3. Decision with Estimated σ2
• 4.4. Problems, Exercises and Suggested Reading
• References
• 5. Data from Other Distributions
• 5.1. Binary Outcomes
• 5.2. Poisson Counts
• 5.3. Continuous Distributions: Transformations and Mixtures
• 5.4. Problems, Exercises and Suggested Reading
• References
• 6. Classification
• 6.1. Introduction
• 6.2. Normally Distributed Marker
• 6.3. Markers with Other Distributions
• 6.3.1. Markers with t Distribution
• 6.3.2. Beta Distributed Markers
• 6.3.3. Gamma Distributed Markers
• 6.4. Looking for Contaminants
• 6.5. Problems, Exercises and Suggested Reading
• References
• 7. Small-Area Estimation
• 7.1. Composition and Empirical Bayes Models
• 7.2. Estimation for a Policy
• 7.3. Application
• 7.3.1. Limited Budget
• 7.4. Conclusion
• 7.5. Appendix: Estimating
• 7.6. Problems, Exercises and Suggested Reading
• References
• 8. Study Design
• 8.1. Sample Size Calculation for Hypothesis Testing
• 8.2. Sample Size for Decision Making
• 8.3. Problems, Exercises and Suggested Reading
• References.

This monograph presents a radical rethinking of how elementary inferences should be made in statistics, implementing a comprehensive alternative to hypothesis testing in which the control of the probabilities of the errors is replaced by selecting the course of action (one of the available options) associated with the smallest expected loss. Its strength is that the inferences are responsive to the elicited or declared consequences of the erroneous decisions, and so they can be closely tailored to the client's perspective, priorities, value judgments and other prior information, together with the uncertainty about them.
(source: Nielsen Book Data)