Subject Index

The appendices are not indexed. Bold type refers to the extracts of original material.

Abbe's Criterion, 77 accuracy of observations, 37-40, 41 aleatory contracts, 2 arrangements, 20, 26-29 Ars conjectandi, 3 association of attributes, 137, 141,

measure of, 137, partial, 137, illusory, 138 142

asymptotic relative efficiency, 51-55

Bayesian confidence interval, 38 Bayesian methods, 38, 131-132, 187-

190, 194-201 Bayes's rule, 131, 134 Bernoulli 's theorem. See law of large

numbers Bernoulli trials, 146. See also bino­

mial distribution binomial coefficients, 13, 14, 132, 133 binomial distribution, 9, 10, 13, 14,

115, 130-132, 134, contin­uous, 132-133

binomial parameter, estimation of, 129-133,134-136,187,191

births, male and female, 9, 13-17 blind fate, 8, 11 Boyle Lectures, 7 Bradley-Terry model. See paired­

comparison model

central limit theorem, 38, 51 Chance and Design, 7 chi-squared distribution, 103-107 circular serial correlation coefficient,

77 coincidences, 19-23 combinations, 21 comets, 8 confidence coefficient, 191 confidence concept, 187, 190

confidence distribution, 191 confidence interval, 38, 187-193 confidence limits. See confidence in-

terval consistency, 130 contingency table, 137, 138 contour integration, 78 correlation, spurious, 137, 143 corelation coefficient, 137, 188, 200,

201

De ratiociniis in ludo alete, 2, 9 design, argument from, 7,118-121,

129. See also Divine Prov­idence

direct probability methods, 38, 116, 131, 187-189, 196

Divine Providence, 13 division problem. See Problem of Points drawn games. See ties

Empirical Logic, 116 equations of condition, 51, 57-59 Essay on the Uselulness 01 Mathe-

matical Learning, 9 Essay on the Principle 01 Popula-

tion, 65 Euler diagram, 115 Evidences, 7 exchangeable events, 19, 21, 22 expectation, 1-6, 15, 26-28, 135,

151 expected value. See expectation exponential growth, 65, 66, 71, 74 extreme-value theory, 145-150

fair game, 1 fiducial distribution, 188, 189, 200,

201 fiducial limits, 191

248 Subject Index

fiducial probability, 188-192, 199-201

fractal, 115-116

gamble, value of, 1, 2 Game of Thirteen, 20, 25, 31 Gaussian law of error, 109, 151, 155,

159 goodness-of-fit statistics, 77-79. See

also chi-squared distribu­tion

half-invariants, 130 Helmert transformation, 103, 104 homogeneity of variance, test of, 22 hypothesis-testing. See Neyman-Pearson

theory

inclusion and exclusion, method of, 19-23

insufficient reason, doctrine of, 194 interval estimation. See confidence

interval; fiducial limits inverse probability, 37, 38, 119, 188,

189, 194

L1- and L2-estimation, 51 law of large numbers, 127, 147, 158 least squares, 37, 41, 51, 53, 82, 105 Lectures on the General Theory of

Observations, 129, 134 likelihood, 129-133, 134, 187, 198.

See also maximum likeli­hood

likelihood function, 129-133 likelihood ratio, 10 linear model, 51 linear regression, 51, 52 logistic distribution, 66 logistic growth curve, 65-67, 73, 74

males, excess of, 9-11, 15 matches. See coincidences maximum likelihood, 38, 129, 130,

132, 161, 162, 188, 198 maximum probability, 38, 41, 43, 46,

48,188,197 Mecanique dleste, 57 median, 51-53, 196, 197

median absolute deviation, 38 mean deviation, 103 mean difference, 103 mean error, 86, 103, 109, 112, 113 mean squared error, 112 mode, 130, 134, 188, 196, 197 most advantageous method. See least

squares

Neyman-Pearson theory, 191 null hypothesis, 7, 11

odds ratio, 138 Of the Laws of Chance, 9 Opticks, 8 order statistics, 51, 52, 146

paired-comparison model, 161, 164; method,162

parameter, 195-199 Pascal's wager, 3 pi (7l'), randomness of digits, 121-

128 planets, 8, 10 population growth, law of, 69 precision, 37, 43, 82, 103 probable error, 42, 46, 82, 103, 109,

187 probable limits, 44-48 Problem of Points, 1-3, 4

Q,139

randomness, 117 random walk, 115-116; figure, 118 range, 145, 146, 151, 155 recursion, 1-3 regression coefficient, 51 regular tournaments. See Round Robins rejection region, 11 repeated-sampling methods. See di-

rect probability methods Round Robins, 161-165 Royal Society, 9 Royal Society theology, 7, 10

sampIe variance, distribution of, 103-107

significance level, 188

Simpson's paradox. See Yule's para-dox

situation, method of, 51, 61, 63, 64 stake, 1-3 standard deviation, 105, 151, 155 stars, arrangement of, 118, 119 statistic, 198-200 Stigler's Law, 138 sum of squares, 82, 87, 98, 111 support, 129 Symbolic Logic, 116

t-distribution, 187 test of significance, 7-12, 188 The Doctrine 0/ Chances, 7, 10, 21,

32 The Logic 0/ Chance, 115, 117 The Genetical Theory 0/ Natural Se­

lection, 11

Subject Index 249

Theoria M otus Corporum Coelestium, 41,43

Theorie analytique des probabilites, 51, 53, 61-63

ties, 164-165 tournament outcomes, 161-166, 167 Traite du triangle arithmetique, 2, 3,

5

variance, estimation of, 105 Venn diagram, 115

Wahrscheinlichkeit, Statistik und Wahrheit, 148

weighted median estimator, 51-53

Yule's coefficient Q, 139 Yule's paradox, 137-140

Name Index

Commentators, modern contributors, and names in the appendices are not indexed. Bold type refers to the extracts of original material.

Abbe, 77-79, 81-101, 104 Anne, Queen, 9 Arbuthnott, 7-12, 13-17

Bayes, 37, 131, 134, 135, 189, 194 Bentley, 7, 8, 10 Bernoulli, Daniel, 10, 129 Bernoulli, James, 3, 10, 127, 158 Bernoulli, Nicholas, 10, 19-23, 31,

145 Bessel, 37, 48, 49 Bienayme, 77, 104 Bing, 131, 135 Boole,197 Bortkiewicz, 145-150, 151-153, 155,

156, 159 Boscovich, 52 BuB, 9

Carcavi, 2, 4 Cauchy, 78, 84, 89 Clarke,7 Clopper, 191 Cochran,22 Cournot, 187

Darwin, 7, 11 De Mere, 4 De Moivre, 7, ~, 10, 19-23, 32-36 Derham, 7, 9, 10 Dirichlet, 38, 78, 84 Dodd,147

Encke,38 Ezekiel, 200

Fermat,1-4 Fisher, 7, 11, 51, 104, 105, 116, 129,

130,147,148,187-193,194-201

Frechet, 147 Frobenius, 164

Gauss, 37-40, 41-49, 77, 81, 103-105, 145, 187, 194, 197

Gnedenko, 147, 148 Gumbel,147

Hauber,38 Helmert, 77, 103-107, 109-113 Hitler, 149, 165 Huygens, 2, 3

Jacobi,89

Lambert, 129 Landau, 163, 164 Laplace, 37, 38, 45, 51-55, 57-64,

134, 187, 194 Legendre, 52

Malthus, 65, 72 Montmort, 10, 19-23, 25-29, 31

Newton, 7-9, 125 Neyman, 148, 187-192

Paley,7 Pascal, 1-4, 4, 115 Pearson, E.S., 187, 191 Pearson, Karl, 104, 105, 115, 116,

137, 143, 146 Pizzetti, 104, 187 Planck, 165 Poisson, 66, 78 Price,194

Quetelet, 65

252 Name Index

Rayleigh, 116 Riemann,85 Rilke, 148 Roberval, 2, 4

'sGravesande, 10 "Student," 78, 187, 188 Swift,9

Tartaglia, 1 Thiele, 129-133, 134-136 Thurstone, 162

Tippett, 147, 148

Venn, 115-116, 117-128, 197 Verhulst, 65-67, 69-75 von Mises, 155-160

Yule, 137-140, 141-143

Zeiss, 78 Zermelo, 161-166, 167-186

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