PATTERNS OF PLAUSIBLE INFERENCE
CONTENTS PART I PRINCIPLES AND ELEMENTARY APPLICATIONS PLAUSIBLE REASONING DEDUCTIVE AND PLAUSIBLE REASONING ANALOGIES WITH PHYSICAL THEORIES THE THINKING COMPUTER INTRODUCING THE ROBOT BOOLEAN ALGEBRA ADEQUATE SETS OF OPERATIONS THE BASIC DESIDERATA COMMENTS COMMON LANGUAGE VS FORMAL LOGIC NITPICKING THE QUANTITATIVE RULES THE PRODUCT RULE THE SUM RULE QUALITATIVE PROPERTIES NUMERICAL VALUES NOTATION AND ?NITE-SETS POLICY ‘SUBJECTIVE’ VS ‘OBJECTIVE’ G¨ODEL’S THEOREM VENN DIAGRAMS THE ‘KOLMOGOROV AXIOMS’ ELEMENTARY SAMPLING THEORY SAMPLING WITHOUT REPLACEMENT LOGIC VS PROPENSITY REASONING FROM LESS PRECISE INFORMATION EXPECTATIONS OTHER FORMS AND EXTENSIONS PROBABILITY AS A MATHEMATICAL TOOL THE BINOMIAL DISTRIBUTION SAMPLING WITH REPLACEMENT DIGRESSION: A SERMON ON REALITY VS MODELS CORRECTION FOR CORRELATIONS SIMPLI?CATION A LOOK AHEAD ELEMENTARY HYPOTHESIS TESTING PRIOR PROBABILITIES TESTING BINARY HYPOTHESES WITH BINARY DATA NONEXTENSIBILITY BEYOND THE BINARY CASE MULTIPLE HYPOTHESIS TESTING DIGRESSION ON ANOTHER DERIVATION CONTINUOUS PROBABILITY DISTRIBUTION FUNCTIONS TESTING AN IN?NITE NUMBER OF HYPOTHESES HISTORICAL DIGRESSION SIMPLE AND COMPOUND (OR COMPOSITE) HYPOTHESES ETYMOLOGY WHAT HAVE WE ACCOMPLISHED? QUEER USES FOR PROBABILITY THEORY EXTRASENSORY PERCEPTION MRS STEWART’S TELEPATHIC POWERS DIGRESSION ON THE NORMAL APPROXIMATION BACK TO MRS STEWART CONVERGING AND DIVERGING VIEWS VISUAL PERCEPTION – EVOLUTION INTO BAYESIANITY? THE DISCOVERY OF NEPTUNE DIGRESSION ON ALTERNATIVE HYPOTHESES BACK TO NEWTON HORSE RACING AND WEATHER FORECASTING DISCUSSION PARADOXES OF INTUITION BAYESIAN JURISPRUDENCE WHAT IS QUEER? ELEMENTARY PARAMETER ESTIMATION INVERSION OF THE URN DISTRIBUTIONS BOTH N AND R UNKNOWN UNIFORM PRIOR PREDICTIVE DISTRIBUTIONS TRUNCATED UNIFORM PRIORS A CONCAVE PRIOR THE BINOMIAL MONKEY PRIOR METAMORPHOSIS INTO CONTINUOUS PARAMETER ESTIMATION ESTIMATION WITH A BINOMIAL SAMPLING DISTRIBUTION DIGRESSION ON OPTIONAL STOPPING COMPOUND ESTIMATION PROBLEMS A SIMPLE BAYESIAN ESTIMATE: QUANTITATIVE PRIOR INFORMATION FROM POSTERIOR DISTRIBUTION FUNCTION TO ESTIMATE EFFECTS OF QUALITATIVE PRIOR INFORMATION CHOICE OF A PRIOR ON WITH THE CALCULATION! THE JEFFREYS PRIOR THE POINT OF IT ALL INTERVAL ESTIMATION CALCULATION OF VARIANCE GENERALIZATION AND ASYMPTOTIC FORMS RECTANGULAR SAMPLING DISTRIBUTION SMALL SAMPLES MATHEMATICAL TRICKERY THE CENTRAL, GAUSSIAN OR NORMAL DISTRIBUTION THE GRAVITATING PHENOMENON THE HERSCHEL–MAXWELL DERIVATION THE GAUSS DERIVATION HISTORICAL IMPORTANCE OF GAUSS’S RESULT THE LANDON DERIVATION WHY THE UBIQUITOUS USE OF GAUSSIAN DISTRIBUTIONS? WHY THE UBIQUITOUS SUCCESS? WHAT ESTIMATOR SHOULD WE USE? ERROR CANCELLATION THE NEAR IRRELEVANCE OF SAMPLING FREQUENCY DISTRIBUTIONS THE REMARKABLE EF?CIENCY OF INFORMATION TRANSFER OTHER SAMPLING DISTRIBUTIONS NUISANCE PARAMETERS AS SAFETY DEVICES MORE GENERAL PROPERTIES CONVOLUTION OF GAUSSIANS THE CENTRAL LIMIT THEOREM ACCURACY OF COMPUTATIONS GALTON’S DISCOVERY POPULATION DYNAMICS AND DARWINIAN EVOLUTION EVOLUTION OF HUMMING-BIRDS AND ?OWERS APPLICATION TO ECONOMICS THE GREAT INEQUALITY OF JUPITER AND SATURN RESOLUTION OF DISTRIBUTIONS INTO GAUSSIANS HERMITE POLYNOMIAL SOLUTIONS FOURIER TRANSFORM RELATIONS THERE IS HOPE AFTER ALL TERMINOLOGY AGAIN SUF?CIENCY, ANCILLARITY, AND ALL THAT SUF?CIENCY FISHER SUF?CIENCY EXAMPLES THE BLACKWELL–RAO THEOREM GENERALIZED SUF?CIENCY SUF?CIENCY PLUS NUISANCE PARAMETERS THE LIKELIHOOD PRINCIPLE ANCILLARITY GENERALIZED ANCILLARY INFORMATION ASYMPTOTIC LIKELIHOOD: FISHER INFORMATION COMBINING EVIDENCE FROM DIFFERENT SOURCES POOLING THE DATA FINE-GRAINED PROPOSITIONS SAM’S BROKEN THERMOMETER THE FALLACY OF SAMPLE RE-USE A FOLK THEOREM EFFECT OF PRIOR INFORMATION CLEVER TRICKS AND GAMESMANSHIP REPETITIVE EXPERIMENTS: PROBABILITY AND FREQUENCY PHYSICAL EXPERIMENTS THE POORLY INFORMED ROBOT INDUCTION ARE THERE GENERAL INDUCTIVE RULES? MULTIPLICITY FACTORS PARTITION FUNCTION ALGORITHMS SOLUTION BY INSPECTION ENTROPY ALGORITHMS ANOTHER WAY OF LOOKING AT IT ENTROPY MAXIMIZATION PROBABILITY AND FREQUENCY SIGNI?CANCE TESTS IMPLIED ALTERNATIVES COMPARISON OF PSI AND CHI-SQUARED THE CHI-SQUARED TEST GENERALIZATION HALLEY’S MORTALITY TABLE THE IRRATIONALISTS SUPERSTITIONS PHYSICS OF ‘RANDOM EXPERIMENTS’ AN INTERESTING CORRELATION HISTORICAL BACKGROUND HOW TO CHEAT AT COIN AND DIE TOSSING EXPERIMENTAL EVIDENCE BRIDGE HANDS GENERAL RANDOM EXPERIMENTS INDUCTION REVISITED BUT WHAT ABOUT QUANTUM THEORY? MECHANICS UNDER THE CLOUDS MORE ON COINS AND SYMMETRY INDEPENDENCE OF TOSSES THE ARROGANCE OF THE UNINFORMED PART II ADVANCED APPLICATIONS DISCRETE PRIOR PROBABILITIES: THE ENTROPY PRINCIPLE A NEW KIND OF PRIOR INFORMATION ENTROPY: SHANNON’S THEOREM THE WALLIS DERIVATION AN EXAMPLE GENERALIZATION: A MORE RIGOROUS PROOF FORMAL PROPERTIES OF MAXIMUM ENTROPY DISTRIBUTIONS CONCEPTUAL PROBLEMS – FREQUENCY CORRESPONDENCE IGNORANCE PRIORS AND TRANSFORMATION GROUPS WHAT ARE WE TRYING TO DO? IGNORANCE PRIORS CONTINUOUS DISTRIBUTIONS TRANSFORMATION GROUPS LOCATION AND SCALE PARAMETERS A POISSON RATE UNKNOWN PROBABILITY FOR SUCCESS BERTRAND’S PROBLEM DECISION THEORY, HISTORICAL BACKGROUND INFERENCE VS DECISION DANIEL BERNOULLI’S SUGGESTION THE RATIONALE OF INSURANCE ENTROPY AND UTILITY THE HONEST WEATHERMAN REACTIONS TO DANIEL BERNOULLI AND LAPLACE WALD’S DECISION THEORY PARAMETER ESTIMATION FOR MINIMUM LOSS REFORMULATION OF THE PROBLEM EFFECT OF VARYING LOSS FUNCTIONS GENERAL DECISION THEORY ‘OBJECTIVITY’ OF DECISION THEORY LOSS FUNCTIONS IN HUMAN SOCIETY A NEW LOOK AT THE JEFFREYS PRIOR DECISION THEORY IS NOT FUNDAMENTAL ANOTHER DIMENSION? SIMPLE APPLICATIONS OF DECISION THEORY DE?NITIONS AND PRELIMINARIES SUF?CIENCY AND INFORMATION LOSS FUNCTIONS AND CRITERIA OF OPTIMUM PERFORMANCE A DISCRETE EXAMPLE HOW WOULD OUR ROBOT DO IT? HISTORICAL REMARKS THE CLASSICAL MATCHED ?LTER THE WIDGET PROBLEM SOLUTION FOR STAGE PARADOXES OF PROBABILITY THEORY HOW DO PARADOXES SURVIVE AND GROW? SUMMING A SERIES THE EASY WAY NONCONGLOMERABILITY THE TUMBLING TETRAHEDRA SOLUTION FOR A ?NITE NUMBER OF TOSSES FINITE VS COUNTABLE ADDITIVITY THE BOREL–KOLMOGOROV PARADOX THE MARGINALIZATION PARADOX ON TO GREATER DISASTERS SUMMARY A USEFUL RESULT AFTER ALL? HOW TO MASS-PRODUCE PARADOXES ORTHODOX METHODS: HISTORICAL BACKGROUND THE EARLY PROBLEMS SOCIOLOGY OF ORTHODOX STATISTICS RONALD FISHER, HAROLD JEFFREYS, AND JERZY NEYMAN PRE-DATA AND POST-DATA CONSIDERATIONS THE SAMPLING DISTRIBUTION FOR AN ESTIMATOR PRO-CAUSAL AND ANTI-CAUSAL BIAS WHAT IS REAL, THE PROBABILITY OR THE PHENOMENON? COMMUNICATION DIF?CULTIES PRINCIPLES AND PATHOLOGY OF ORTHODOX STATISTICS INFORMATION LOSS UNBIASED ESTIMATORS PATHOLOGY OF AN UNBIASED ESTIMATE THE FUNDAMENTAL INEQUALITY OF THE SAMPLING VARIANCE PERIODICITY: THE WEATHER IN CENTRAL PARK THE FOLLY OF PRE-?LTERING DATA A BAYESIAN ANALYSIS THE FOLLY OF RANDOMIZATION FISHER: COMMON SENSE AT ROTHAMSTED THE BAYESIAN SAFETY DEVICE MISSING DATA TREND AND SEASONALITY IN TIME SERIES ORTHODOX METHODS THE BAYESIAN METHOD COMPARISON OF BAYESIAN AND ORTHODOX ESTIMATES AN IMPROVED ORTHODOX ESTIMATE THE ORTHODOX CRITERION OF PERFORMANCE THE GENERAL CASE THE AP DISTRIBUTION AND RULE OF SUCCESSION MEMORY STORAGE FOR OLD ROBOTS RELEVANCE A SURPRISING CONSEQUENCE OUTER AND INNER ROBOTS AN APPLICATION LAPLACE’S RULE OF SUCCESSION JEFFREYS’ OBJECTION BASS OR CARP? SO WHERE DOES THIS LEAVE THE RULE? CON?RMATION AND WEIGHT OF EVIDENCE IS INDIFFERENCE BASED ON KNOWLEDGE OR IGNORANCE? CARNAP’S INDUCTIVE METHODS PROBABILITY AND FREQUENCY IN EXCHANGEABLE SEQUENCES PREDICTION OF FREQUENCIES ONE-DIMENSIONAL NEUTRON MULTIPLICATION THE FREQUENTIST SOLUTION THE LAPLACE SOLUTION THE DE FINETTI THEOREM PHYSICAL MEASUREMENTS REDUCTION OF EQUATIONS OF CONDITION REFORMULATION AS A DECISION PROBLEM SERMON ON GAUSSIAN ERROR DISTRIBUTIONS THE UNDERDETERMINED CASE: K IS SINGULAR THE OVERDETERMINED CASE: K CAN BE MADE NONSINGULAR NUMERICAL EVALUATION OF THE RESULT ACCURACY OF THE ESTIMATES A PARADOX MODEL COMPARISON FORMULATION OF THE PROBLEM THE FAIR JUDGE AND THE CRUEL REALIST PARAMETERS KNOWN IN ADVANCE PARAMETERS UNKNOWN BUT WHERE IS THE IDEA OF SIMPLICITY? AN EXAMPLE: LINEAR RESPONSE MODELS DIGRESSION: THE OLD SERMON STILL ANOTHER TIME FINAL CAUSES OUTLIERS AND ROBUSTNESS THE EXPERIMENTER’S DILEMMA ROBUSTNESS THE TWO-MODEL MODEL EXCHANGEABLE SELECTION THE GENERAL BAYESIAN SOLUTION PURE OUTLIERS ONE RECEDING DATUM INTRODUCTION TO COMMUNICATION THEORY ORIGINS OF THE THEORY THE NOISELESS CHANNEL THE INFORMATION SOURCE DOES THE ENGLISH LANGUAGE HAVE STATISTICAL PROPERTIES? OPTIMUM ENCODING: LETTER FREQUENCIES KNOWN BETTER ENCODING FROM KNOWLEDGE OF DIGRAM FREQUENCIES RELATION TO A STOCHASTIC MODEL THE NOISY CHANNEL