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| DeGroot M.H. — Optimal statistical decisions |
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| Предметный указатель |
Posterior distribution, approximation for large samples 215—219
Posterior distribution, computation in stages 147—148
Posterior distribution, convergence to correct value 202—204
Posterior distribution, limiting 191 222—223
Posterior distribution, ratio of values of 220—221
Pratt, J.W. 75 100 115 138 306 456 459 469
Precise measurement 198—201
Precision matrix of multivariate normal distribution 56
Precision matrix of multivariate t distribution 59
Precision matrix of Wishart distribution 59
Precision of normal distribution 38
Precision of t distribution 42
Preferences among gambles 93
Preferences among lotteries 89 92
Preferences among probability distributions 88—90
Preferences among repeated gambles 100
Preferences among rewards 86—88
Prescott, E.C. 389 459
Principle of optimality 278 300
Prior distribution 139
Prior distribution, improper 190—198
Prior distribution, invariant 196
Probability density function 17
Probability density function, joint, of several random variables 18
probability distribution 10
Probability distribution of parameter in decision problem 121—122
Probability distribution of parameter in decision problem, use of inappropriate distribution 127—128 see "Prior
Probability distribution, multivariate 18
Probability distribution, univariate 17
Probability distributions of rewards, bounded 90
Probability distributions of rewards, bounded, equivalence relations for 107—109
Probability distributions of rewards, unbounded 110—115
Probability function 17
Probability function, joint, of several random variables 18
Probability space 10
Product space 8
Pure decision 129
Purves, R. 394 454
Quisel, K. 405 459
Radner, R. 115 433 459
Raiffa, H. 82 115 138 141 142 159 164 236 249 259 457 459 460
Ramsey, F.P. 75 81 460
Random number of observations 273—275 288 347
Random sample 20 29
Random sample from distribution with unknown parameter 157
Random sample of random vectors 23
Random variable 16
Random vector 22
Randomization 129—130
Randomized decision 128
Rank of a matrix 21
Rao, C.R. 5 27 57 203 210 251 253—255 460
Rao, M.M. 237 451
Ray, S.N. 297 306 450 460
Real line 8
Recall see "Sampling with recall" "Sampling
Rees, D.H. 249 454
Regression coefficient 256
Regular sequential decision procedure 289
Regular stopping rule 347
Regular supermartingale 365
Regular supermartingale, minimal 368
Reichenbach, H. 4 460
Relative likelihood 70—85
Relative likelihood, agreement with probability distribution 70 78
Relative likelihood, conditional 81—82
Relative likelihood, transitivity of 71
Renyi, A. 433 460
Reward function for Markov process 370
Reward function for Markovian decision process 386
Rewards 86
Rewards in decision problem 121
Rewards, cofinal sequence of 111
Rewards, complete ordering of 87—88
Rewards, interval of 90 110
Rewards, preferences among 86—88
Rewards, probability distributions of 88—89
Rewards, probability distributions of, bounded 90 107—109
Rewards, probability distributions of, preferences among 88—90
Rewards, probability distributions of, unbounded 110—115
Rewards, set of 86
Risk averter 99
Risk function 138
Risk in decision problem 122
Risk in statistical decision problem 137
Risk taker 99
Robbins, H. 293 297 331 335 336 353 365 368 391 404 405 451 455 458—460
Roberts, C.D. 469
Roberts, H.V. 82 460 469
Ross, S.M. 390 453 460
Royden, H.L. 468
Ruben, H. 365 460
Rubin, H. 249 456 468
Sacks, J. 237 297 335 452 456 460
Sacksteder, R. 439 459 460
Sakaguchi, M. 336 433 439 460
Sample space 7
Sample space of composite experiment 8
Sampling cost see "Cost of observation"
Sampling plan 272 see
Sampling plan and stopping sets 273
Sampling with recall 335
Sampling with recall from normal distribution 341—345
Sampling with recall, existence of optimal stopping rule 349—353
Sampling without recall 331—334
Sampling without recall from normal distribution 336—341
Sampling without recall, bounded procedures 332—333
Sampling without recall, existence of optimal stopping rule 349—353
Sampling without recall, unbounded procedures 333—334
Samuel, E. 391 461
Samuels, S.M. 331 451
Savage, L.J. 4 75 81 93 100 115 138 159 199 240 316 394 452 454 455 461 468
Sawaragi, Y. 422 461
Scarf, H. 411 448 461 470
Scheffe, H. 159 198 457 461
Schlaifer, R. 115 138 141 142 159 164 236 249 259 459—461
Schleifer, A., Jr. 249 449
Schwartz, L. 204 461
Schwartz, R. 469
Schwarz inequality 254
Schwarz, G. 297 461
Scott, D. 81 461
Search problem 423—429
Search problem for Markov chain 442 443
Search problem with equal costs 427—429
Secretary problem 325
Seidenberg, A. 75 456
Sequential decision function 272
Sequential decision problem 272
Sequential decision problem, stable 301
Sequential decision procedure 272
Sequential decision procedure and stopping variable 287—288
Sequential decision procedure, Bayes 276
Sequential decision procedure, bounded 277
Sequential decision procedure, bounded, as approximation to optimal procedure 294—297
Sequential decision procedure, bounded, optimal 278—280
Sequential decision procedure, regular 289
Sequential decision procedure, total risk of 275
Sequential decision procedure, truncation of 294
Sequential decision procedure, unbounded 287
Sequential probability-ratio test 306—316
Sequential probability-ratio test, number of observations 311—312
Sequential probability-ratio test, number of observations, expectation of 313—314
Sequential probability-ratio test, optimal properties of 316
Sequential probability-ratio test, probabilities of decisions 309—311
Sequential probability-ratio test, risk of 315
Sequential probability-ratio test, risk of, for small sampling cost 315—316
Sequential sample 267
Sequential sample, gain from 267—271
Sequential sample, sequential random sample 272 346
| Sequential selection of experiments 430—432
Shannon, C.E. 431 461
Shaw, L.G. 470
Shelly, M.W., II 411 461 470
Shiryaev, A.N. 306 454 470
Siegel, S. 96 451
Siegmund, D.O. 353 461 470
Simon, H.A. 41 418 461
Singular matrix 21
Skibinsky, M. 470
Smith, C.A.B. 470
Smokier, H.E. 81 456
Snell, J.L. 353 368 372 456 462 470
Sobel, M. 297 462
Springer, B.G.F. 259 462
Springer, M.D. 470
Square matrix 21
St. Petersburg paradox 95
Stable estimation, principle of 199
Stable sequential decision problem 301—306
Standard deviation 24
Standard normal distribution 38
Standardized t distribution 42
Staroverov, O.V. 429 462
State space of Markov process 370
Stationary procedure for inventory problem 409
Stationary procedure for Markovian decision process 389
Stationary stopping rule 372 373
Stationary transition probabilities 370
Statistic 155
Statistical decision problem, components of 136
Statistical decision problem, components of, and sequential choice of experiments 429—431
Stein, C. 164 193 237 311 455 462
Steinhaus, H. 470
Stochastic transformation 434
Stone, M. 196 259 462 470
Stopping rule 272 347
Stopping rule for martingales 356—365
Stopping rule for search problem 428
Stopping rule, regular 347
Stopping variable 288 347
Strassen, V. 439 462
Strauch, R.E. 389 390 462
Strong Law of Large Numbers 203
Subjective probability 4 69—85
Subjective probability and relative likelihood, agreement of 70 77—78
Subjective probability, auxiliary experiment for construction of 75—77
Subjective probability, uniqueness of 80—81
Submartingale 354
Submartingale, stopping rules for 356—365
Sufficient experiment 433—439
Sufficient experiment, optimality of 437
Sufficient statistics 155—159
Sufficient statistics for exponential family 161
Sufficient statistics, factorization criterion for 156
Sufficient statistics, jointly sufficient statistics 158
Sunahara, Y. 422 461
Supercontinuous functions 205
Supercontinuous functions, convergence of 210
Supermartingale 354
Supermartingale and optimal stopping rule 365—369
Supermartingale, minimal 368
Supermartingale, regular 365
Supermartingale, regular, minimal 368
Supermartingale, stopping rules for 356—365
Suppes, P. 82 96 100 115 451 457 462 470
Supporting hyperplane 131
Suzuki, Y. 470
Symmetric matrix 22
t distribution 41 249
t distribution, as marginal prior distribution 170
Tan, W.Y. 259 462 470
Teicher, H. 336 365 451 452 462
Testing hypotheses, problems of 237
Testing hypotheses, problems of, in linear model 253
Testing hypotheses, problems of, in linear model, about regression coefficients 256
Testing hypotheses, problems of, sequential 297
Thatcher, A.R. 470
Theil, H. 418 462 470
Thompson, J.W. 470
Thompson, W.E. 470
Thompson, W.R. 404 462
Thorp, E.O. 394 462
Thrall, R.M. 115 462
Tiao, G.C. 259 462 464 466 468 470
Tingey, F.H. 470
Total risk 142
Total risk of sequential decision procedure 275
Total risk, behavior of 145
Tou, J.T. 422 463
Trace (Tr) 22
Transformation of random variables, one-to-one 27
Transformation of random variables, probability integral 31
Transformation of random variables, stochastic 434
Transition function for Markovian decision process 386
Transition function of Markov process 370
Truax, D. 469
Tucker, H.G. 5 463
Tversky, A. 467
Tweedie, M.C.K. 365 463
Two-armed-bandit problem 394—405
Two-armed-bandit problem with dependent parameters 399—404
Two-armed-bandit problem with one parameter known 396—399
Uncertainty function 431
Uniform distribution 40
Uniform distribution and construction of subjective probability 76—77
Uniform distribution and sufficient experiment 437
Uniform distribution as approximation to prior distribution 198—201
Uniform distribution in inventory problem 440
Uniform distribution, conjugate family for 172 173
Uniform distribution, estimation problem for 260
Uniform distribution, estimation problem for, sequential 322—323
Uniform distribution, improper 191 197
Uniform distribution, improper prior distribution for 222 224
Uniform distribution, improper, invariance of 196
Uniform distribution, sampling without recall 380 381
Uniform distribution, sequential decision problem for 318 323
Uniform distribution, sufficient statistics for 158 184
Uniformly integrable sequence 359
Union of sets 7
Utility 86—118
Utility function 90
Utility function for ranks in optimal stopping problem 326 327
Utility function in decision problem 122
Utility function, axiomatic development of 101—115
Utility function, bounded 109—110 115
Utility function, concave 99
Utility function, concave in betting problems 393—394
Utility function, convex 99
Utility function, convex in betting problems 391—393
Utility function, linear transformation of 91 108
Utility function, measurability of 106—107
Utility of gambling 94
Utility of insurance policy 99—100
Utility of monetary gain 95-101
Utility of monetary gain, difficulties in measurement of 94
Utility of probability distribution 91
Utility of reward 91
Utility, experimental measurement of 95—96
Vagholkar, M.K. 470
Vague prior information 190—191 193
Vague prior information in estimation problem 230 231 233 235
Vague prior information in testing hypotheses 240
van der Velde, E.A. 394 458
van Eeden, C. 469
Van Ryzin, J.R. 391 455 463
Vande Linde, V.D. 423 463
Variance 23
Veinott, A.F., Jr. 390 411 452 463
Ville, J. 356 463
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