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22
Computer Experiments
, 1996
"... Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, a ..."
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Cited by 119 (6 self)
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Introduction Deterministic computer simulations of physical phenomena are becoming widely used in science and engineering. Computers are used to describe the flow of air over an airplane wing, combustion of gasses in a flame, behavior of a metal structure under stress, safety of a nuclear reactor, and so on. Some of the most widely used computer models, and the ones that lead us to work in this area, arise in the design of the semiconductors used in the computers themselves. A process simulator starts with a data structure representing an unprocessed piece of silicon and simulates the steps such as oxidation, etching and ion injection that produce a semiconductor device such as a transistor. A device simulator takes a description of such a device and simulates the flow of current through it under varying conditions to determine properties of the device such as its switching speed and the critical voltage at which it switches. A circuit simulator takes a list of devices and the
Complete search in continuous global optimization and constraint satisfaction
 ACTA NUMERICA 13
, 2004
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Valuation of Mortgage Backed Securities Using Brownian Bridges to Reduce Effective Dimension
, 1997
"... The quasiMonte Carlo method for financial valuation and other integration problems has error bounds of size O((log N) k N \Gamma1 ), or even O((log N) k N \Gamma3=2 ), which suggests significantly better performance than the error size O(N \Gamma1=2 ) for standard Monte Carlo. But in hig ..."
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Cited by 100 (15 self)
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The quasiMonte Carlo method for financial valuation and other integration problems has error bounds of size O((log N) k N \Gamma1 ), or even O((log N) k N \Gamma3=2 ), which suggests significantly better performance than the error size O(N \Gamma1=2 ) for standard Monte Carlo. But in high dimensional problems this benefit might not appear at feasible sample sizes. Substantial improvements from quasiMonte Carlo integration have, however, been reported for problems such as the valuation of mortgagebacked securities, in dimensions as high as 360. We believe that this is due to a lower effective dimension of the integrand in those cases. This paper defines the effective dimension and shows in examples how the effective dimension may be reduced by using a Brownian bridge representation. 1 Introduction Simulation is often the only effective numerical method for the accurate valuation of securities whose value depends on the whole trajectory of interest Mathematics Departmen...
Latin Supercube Sampling for Very High Dimensional Simulations
, 1997
"... This paper introduces Latin supercube sampling (LSS) for very high dimensional simulations, such as arise in particle transport, finance and queuing. LSS is developed as a combination of two widely used methods: Latin hypercube sampling (LHS), and QuasiMonte Carlo (QMC). In LSS, the input variables ..."
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Cited by 84 (8 self)
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This paper introduces Latin supercube sampling (LSS) for very high dimensional simulations, such as arise in particle transport, finance and queuing. LSS is developed as a combination of two widely used methods: Latin hypercube sampling (LHS), and QuasiMonte Carlo (QMC). In LSS, the input variables are grouped into subsets, and a lower dimensional QMC method is used within each subset. The QMC points are presented in random order within subsets. QMC methods have been observed to lose effectiveness in high dimensional problems. This paper shows that LSS can extend the benefits of QMC to much higher dimensions, when one can make a good grouping of input variables. Some suggestions for grouping variables are given for the motivating examples. Even a poor grouping can still be expected to do as well as LHS. The paper also extends LHS and LSS to infinite dimensional problems. The paper includes a survey of QMC methods, randomized versions of them (RQMC) and previous methods for extending Q...
Monte Carlo variance of scrambled net quadrature
 SIAM Journal on Numerical Analysis
, 1997
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Snobfit  Stable Noisy Optimization by Branch and Fit
"... this paper produces a userspeci ed number of suggested evaluation points in each step; proceeds by successive partitioning of the box (branch) and building local quadratic models ( t); combines local and global search and allows the user to determine which of both should be emphasized; h ..."
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Cited by 26 (3 self)
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this paper produces a userspeci ed number of suggested evaluation points in each step; proceeds by successive partitioning of the box (branch) and building local quadratic models ( t); combines local and global search and allows the user to determine which of both should be emphasized; handles local search from the best point with the aid of trust regions; allows for hidden constraints and assigns to such points a function value based on the function values of nearby feasible points
Monte Carlo Extension Of QuasiMonte Carlo
 Proceedings of the 1998 Winter Simulation Conference
, 1998
"... This paper surveys recent research on using Monte Carlo techniques to improve quasiMonte Carlo techniques. Randomized quasiMonte Carlo methods provide a basis for error estimation. They have, in the special case of scrambled nets, also been observed to improve accuracy. Finally through Latin super ..."
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Cited by 17 (0 self)
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This paper surveys recent research on using Monte Carlo techniques to improve quasiMonte Carlo techniques. Randomized quasiMonte Carlo methods provide a basis for error estimation. They have, in the special case of scrambled nets, also been observed to improve accuracy. Finally through Latin supercube sampling it is possible to use Monte Carlo methods to extend quasiMonte Carlo methods to higher dimensional problems. 1 INTRODUCTION The problem we consider is the estimation of an integral I = Z [0;1] d f(x)dx: (1) Standard manipulations can be applied to express integrals over domains other than the unit cube or with respect to nonuniform measures in the form (1). Similarly, the integrand f in (1) subsumes weighting functions from importance sampling or periodization. We are especially interested in cases where the dimension d is large, and some of the methods considered here apply to the case d = 1. The focus of this article is on ways of combining Monte Carlo and quasiMo...
ACCURATE EMULATORS FOR LARGESCALE COMPUTER EXPERIMENTS
, 1203
"... Largescale computer experiments are becoming increasingly important in science. A multistep procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator inmultiple steps. Inpractice, the procedureshows substantial improvements in overall accuracy, b ..."
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Cited by 11 (2 self)
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Largescale computer experiments are becoming increasingly important in science. A multistep procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator inmultiple steps. Inpractice, the procedureshows substantial improvements in overall accuracy, but its theoretical properties are not well established. We introduce the terms nominal and numeric error and decompose the overall error of an interpolator into nominal and numeric portions. Bounds on the numeric and nominal error are developed to show theoretically that substantial gains in overall accuracy can be attained with the multistep approach.
Estimating Mean Dimensionality
, 2003
"... The mean dimension of a function is defined as a certain weighted combination of its ANOVA mean squares. This paper presents some new identities relating this mean dimension, and some similarly defined higher moments, to the variable importance measures of Sobol' (1993). The methods are applied ..."
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Cited by 11 (1 self)
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The mean dimension of a function is defined as a certain weighted combination of its ANOVA mean squares. This paper presents some new identities relating this mean dimension, and some similarly defined higher moments, to the variable importance measures of Sobol' (1993). The methods are applied to study some functions arising in the bootstrap, in computational finance, and in extreme value theory.
Alternative Sampling Methods for Estimating Multivariate Normal Probabilities
"... We study the performance of alternative sampling methods for estimating multivariate normal probabilities through the GHK simulator. The sampling methods are randomized versions of some quasiMonte Carlo samples (Halton, Niederreiter, NiederreiterXing sequences and lattice points) and some samples ..."
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Cited by 10 (0 self)
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We study the performance of alternative sampling methods for estimating multivariate normal probabilities through the GHK simulator. The sampling methods are randomized versions of some quasiMonte Carlo samples (Halton, Niederreiter, NiederreiterXing sequences and lattice points) and some samples based on orthogonal arrays (Latin hypercube, orthogonal array and orthogonal array based Latin hypercube samples). In general, these samples turn out to have a better performance than Monte Carlo and antithetic Monte Carlo samples. Improvements over these are large for lowdimensional (4 and 10) cases and still signi…cant for dimensions as large as 50.