UNDERSTANDING UNCERTAINTY

By CHARLES WHITE

CONTENTS 1 UNCERTAINTY 1 1 INTRODUCTION 1 2 EXAMPLES 1 3 SUPPRESSION OF UNCERTAINTY 1 4 THE REMOVAL OF UNCERTAINTY 1 5 THE USES OF UNCERTAINTY 1 6 THE CALCULUS OF UNCERTAINTY 1 7 BELIEFS 1 8 DECISION ANALYSIS 2 STYLISTIC QUESTIONS 2 1 REASON 2 2 UNREASON LITERATURE ADVERTISING POLITICS LAW TELEVISION 2 3 FACTS 2 4 EMOTION 2 5 PRESCRIPTIVE AND DESCRIPTIVE APPROACHES 2 6 SIMPLICITY 2 7 MATHEMATICS 2 8 WRITING 2 9 MATHEMATICS TUTORIAL 3 PROBABILITY 3 1 MEASUREMENT 3 2 RANDOMNESS 3 3 A STANDARD FOR PROBABILITY 3 4 PROBABILITY 3 5 COHERENCE 3 6 BELIEF 3 7 COMPLEMENTARY EVENT 3 8 ODDS 3 9 KNOWLEDGE BASE 3 10 EXAMPLES 3 11 RETROSPECT 4 TWO EVENTS 4 1 TWO EVENTS 4 2 CONDITIONAL PROBABILITY 4 3 INDEPENDENCE 4 4 ASSOCIATION 4 5 EXAMPLES 4 6 SUPPOSITION AND FACT 4 7 SEEING AND DOING 5 THE RULES OF PROBABILITY 5 1 COMBINATIONS OF EVENTS 5 2 ADDITION RULE 5 3 MULTIPLICATION RULE 5 4 THE BASIC RULES 5 5 EXAMPLES 5 6 EXTENSION OF THE CONVERSATION 5 7 DUTCH BOOKS 5 8 SCORING RULES 5 9 LOGIC AGAIN 5 10 DECISION ANALYSIS 5 11 THE PRISONERS’ DILEMMA 5 12 THE CALCULUS AND REALITY 6 BAYES RULE 6 1 TRANSPOSED CONDITIONALS 6 2 LEARNING 6 3 BAYES RULE 6 4 MEDICAL DIAGNOSIS 6 5 ODDS FORM OF BAYES RULE 6 6 FORENSIC EVIDENCE 6 7 LIKELIHOOD RATIO 6 8 CROMWELL’S RULE 6 9 A TALE OF TWO URNS 6 10 RAVENS 6 11 DIAGNOSIS AND RELATED MATTERS 6 12 INFORMATION 7 MEASURING UNCERTAINTY 7 1 CLASSICAL FORM 7 2 FREQUENCY DATA 7 3 EXCHANGEABILITY 7 4 BERNOULLI SERIES 7 5 DE FINETTI’S RESULT 7 6 LARGE NUMBERS 7 7 BELIEF AND FREQUENCY 7 8 CHANCE 8 THREE EVENTS 8 1 THE RULES OF PROBABILITY 8 2 SIMPSON’S PARADOX 8 3 SOURCE OF THE PARADOX 8 4 EXPERIMENTATION 8 5 RANDOMIZATION 8 6 EXCHANGEABILITY 8 7 SPURIOUS ASSOCIATION 8 8 INDEPENDENCE 8 9 CONCLUSIONS 9 VARIATION 9 1 VARIATION AND UNCERTAINTY 9 2 BINOMIAL DISTRIBUTION 9 3 EXPECTATION 9 4 POISSON DISTRIBUTION 9 5 SPREAD 9 6 VARIABILITY AS AN EXPERIMENTAL TOOL 9 7 PROBABILITY AND CHANCE 9 8 PICTORIAL REPRESENTATION 9 9 THE NORMAL DISTRIBUTION 9 10 VARIATION AS A NATURAL PHENOMENON 9 11 ELLSBERG’S PARADOX 10 DECISION ANALYSIS 10 1 BELIEFS AND ACTIONS 10 2 COMPARISON OF CONSEQUENCES 10 3 MEDICAL EXAMPLE 10 4 MAXIMIZATION OF EXPECTED UTILITY 10 5 MORE ON UTILITY 10 6 SOME COMPLICATIONS 10 7 REASON AND EMOTION 10 8 NUMERACY 10 9 EXPECTED UTILITY 10 10 DECISION TREES 10 11 THE ART AND SCIENCE OF DECISION ANALYSIS 10 12 FURTHER COMPLICATIONS 10 13 COMBINATION OF FEATURES 10 14 LEGAL APPLICATIONS 11 SCIENCE 11 1 SCIENTI?C METHOD 11 2 SCIENCE AND EDUCATION 11 3 DATA UNCERTAINTY 11 4 THEORIES 11 5 UNCERTAINTY OF A THEORY 11 6 THE BAYESIAN DEVELOPMENT 11 7 MODI?CATION OF THEORIES 11 8 MODELS 11 9 HYPOTHESIS TESTING 11 10 SIGNI?CANCE TESTS 11 11 REPETITION 11 12 SUMMARY 12 EXAMPLES 12 1 INTRODUCTION 12 2 CARDS 12 3 THE THREE DOORS 12 4 THE NEWCOMERS TO YOUR STREET 12 5 THE TWO ENVELOPES 12 6 Y2K 12 7 UFOS 12 8 CONGLOMERABILITY