Lad F. — Operational Subjective Statistical Methods. A Mathematical, Philosophical, and Historical Introduction :: Электронная библиотека попечительского совета мехмата МГУ

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Lad F. — Operational Subjective Statistical Methods. A Mathematical, Philosophical, and Historical Introduction

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Название: Operational Subjective Statistical Methods. A Mathematical, Philosophical, and Historical Introduction

Автор: Lad F.

Аннотация:

The first book to present Bruno de Finetti's theory of probability and logic of uncertainty in a systematic format. The author identifies de Finetti's "fundamental theorem of coherent prevision" as the unifying structure of probabilistic logic, highlighting the judgment of exchangeability rather than causal independence as the key probabilistic component of statistical inference. Throughout the text, readers are invited to address the subjective personalistic meaning of probability as motivating the mathematical construction. Philosophical attention to meaning is shown to support a difference approach to statistical practice that is widely prevalent today. Includes numerous examples, problems, and illustrations to facilitate understanding.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 484

Добавлена в каталог: 08.12.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$2\times 2$ table      231
Actuarial probabilities      53
Additivity, finite      15 33
annuities      22
Approximation error      423
Aquinas, T.      20
Arithmetic      50 54—55 82
artificial intelligence      119—120
assertion      62 115
Assertion, confirmational commitment      164
Assertion, of an inequality      115
Assertion, of inference      123
Associative mean function      257 259
Autoregression      431—435 440—446
Axioms      111
Barycentric coordinates      196
Bayes, T.      23
Bayes/non-Bayes synthesis      4—5
Bayesian statistics      4—5 30 159 457—458
Bayes’ Theorem      24 30 150—153 217
Belief relations      64
Belief, degree of      12 20
Bernardo, J.      353—354
Bernoulli distribution      292
Bertrand, J.      31
Bertrand’s paradox      32
Beta distribution      292—295
Betting, price      30
Bid-ask spread      114 120
Bienayme — Chebyshev inequality      106 112 251—252
Bienayme, I.J.      253
Binomial distribution      291
Bishop, E.      16
Bold play      30
Bonferroni, C      358—359
Boole, G.      26 54 89 105
Boole, G., challenge problem      136
Borel, E.      24 31 33—35
Bourbaki, N.      13
Bowley, A.L.      3
Bridgman.P.      12
Brier score      339 363—367
Brouwer, L.E.J.      15
Calibration of probabilities      358—369
Cantor function      271
Capture-recapture methods      220
Cartesian product      78
Casuistry      20
Category sum      320
Category sum, definition      311
Causation      71 170 452—453
Central limit theorem      401
Certainty      57
Characteristic function      275
Chebyshev system      269
Chebyshev, P.      see “Bienayme — Chebyshev”
Chebyshev, P., materialist ideas      29
Christianity, early      21
Closure of assertions      111
Coherence of prevision      67 87 158
Coherence of prevision, algebraic condition      69
Coherence of prevision, computational condition      100
Coherence of prevision, geometrical condition      75
Coherency      33 115 117 149
Coherent inference      150
Combinatorics      87 175—179
Complete additivity      112
Complete lack of knowledge      120
Computability      16
Comte, A      28—29
Conditional prevision      121—122 161
Conditional prevision, bounds on      139
Conditional prevision, coherency condition      124
Conditional prevision, definition      123
Conditional quantity      121—124 161
Conditional quantity, definition      123
Condorcet, M.      24
Confidence interval      2 35
Consensus      334
Constituent of a partition      82—84
Constructivism      15—16
Contingency      51
Contradiction      16 30 52 55—56 67
Controlled experiments      235
Convex function      256
Convex hull      74 75
Correct model      454
Correct prevision      59
Correlation      250 255
Cournot, A.A.      28
Covariance      250
Crisma, L.      209
Currency exchange      157.439—449
Dairy cows, example      294—300
Daston, L.      24
Data analysis      165
Data reduction      325—326
Davidson and MacKinnon text      455—456
Dawid, P.      359
de Finetti representation theorem      319
de Finetti, B.      5—6 16—17 30—31 33—36 62 105 111—113 125 138 188—189 359
De Morgan, A.      25—26
Deductive logic      54 62 111 119
DeGroot, M.      6 35
Density function      270
Dependence      see “Independence”
Diaconis, P.      209 232 325
Dirichlet distribution      320
Dirichlet distribution, negative covariance      321
Distribution functions      270—272
Distributions, probability      265—266 (see also “Specific types”)
Distributions, probability, conditional      281—282
Distributions, probability, joint      278
Distributions, probability, marginal      261
Distributions, probability, mixing      402
Distributions, probability, mixture      289
Distributions, probability, natural conjugate      290
Distributions, probability, nested      443—444
Duality      109—111
D’Alembert, J.      24
Econometrics      452—457
Edgeworth, F.      452
Efficient markets      7 262
Empire of Chance      27
Endogenous variables      457
entropy      346
Estienne.J.E.      30
Estimation of Animal Abundance      222
Event, definition      42
Event, definition, idempotence      44
exchange rates      432 439—449
Exchangeability      28 31 33 169 287 453
Exchangeability, definition      179 183 309—310
Exchangeability, examples      170—175 294—302 310 312—315
Exchangeability, extendability      204 317
Exchangeability, history      188 209
Exchangeability, infinite extendability      207
Exchangeability, mixture-normal      394—402
Exchangeability, multivariate normal distribution      386
Exchangeability, partial      228
Exchangeability, representation theorem      207 319
Excluded middle, law of      68
Excluded variables      453
Exhaustive events, definition      82
Exogenous variables      457
Expectation      105
Expectations, rational      7
Expert opinion      337—338
Expert Systems      119
Exponential family of distributions      323—331

exports      143
Feller, W.      222
Finance, mathematics of      24
Finitism      15
Fisher, R.A      3 35
Formalism      15 35
Fractional programming      140
Frechet, M.      24 33 35 112—113 358—359
Frege, G.      32 54—55 62
frequency      18 20 27 359
Functional dependence      78 81
Functional form      453—454
Functional, linear      69
Functional, linear, definition      245
Fundamental theorem of prevision, general comments      11 66 115 119 459
Fundamental theorem of prevision, part I      98 100—105 118
Fundamental theorem of prevision, part II      138
Fundamental theorem of prevision, part III?      255
Fuzzy logic      119
g-prior      431
Galton, F      426
Gamma distribution      405—406
Gamma function      292—293
GDP      49
General conditional prevision      154
Generalized mean      258
Geneva Colloquium on Probability      188
Ghazal      14
Gibbs sampling      286 459
Gillies, D.      23
Gnedenko, B.V.      18—19
Gnosticism      21
gnp      49
Godel, K.      55
Goldstein, M.      164
Good, I.J.      4 35 120
Granger causality      453
Haag, J.      31 188
Hacking, I.      20 27
Hailperin, T.      54 89 105 136
Hausdorff’s theorem      274
Hempel, C.      12
Hendry.D.      456—457
Heyting, A      15 17
Hierarchical mixtures      448—449
Hilbert — Ackermann closure theorem      111 119
Hilbert, D.      15 32 54
Hilbert, D., sixth problem      32
Hill, B.      120 165.426
histogram      see “Category sum”
Hume, D.      23 71 452
Huygens, C.      20
Hypergeometric distribution      191 223—226 287—290
Hypergeometric distribution, multiple category      311—313
Hyperplane      75
Hypothesis testing      2 35 334
I Ching      21
Idealism, subjective      18
Idempotence      44
Incompatible events      82 92
Independence, conditional      31
Independence, logical      50 78 81.87—97
Independence, stochastic      31 33 166—169
Indeterminacy      28 31
Indifference principle      24 31 120
Indifference, assesrtion of      58 113 157
Inequalities      see “Specific names”
Inflation      49
information      123 345—346 355 445
Information transfer functions      397—399
Instrumental variables      457
International Congress on the Philosophy of Science      10 113 358—359
Interval probability assertions      30—31 66 113 120
Intuitionism      15—16 68
Jeffreys, H.      4 35 62
Jensen’s Inequality      256
Jevons, W.S.      26
Johnson, W.E.      35
Judgment, personal      12 28
Keynes, J.M.      17—18 31 35
Kolmogorov axioms      33—35
Kolmogorov, A.N.      14 32 125
Kolmogorov’s inequality      106 112
Kuhn, T.      13 451
Kyburg, H.      164
Language, mathematics as      13—14
Laplace, P.      20 24—25 188
Law of the excluded middle      68
Laws of chance      28
Laws of large numbers      27
Le Play, F.      28
Learner, E.      4 426 459
Learning      368—369
Learning, confirmational commitment      158
Learning, temporal      136
Least-squares estimate      455
Leibniz, G      20
Levi, I.      32 62 120 153 164
Liagre, J.B.J.      29
Likelihood functions      217 222 397—399
Likelihood functions, definition      397
Likelihood principle      215 354
Lindley, D.V.      4 35 120
Linear programming      99 102—103 109 119 140
Linear regression equations      375 (see also “Regression”)
Linear-logarithmic ratio score      340
Linearity of coherent prevision      69 75 111
LINEX scoring function      342
Locality property of logarithmic score      353—354
Logic      50
Logic, deductive      2 99
Logic, inferential      8 13 17
Logic, inferential, many-valued      17—18 21 25 95
Logic, probabilistic      26
Logic, propositional      50—55 68 95
Logical dependence      78 81
Logical dependence, geometrical examples      87—97
logical functions      51 79
Logical operations, algebraic representations      54
Logical operations, as arithmetic      50—52
Logical relations      50 78
Lyapunov’s inequality      274
Mach, E.      12
Mahabharata      21
Maistrov.L.      29
Many-valued logic      17—18 21 25 95
Markov chains      239
Markov’s inequality      251
Marxist philosophy      18—19 29
Mass phenomena      18 28
Mathematics, foundations      15
Matrix-t-distribution      422—423
Maximum stake      60—61
Meaning      1 3
Measure theory      34—35
Measurement      11 48—49 55 65 247
Measurement error      48
Measurement, operationally defined      39
Median      249 342
Mercantilism      21—22
Metaphysics      12
Mill, J.S.      27
Minimum stake      65
Mixing functions      397 402 442
Mixture distribution      289
Mixture-normal distribution      396
MODE      248
Model fitting      334
Moment generating function      269 275
Moments of a distribution      272

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