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Fishman G.S. — Monte Carlo: concepts, algorithms, and applications
Fishman G.S. — Monte Carlo: concepts, algorithms, and applications

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Название: Monte Carlo: concepts, algorithms, and applications

Автор: Fishman G.S.

Аннотация:

This volume presents a comprehensive first course in the Monte Carlo method which will be suitable for graduate and undergraduate students in the mathematical sciences and engineering, principally in operations research, statistics, mathematics, and computer science. The reader is assumed to have a sound understanding of calculus, introductory matrix analysis, probability, and intermediate statistics, but otherwise the book is self-contained. As well as a thorough exploration of the important concepts of the Monte Carlo method, the volume includes over 90 algorithms which allow the reader to move rapidly from the concepts to putting them into practice. The book also contains numerous exercises, many of them hands-on implementations of selected algorithms to demonstrate the application of these ideas in realistic settings. Software, freely available via ftp and portable across computing platforms, provides programs for pseudorandom number generation and statistical sample path data analysis. The software is suitable for use with the exercises as well as for more general applications. For professional mathematical scientists and engineers this book provides a ready reference to the Monte Carlo method, especially to implementatable algorithms for performing sampling experiments on a computer and for analyzing their results.


Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 698

Добавлена в каталог: 29.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
#P-complete      57 81 95 453
$\pi$-irreducible      339
$\sigma$-field      534
570 MAIN program      667
ABATCH rule      510 554—565 582—584
Absolute error      22 47 51 69 71 506
Absolute error, worst-case      18
Absorbing state      467
Acceptance region      27
Acceptance-rejection      46 60
Acceptance-rejection method      149 171—179 181 201 207 243
Activity networks      136
Additive increments      343
Affine transformation      601
Algebraic multiplicity      415
Algorithm, $\overline\xi_n$      76 77 67 69 70 73 74
Algorithm, $\tilde \xi_n$      76 77
Algorithm, A      142
Algorithm, ABATCH      561 565
Algorithm, ALIAS      165 250
Algorithm, ALSET      167 168 250
Algorithm, ANNEAL      404 406
Algorithm, APPROX      519
Algorithm, AR      172 609
Algorithm, ARS      174
Algorithm, ATABLE      239
Algorithm, AW      202
Algorithm, B      142
Algorithm, BB      205
Algorithm, BB*      204 205 248 251
Algorithm, BC*      206
Algorithm, BER      215
Algorithm, BISECTION      26 28 29 38 74
Algorithm, BRUA      217
Algorithm, BRUA*      217 218 248 251
Algorithm, BTABLE      240 241
Algorithm, CA      187 191 192
Algorithm, CM      156
Algorithm, CM*      159
Algorithm, CMC      322—323
Algorithm, CMNB      160 250
Algorithm, CMSET      157 158 250
Algorithm, COEFF      86 106
Algorithm, COMPM      162
Algorithm, CON      116 142
Algorithm, CONCENTRIC      446
Algorithm, CONVOL      445 449
Algorithm, CUPCUBE      461
Algorithm, DFI      34 72
Algorithm, DI      153
Algorithm, DUAL      470
Algorithm, EA      188 189
Algorithm, EAM      186
Algorithm, EUNIFORM      227 228
Algorithm, FGRB      94—95
Algorithm, FGRW      91—92 98
Algorithm, FSR      652—653 655
Algorithm, FTOUR      362—363
Algorithm, GEO      221
Algorithm, GKM1      197 199 250
Algorithm, GKM2      199 200 247 251
Algorithm, GKM3      200 223
Algorithm, GORDER      227 228 230
Algorithm, GS      194 195
Algorithm, GS*      194 195
Algorithm, HRUA*      220 249
Algorithm, HYP      219
Algorithm, INOUT      379 380 486
Algorithm, IORDER      226 227
Algorithm, ITM      149
Algorithm, ITR      153 178 212 215 218 221
Algorithm, LBATCH      556
Algorithm, LTM      223 224
Algorithm, MARKO      376—378 414
Algorithm, MATCH      453—454 456 459
Algorithm, MC      18 19 25 27 29 34 35 42 51 52 57
Algorithm, MC*      44—47 51 52 55 57
Algorithm, MCMC      496 505
Algorithm, METRO      386 404
Algorithm, MIX      380—381 383—384
Algorithm, MN      224
Algorithm, MULTN      225
Algorithm, NA      190
Algorithm, NEGBIN      222
Algorithm, NETWORK      60 61 63
Algorithm, N—R      150
Algorithm, OMAX      229 230
Algorithm, OSIMP      232 233
Algorithm, OSPHERE      235
Algorithm, PD      214 215
Algorithm, PERF      456—458
Algorithm, PM      606
Algorithm, PRUA      213 223
Algorithm, PRUA'      213
Algorithm, PRUA*      214—215 217 248 251
Algorithm, ROU      181 182
Algorithm, RPERM      231
Algorithm, RT      190
Algorithm, RWTE      164
Algorithm, SA      188
Algorithm, SAMPLE      440—442
Algorithm, SEQ      270—271
Algorithm, SEQ*      272—273
Algorithm, SETUP      239 240
Algorithm, SKIP      236
Algorithm, SST      466
Algorithm, T3T*      208 209 248
Algorithm, TOUR      241 242 378 380 484—486
Algorithm, UNION      81 82
Algorithm, UNION*      262—263
Algorithm, VOLUME      15 18 22
Alias method      165—170 243
All-points connectedness      83 84 95
Almost everywhere      20
Almost surely      20
Anonymous ftp      10 565 582 603 667
Antithetic variates      320 331
Aperiodic      339
Arc set      55
ARPANET      98
ASA      532 545
Assumption of strong approximation      532
Assumption of weak approximation      502 544
Asymptotic consistency      118
Asymptotic efficiency      118
Asymptotic validity of confidence intervals      559
Asymptotically valid $100\times(1-\delta)$ percent confidence interval      502—504 544—545
Augmented graph      455
Autocorrelation function      522
Autocorrelation function, M/M/1 waiting time      550
Autocovariance      521 538 540
Autocovariance function      520—522 529
AWA      502 532 544
A—D distribution      630
Ball — Provan method      98
Barker's method      580
Basic variables      93
Batch means, ABATCH rule      510 554—565 582—584
Batch means, analysis programs      565—572
Batch means, constant number of batches      544—545
Batch means, FNB rule      546—548
Batch means, increasing number of batches      545—546
Batch means, LBATCH rule      554—565 582—583
Batch means, method      495 540—565 581
Batch means, SQRT rule      548—549
Batch_Means subroutine      567 568 571
Bayesian posterior distributions      406 411 487 584
Bayesian posterior distributions, Gamma conjugate distributions      409—411
bernoulli      25 27 110 114 116 215 221 222
Bernoulli distribution      235—236
Beta distribution      28 29 151 200—206 248 251
beta function      28
Beyer quotient      624 626—628
Beyer ratio      628
Binary computer      597 602
Binary control variates      285—291
Binary point      597
Binomial distribution      19 25 27 63 81 153 210 215—218 248
Bipartite graph      452
bit shifting      601
Bivariate uniformity      631
Boltzmann constant      399
Bonferroni's inequality      104
Bonferroni's inequality of the first kind      104
Boundary sites      412
Boundary-value problem      336
Bounded variation      66
Bounds on volume      35
Brownian motion      346
Budgeting constraints      37
Buffer exceedance      353—358 476
Buffer sizes      517
Candidate state      385
Capacity constraints      292
Cartesian-product formula      65
Catastrophic failure      363—368
Cauchy distribution      151 186—187 191 192 246
Cauchy — Schwarz inequality      328 421 423 428 432
Central limit theorem      8 22 29 501
Chain splitting      495 575
Chaos      589
Chaotic dynamical system      589
Chapman — Kolmogorov equations      339
Characteristic polynomial      646
Chebyshev intervals      30 77
Chebyshev's inequality      21 22 26 29 31 438 446 458 460 463 466 472
Cheeger's inequality      426
Chi-squared distribution      193 502
Child mode      567
CLIQUE      399—401
Coefficient of variation      61 71 101
Combinatorial probability      80
Communication network      483 583
Companion matrix      659
Component failures      366
Composition method      50 149 160—165
Computational complexity      3
Concentric hyperspheres      51
Conditional mean      499
Conditional mean, function      513 520
Conditional Monte Carlo      321—325 328
Conditional probability      77
Conditional variance      499
Conductance      425—430 478 513
Confidence coefficient      27 29
Confidence interval      4 14 20 27—34 79 308—309 485 494—495 544 500—504 544 546 551 580
Confidence interval, approximating $100\times(1-\delta)$ percent normal      74 76 559
Confidence interval, approximating normal      63
Confidence interval, asymptotic validity      554
Confidence interval, asymptotically valid      68 502—504 544—545
Confidence interval, based on binomial distribution      27 29
Confidence interval, Chebyshev      30
Confidence interval, distribution-free      63
Confidence interval, normal      30
Confidence level      27
Connected      55 56 80
Constant number of batches      544—545
Constraint vector      384
Contingency tables      583
Continuity correction      31
Continuous distributions      150
Continuous-time Markov chain      365
Control variate method      6
Control variates      277—295 326 329
Control variates, binary control variates      285—290
Control variates, estimating a distributional constant      330
Control variates, maximal flow distribution      291—296
Control variates, maximal s—t flow      326
Control variates, normal      281—284
Control variates, stochastic ordering      285
Convergence in probability      21
Convex polytope      5 477
Correlated sampling      5
Correlation      155
Correlation, structures      529
Cost-minimizing problem      526
COUNT      5 13
Counting problems      78 79
Coupling      414 459—464 469 479
Coupling time      459
Coverage      552
Coverage probability      27
Covering time      485
Cramer — Legendre transform      267
Cross-conditional probabilities      469
Cutpoint method      156 160 161 243 250
Dangerous multipliers      600—601
DATUM      569
DECstation 500/240      565
Dedicated link      485
Dependence      147
Destination node      515
Detailed balance      340 584
Diagonalizable transition matrix      473
Diagonizable      416
Dirichlet boundary-value problem      2
Discrepancy      621—627 647 670 673
Discrete distributions      153
Discrete dynamical system      589
Discrete optimization      79
Discrete-event simulation      336
Discrete-state, discrete-time chain      341
Discrete-time, time-homogeneous Markov process      338
Disjoint subsets      84
Distribution-free approach      60
Distribution-free confidence region      371
Distributional properties      655 678 667 670
Doubly stochastic      340
Dual space      613
DUNIF      605
Edge effects      411—413 477
Edge set      55 80
Edge sites      412
Edge-disjoint cutsets      59 60
Edge-disjoint paths      59 60
Efficiency-improving techniques      15
Eigenvalue      415 426 473
Eigenvalues      497
Elliptic partial differential equation      2
Empirical d.f.      621 629
End effects      562
Energy function      398
Equal tail probabilities      28 37
Equidistributed points      65
Equidistributed sequence      65 66
Equilibrium distribution      340
EQUIVALENCE      663
Erlang distribution      193
Error bound      41
Estimating a distribution constant      304—307 330
Estimating path length      510—512
Euclidean distance      611
Euler totient function      594 647
Euler's constant      463 472
Exact-approximate method      149 185—188 246
EXAMPLE.FOR      566 568
Exceedance probability      265 325
Excess kurtosis      563
Exclusive or operation      651
Exponential change of measure      265—269
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