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Fishman G.S. — Monte Carlo: concepts, algorithms, and applications
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Название: Monte Carlo: concepts, algorithms, and applicationsАвтор: 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: Рубрика: Математика /Вероятность /Статистика и приложения /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1996Количество страниц: 698Добавлена в каталог: 29.05.2005Операции: Положить на полку |
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#P-complete 57 81 95 453 339 534 570 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, 76 77 67 69 70 73 74 Algorithm, 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 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 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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