Elementary Decision Theory

Title Page; Copyright Page; Dedication; Preface; Acknowledgments; Table of Contents; CHAPTER 1 -- Introduction; 1. INTRODUCTION; 2. AN EXAMPLE; 3. PRINCIPLES USED IN DECISION MAKING; 4. SUMMARY; SUGGESTED READINGS; CHAPTER 2 -- Data Processing; 1. INTRODUCTION; 2. DATA REPRESENTATION; 3. GRAPHICAL REPRESENTATIONS: HISTOGRAM; 4. GRAPHICAL REPRESENTATIONS: CUMULATIVE FREQUENCY POLYGON; 5. DESCRIPTIVE MEASURES: SUMMATION; 6. DESCRIPTIVE MEASURES: SAMPLE MEAN AND VARIANCE; 7. SIMPLIFIED COMPUTATION SCHEME FOR SAMPLE MEAN AND STANDARD DEVIATION USING GROUPED DATA; 8. SUMMARY; SUGGESTED READINGS.;This well-known and highly respected introduction to decision theory was developed at Stanford University. It furnishes a simple and clear-cut method of exhibiting the fundamental aspects of statistical problems. Beginners will find this treatment a motivating introduction to important mathematical notions such as set, function, and convexity. Title Page Copyright Page Dedication Preface Acknowledgments Table of Contents CHAPTER 1 -- Introduction 1. INTRODUCTION 2. AN EXAMPLE 3. PRINCIPLES USED IN DECISION MAKING 4. SUMMARY SUGGESTED READINGS CHAPTER 2 -- Data Processing 1. INTRODUCTION 2. DATA REPRESENTATION 3. GRAPHICAL REPRESENTATIONS: HISTOGRAM 4. GRAPHICAL REPRESENTATIONS: CUMULATIVE FREQUENCY POLYGON 5. DESCRIPTIVE MEASURES: SUMMATION 6. DESCRIPTIVE MEASURES: SAMPLE MEAN AND VARIANCE 7. SIMPLIFIED COMPUTATION SCHEME FOR SAMPLE MEAN AND STANDARD DEVIATION USING GROUPED DATA 8. SUMMARY SUGGESTED READINGS. CHAPTER 3 -- Introduction to Probability and Random Variables1. INTRODUCTION 2. TWO EXAMPLES 3. PROBABILITY DISTRIBUTIONS AND CUMULATIVE DISTRIBUTION FUNCTIONS 4. PROBABILITY DENSITY FUNCTION-DISCRETE CASE 5. PROBABILITY DENSITY FUNCTION-CONTINUOUS CASE . POPULATION AND RANDOM SAMPLES 7. THE NORMAL POPULATION 8. SETS AND FUNCTION 9. REVIEW OF PROBABILITY SUGGESTED READING CHAPTER 4 -- Utility and Descriptive Statistics 1. INTRODUCTION 2. UTILITY 3. PROBABILITY AND EXPECTATION . APPLICATION OF UTILITY TO FAIR BETS . THE ST. PETERSBURG PARADOX 6. DESCRIPTIVE PARAMETERS. 7. THE MEAN AND VARIANCE8. SUMMARY SUGGESTED READINGS CHAPTER 5 -- Uncertainty due to Ignorance of the State of Nature 1. INTRODUCTION 2. TWO STATES OF NATURE-AN EXAMPLE 3. TWO STATES OF NATURE: CONVEX SETS AND LINES 4. TWO STATES OF NATURE: BAYES STRATEGIES AND SUPPORTING LINES 5. TWO STATES OF NATURE: MINIMAX STRATEGIES 6. TWO STATES OF NATURE: REGRET 7. LINES, PLANES, AND CONVEX SETS IN HIGHER DIMENSIONS 8. THREE OR MORE UNKNOWN STATES OF NATURE 9. SUMMARY SUGGESTED READINGS CHAPTER 6 -- The Computation of Bayes Strategies 1. A POSTERIORI PROBABILITY AND THE NO-DATA PROBLEM. 2. CONDITIONAL PROBABILITY3. A POSTERIORI PROBABILITY 4. COMPUTATION OF BAYES STRATEGIES 5. INDEPENDENCE 6. SUMMARY 7. REVIEW AT THE END OF CHAPTER 6 SUGGESTED READINGS CHAPTER 7 -- Introduction to Classical Statistics 1. INTRODUCTION 2. AN EXAMPLE OF HYPOTHESIS TESTING 3. ESTIMATION 4. CONFIDENCE INTERVALS . SIGNIFICANCE TESTING . A DECISION MAKING PROBLEM WHERE COMMON STATISTICAL PROCEDURES DO NOT APPLY 7. SUMMARY CHAPTER 8 -- Models 1. INTRODUCTION 2. MODELS OF PROBABILITY AND UTILITY 3. MODELS OF THE SET OF AVAILABLE ACTIONS. 4. MODELS OF SETS OF POSSIBLE STATES OF NATURE5. MODELS OF REGRET FUNCTIONS 6. MODELS OF EXPERIMENTS 7. MODELS OF THE SET OF AVAILABLE STRATEGIES 8. THE MODELS FOR THE PROBLEMS OF TESTING AND ESTIMATION 9. SUMMARY CHAPTER 9 -- Testing Hypotheses 1. INTRODUCTION 2. NOTATION 3. SIMPLE HYPOTHESIS VERSUS SIMPLE HYPOTHESIS (TWO STATES OF NATURE) 4. COMPOSITE HYPOTHESES INVOLVING ONE PARAMETER 5. COMPOSITE HYPOTHESES INVOLVING ONE PARAMETER: TWO-TAILED TESTS 6. SEVERAL PARAMETERS 7. DESIGN OF EXPERIMENTS 8. SEQUENTIAL ANALYSIS 9. SUMMARY SUGGESTED READINGS. CHAPTER 10 -- Estimation and Confidence Intervals. "The text is very clearly written [with] many illustrative examples and exercises [and] should be considered by those instructors who would like to introduce a more modern (and a more logical) approach in a basic course in statistics." — Journal of the American Statistical Association This volume is a well-known, well-respected introduction to a lively area of statistics. Professors Chernoff and Moses bring years of professional expertise as classroom teachers to this straightforward approach to statistical problems. And happily, for beginning students, they have by-passed involved computational reasonings which would only confuse the mathematical novice. Developed from nine years of teaching statistics at Stanford, the book furnishes a simple and clear-cut method of exhibiting the fundamental aspects of a statistical problem. Beginners will find this book a motivating introduction to important mathematical notions such as set, function and convexity. Examples and exercises throughout introduce new topics and ideas. The first seven chapters are recommended for beginning courses in the basic ideas of statistics and require only a knowledge of high school math. These sections include material on data processing, probability and random variables, utility and descriptive statistics, uncertainty due to ignorance of the state of nature, computing Bayes strategies and an introduction to classical statistics. The last three chapters review mathematical models and summarize terminology and methods of testing hypotheses. Tables and appendixes provide information on notation, shortcut computational formulas, axioms of probability, properties of expectations, likelihood ratio test, game theory, and utility functions. Authoritative, yet elementary in its approach to statistics and statistical theory, this work is also concise, well-indexed and abundantly equipped with exercise material. Ideal for a beginning course, this modestly priced edition will be especially valuable to those interested in the principles of statistics and scientific method.