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


Язык: en

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
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Предметный указатель
Moments of a distribution, central      273
Moments of a distribution, joint product      284
Monte Carlo sampling      277 286
moving averages      436—446
Multiple-category hypergeometric distribution      312
Multiple-category Polya distribution      322—323
Multivariate normal distribution      372
Multivariate normal distribution, independence      376
Multivariate normal distribution, Linear transformations      384
Multivariate normal distribution, mixtures      394—397
Multivariate normal distribution, quadratic transformations      385
Multivariate normal distribution, standard form      385
Multivariate t-distribution      413
Nalimov, V.V.      19 55
National Bureau of Standards      49
Natural conjugate distribution      292 309
Needham, J.      21
Negative binomial distribution      328
Nekrasov, P.A.      18
New Zealand Official Statistical Yearbook      439
Nightingale, F.      28
Noncontradiction      51 68
Nonlinear programming      255
Nonstationary autoregression      433
Normal distribution, multivariate      372
Normal distribution, multivariate, conditional and marginal      375
Normal-gamma distribution      405 408
Odds      342
Omitted variable bias      453 454
Operational definitions      12 48 81
Operational subjective statistics      55 57 119
Operationally defined measurements      165
Optimal Statistical Decisions      6
Parameter estimation      334
Parameter space      289
Parameterization      308
Parametric family of distributions, definition      289
Pareto.W.      5
Partial assertion      114 118
Partial exchangeability      228—242 433 435
Partial exchangeability, definition      228
Partially asserted prevision      116
Partition      82—83 97
Partition, generated by $X_N$      45 85
Partitioned prevision      253
Partitioned variance      253
Pearson, E.      20
Pearson, K.      20 24
Permutation      176—177
Philosophy      see “Operational definitions”
Philosophy, as activity      1 7
Philosophy, empiricist      23
Philosophy, of probability      35
Philosophy, of science      10
Philosophy, of science, Marxist materialist view      18—19 29
Philosophy, Platonic      13
Philosophy, scholastic      12 20
Poincare, H.      31
Poisson distribution      327
Poisson distribution, gamma mixture      328
Poisson, S.D.      27
Polanyi, M.      13
Polya distribution      303—309
Polya distribution, multiple category      322
Polya urn      175
Polytope      78
Pope, A.      26
Popper, K.      12—13
Portfolio selection      260—264
Pratt J.      359
Precision Measurement      48—49
Precision, definition      372—373
Predication, Jaina theory      21
Prevision      14 33 52 55—59 114
Prevision boundaries      115—118
Prevision, definition      60
Prevision, for a vector of quantities      61
Price, R.      23
Probabilism      20
Probabilistic Revolution      27
probability      1
Probability, axiomatic      8 32
Probability, boundary or interval      120
Probability, conditional      33
Probability, definition      60
Probability, distribution function      265
Probability, formalist formulation      8
Probability, interval      31 99
Probability, Marxist view      17—19
Probability, mass function      86 265
Probability, meaning      2 32
Probability, objectivist formulation      7—8 11 28
Probability, of an isolated event      35
Probability, subjectivist formulation      8—9 30—31
Product Reliability      146
Product rule      124 148
Productivity      7
Propensity      8 27
Proper scoring rule(s)      336
Proper scoring rule(s), distinguishing properties      351—354
Proper scoring rule(s), separate components      363—367
Propositional logic      50—55 68 95
Psychologism      32
Quadratic score      339 343
Quality of products      145
Quantity vector, definition      44
Quantity, definition      39
Quetelet, A.      28
Ramsey, F.      4 7 18 31 64
Random sampling      215
Randomization      215
Randomness      13 28
Rational expectations      262
Realm matrix      45
Realm of a quantity, definition      41
Realm of a quantity, size      41
Regression equation      376 412 424
Regression equation, definition, linear      426
Regression equation, function      425 426
Regression equation, multivariate normal context      381—383
Regression equation, reverse      453
Regression equation, spurious      453
Reification      19
Reliability      331—332
Religion      12 56
repeat rate      345
Repetition      8 18—19 26 42
Representation theorem      188
Reserve Bank of New Zealand      439
Reverse regression      453
Russell, B.      55 62 452
Russell’s paradox      17
Salamanders, example      129—133
Saunderson, N.      154
Savage, L.J.      3—4 64 215
Scale of maximum stake, definition      60—61
Scale of maximum stake, problem      62
Schervish, M.      359
Scholasticism      20
science      56
Scoring rule(s), definition      335 336
Scoring rule(s), definition, for continuous approximating distributions      350
Scoring rule(s), definition, for previsions      339—341
Scoring rule(s), definition, for probability distributions      343—347
Scoring rule(s), definition, for probability distributions, geometrical display      348—349
Scoring rule(s), definition, separate components      363—367
Scrambling procedure      214
Seber, G.      222
Separating hyperplane theorem      76
Sequential forecasts      284 334 436
Sequential scoring      334 430
Shafer, G.      120
Shannon, C.      356—357
Significance, statistical      2
Simplex, unit      97 181
Skepticism      12
Sociology      28
Sonnet      14
Specification error      453 454
Spherical symmetry      384 400
Spurious regression      453 456
Stable estimation      423
Standard procedure of prevision assessment      57 59
State-dependent preferences      158
Stationary autoregression      432
Statistic, definition      193
Statistical theory      56
Statistics, operational subjective      5—7 11
Stieltjes integral      202 271
Stigler, S.      24 154
Stochastic independence      166 169—170
Subjectivism, dangers      32
Sufficient statistic(s)      193—195 389 401 433 435
Sufficient statistic(s), definition      194
Sufficient statistic(s), exponential family      323—326 331—332
Sufficient statistic(s), fixed dimension      320 438
Sufficient statistic(s), for partial exchangeability      228
Support, degree of logical      17
Supporting hyperplane      74
Sure loser      67 136
Swift.J.      26
Synthesis, Bayes/non-Bayes      4—5
t-distribution      405
Taming of Chance      27
Tautology      51
Tavernier, J.B.      22
Temporal coherence      161
Theorem of total prevision      149
Theory of probability      5 34—35
Todhunter, I.      20 26
Trade war      101
Truth function      50
U.N. Standardized System of National Accounts      49
U.S. Bureau of Standards      48
Uncertainty      23—25 27—29 55 57 450
Unit simplex      97 181
Unit(s) of population      213
Unit(s) of population, scrambled      213
Usury      21 23
Util(s)      60
Utility      56—57 64 257 262—264 336—337
Utility theory      247 260
Utility valuations      350
Value judgments      56
Van Deuren, P.      30—31
Vandermonde matrix      268—269
Variance      250—254
Variance, covariance matrix      250
Variance, for linear combinations      253
Venn, J.      26
Walley, P.      120
Waring, M.      49
Weibull distribution      331
Whale strandings      72
Whitehead, A.      62
Wishart distribution      417
Wittgenstein, L.      452
Zellner.A.      4 426
Zero probabilities      33 66
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