Strategies for Quasi-Monte Carlo (International Series in Operations Research & Management Science, 22)

__Strategies for Quasi-Monte Carlo__ builds a framework to design and analyze strategies for randomized quasi-Monte Carlo (RQMC). One key to efficient simulation using RQMC is to structure problems to reveal a small set of important variables, their number being the effective dimension, while the other variables collectively are relatively insignificant. Another is smoothing. The book provides many illustrations of both keys, in particular for problems involving Poisson processes or Gaussian processes. RQMC beats grids by a huge margin. With low effective dimension, RQMC is an order-of-magnitude more efficient than standard Monte Carlo. With, in addition, certain smoothness - perhaps induced - RQMC is an order-of-magnitude more efficient than deterministic QMC. Unlike the latter, RQMC permits error estimation via the central limit theorem. For random-dimensional problems, such as occur with discrete-event simulation, RQMC gets judiciously combined with standard Monte Carlo to keep memory requirements bounded. This monograph has been designed to appeal to a diverse audience, including those with applications in queueing, operations research, computational finance, mathematical programming, partial differential equations (both deterministic and stochastic), and particle transport, as well as to probabilists and statisticians wanting to know how to apply effectively a powerful tool, and to those interested in numerical integration or optimization in their own right. It recognizes that the heart of practical application is algorithms, so pseudocodes appear throughout the book. While not primarily a textbook, it is suitable as a supplementary text for certain graduate courses. As a reference, it belongs on the shelf of everyone with a serious interest in improving simulation efficiency. Moreover, it will be a valuable reference to all those individuals interested in improving simulation efficiency with more than incremental increases. Strategies for Quasi-Monte Carlo builds a framework to design and analyze strategies for randomized quasi-Monte Carlo (RQMC). One key to efficient simulation using RQMC is to structure problems to reveal a small set of important variables, their number being the effective dimension, while the other variables collectively are relatively insignificant. Another is smoothing. Both keys get many illustrations, in particular for problems involving Poisson processes or Gaussian processes.. This monograph has been designed to appeal to a diverse audience, including those with applications in queuing, operations research, computational finance, mathematical programming, partial differential equations (both deterministic and stochastic), or particle transport as well as to probabilists and statisticians wanting to see how to apply effectively a powerful tool and to those interested in numerical integration or optimization in their own right. While not primarily a textbook, it is suitable as a supplementary text for certain graduate courses. As a reference, it belongs on the shelf of everyone with a serious interest in improving simulation efficiency. Moreover, it will be a valuable reference to all those individuals interested in improving simulation efficiency with more than incremental increases. Front Matter....Pages i-xxxiv Introduction....Pages 1-50 Smoothing....Pages 51-93 Generating Poisson Processes....Pages 95-113 Permuting Order Statistics....Pages 115-120 Generating Bernoulli Trials....Pages 121-131 Generating Gaussian Processes....Pages 133-168 Smoothing Summation....Pages 169-175 Smoothing Variate Generation....Pages 177-182 Analysis Of Variance....Pages 183-208 Bernoulli Trials: Examples....Pages 209-235 Poisson Processes: Auxiliary Matter....Pages 237-254 Background On Deterministic QMC....Pages 255-285 Optimization....Pages 287-303 Background on Randomized QMC....Pages 305-325 Pseudocodes....Pages 327-348 Back Matter....Pages 349-368