Elementary Decision Theory

Description

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.