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27
Simulation estimation of mixed discrete choice models using randomized and scrambled halton sequences
 Transportation Research Part B
, 2002
"... The use of simulation techniques has been increasing in recent years in the transportation and related fields to accommodate flexible and behaviorally realistic structures for analysis of decision processes. This paper proposes a randomized and scrambled version of the Halton sequence for use in sim ..."
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Cited by 27 (3 self)
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The use of simulation techniques has been increasing in recent years in the transportation and related fields to accommodate flexible and behaviorally realistic structures for analysis of decision processes. This paper proposes a randomized and scrambled version of the Halton sequence for use in simulation estimation of discrete choice models. The scrambling of the Halton sequence is motivated by the rapid deterioration of the standard Halton sequence's coverage of the integration domain in high dimensions of integration. The randomization of the sequence is motivated from a need to statistically compute the simulation variance of model parameters. The resulting hybrid sequence combines the good coverage property of quasiMonte Carlo sequences with the ease of estimating simulation error using traditional Monte Carlo methods. The paper develops an evaluation framework for assessing the performance of the traditional pseudorandom sequence, the standard Halton sequence, and the scrambled Halton sequence. The results of computational experiments indicate that the scrambled Halton sequence performs better than the standard Halton sequence and the traditional pseudorandom sequence for simulation estimation of models with high dimensionality of integration.
Computational Investigation of LowDiscrepancy Sequences in . . .
 PROCEEDINGS OF THE SIXTEENTH ANNUAL CONFERENCE ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE (UAI2000)
, 2000
"... Monte Carlo sampling has become a major vehicle for approximate inference in Bayesian networks. In this paper, we investigate a family of related simulation approaches, known collectively as quasiMonte Carlo methods based on deterministic lowdiscrepancy sequences. We first ..."
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Cited by 12 (2 self)
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Monte Carlo sampling has become a major vehicle for approximate inference in Bayesian networks. In this paper, we investigate a family of related simulation approaches, known collectively as quasiMonte Carlo methods based on deterministic lowdiscrepancy sequences. We first
Parallel and distributed computing issues in pricing financial derivatives through Quasi Monte Carlo
 IN PROCEEDINGS OF THE INTERNATIONAL PARALLEL AND DISTRIBUTED PROCESSING SYMPOSIUM (IPDPS.02
, 2002
"... Monte Carlo (MC) techniques are often used to price complex financial derivatives. The computational effort can be substantial when high accuracy is required. However, MC computations are latency tolerant, and are thus easy parallelize even with high communication overheads, such as in a distributed ..."
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Cited by 10 (0 self)
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Monte Carlo (MC) techniques are often used to price complex financial derivatives. The computational effort can be substantial when high accuracy is required. However, MC computations are latency tolerant, and are thus easy parallelize even with high communication overheads, such as in a distributed computing environment. A drawback of MC is its relatively slow convergence rate, which can be overcome through the use of Quasi Monte Carlo (QMC) techniques, which use low discrepancy sequences. We discuss the issues that arise in parallelizing QMC, especially in a heterogeneous computing environment, and present results of empirical studies on arithmetic Asian options, using three parallel QMC techniques that have recently been proposed. We expect the conclusions to be valid for other applications too.
Efficient Recursive Prediction of Stochastic Nonlinear Systems Based on Dirac Mixture Approximations
 In Proceedings of the American Control Conference
, 2007
"... Abstract — This paper introduces a new approach to the recursive propagation of probability density functions through discretetime stochastic nonlinear dynamic systems. An efficient recursive procedure is proposed that is based on the optimal approximation of the posterior densities after each pred ..."
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Cited by 8 (6 self)
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Abstract — This paper introduces a new approach to the recursive propagation of probability density functions through discretetime stochastic nonlinear dynamic systems. An efficient recursive procedure is proposed that is based on the optimal approximation of the posterior densities after each prediction step by means of Dirac mixtures. The parameters of the individual components are selected by systematically minimizing a suitable distance measure in such a way that the future evolution of the approximate densities is as close to the exact densities as possible. ˜f x (x) f x (x) ˜F x (x),F x (x) δ(x) H(x)
On the performance of shuffled Halton sequences in the estimation of discrete choice models
, 2003
"... The area of travel demand analysis has in recent years been greatly enriched by the development of new model forms that can accommodate complex patterns of substitution and taste variation. However, this added flexibility comes at a cost of greater complexity in estimation, to the degree that these ..."
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Cited by 8 (5 self)
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The area of travel demand analysis has in recent years been greatly enriched by the development of new model forms that can accommodate complex patterns of substitution and taste variation. However, this added flexibility comes at a cost of greater complexity in estimation, to the degree that these models need to be estimated through simulation. While basic MonteCarlo integration can lead to acceptable results, the cost of the simulation process can be decreased significantly by using quasiMonteCarlo integration, where the simulation process is based on quasirandom number draws rather than pseudorandom number draws. A popular type of quasirandom sequence in this context is the Halton sequence, in its different forms. In this paper, we compare the performance of standard, scrambled and shuffled Halton sequences in the estimation of various Mixed Logit models. The analysis shows that, while the scrambled Halton sequence offers some improvements over the standard Halton sequence, it is generally outperformed by the shuffled Halton sequence. The fact that the shuffled Halton sequence has further advantages in terms of implementation and generalisation makes it an appealing alternative to the scrambled Halton sequence in the simulationbased estimation of highdimensional models.
LowDiscrepancy Curves and Efficient Coverage of Space
 Workshop on Algorithmic Foundations of Robotics VII
, 2006
"... We introduce the notion of lowdiscrepancy curves and use it to solve the problem of optimally covering space. In doing so, we extend the notion of lowdiscrepancy sequences in such a way that sufficiently smooth curves with low discrepancy properties can be defined and generated. Based on a class o ..."
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Cited by 7 (1 self)
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We introduce the notion of lowdiscrepancy curves and use it to solve the problem of optimally covering space. In doing so, we extend the notion of lowdiscrepancy sequences in such a way that sufficiently smooth curves with low discrepancy properties can be defined and generated. Based on a class of curves that cover the unit square in an efficient way, we define induced low discrepancy curves in Riemannian spaces. This allows us to efficiently cover an arbitrarily chosen abstract surface that admits a diffeomorphism to the unit square. We demonstrate the application of these ideas by presenting concrete examples of lowdiscrepancy curves on some surfaces that are of interest in robotics.
Parallel QuasiMonte Carlo Integration using (t,s)Sequences
"... . Currently, the most effective constructions of lowdiscrepancy point sets and sequences are based on the theory of (t; m; s)nets and (t; s)sequences. In this work we discuss parallelization techniques for quasiMonte Carlo integration using (t; s)sequences. We show that leapfrog parallelization ..."
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Cited by 6 (3 self)
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. Currently, the most effective constructions of lowdiscrepancy point sets and sequences are based on the theory of (t; m; s)nets and (t; s)sequences. In this work we discuss parallelization techniques for quasiMonte Carlo integration using (t; s)sequences. We show that leapfrog parallelization may be very dangerous whereas blockbased parallelization turns out to be robust. 1 Introduction Currently, the most effective constructions of lowdiscrepancy point sets and sequences, which are of great importance for quasiMonte Carlo methods in multidimensional numerical integration, are based on the concept of (t; m; s) nets and (t; s)sequences. A detailed theory was developed in Niederreiter [10]. High dimensional numerical integration problems may require a significant amount of computations. Therefore, substantial effort has been invested into finding techniques for performing these computations on all kinds of parallel architectures (see [8] for an exhaustive overview). In orde...
P.: Infinitedimensional highlyuniform point sets defined via linear recurrences in F2w
 and QuasiMonte Carlo Methods 2004
, 2006
"... Summary. We construct infinitedimensional highlyuniform point sets for quasiMonte Carlo integration. The successive coordinates of each point are determined by a linear recurrence in F2 w, the finite field with 2w elements where w is an integer, and a mapping from this field to the interval [0, 1 ..."
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Cited by 4 (0 self)
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Summary. We construct infinitedimensional highlyuniform point sets for quasiMonte Carlo integration. The successive coordinates of each point are determined by a linear recurrence in F2 w, the finite field with 2w elements where w is an integer, and a mapping from this field to the interval [0, 1). One interesting property of these point sets is that almost all of their twodimensional projections are perfectly equidistributed. We performed searches for specific parameters in terms of different measures of uniformity and different numbers of points. We give a numerical illustration showing that using randomized versions of these point sets in place of independent random points can reduce the variance drastically for certain functions. 1
Generalized Halton Sequences in 2008: A Comparative Study
"... Halton sequences have always been quite popular with practitioners, in part because of their intuitive definition and ease of implementation. However, in their original form, these sequences have also been known for their inadequacy to integrate functions in moderate to large dimensions, in which ca ..."
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Cited by 4 (1 self)
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Halton sequences have always been quite popular with practitioners, in part because of their intuitive definition and ease of implementation. However, in their original form, these sequences have also been known for their inadequacy to integrate functions in moderate to large dimensions, in which case (t, s)sequences such as the Sobol ’ sequence are usually preferred. To overcome this problem, one possible approach is to include permutations in the definition of Halton sequences— thereby obtaining generalized Halton sequences—an idea that goes back to almost thirty years ago, and that has been studied by many researchers in the last few years. In parallel to these efforts, an important improvement in the upper bounds for the discrepancy of Halton sequences has been made by Atanassov in 2004. Together, these two lines of research have revived the interest in Halton sequences. In this paper, we review different generalized Halton sequences that have been proposed recently, and compare them by means of numerical experiments. We also propose a new generalized Halton sequence which, we believe, offers a practical advantage over the surveyed constructions, and that should be of interest to practitioners.
Adaptive Sampling and Modeling of Analog Circuit Performance Parameters
 In Proc. VLSISOC
, 2003
"... Many approaches to analog performance parameter macro modeling have been investigated by the research community. These models are typically derived from discrete data obtained from circuit simulation using numerous input combinations of component sizes for a given circuit topology. The simulations a ..."
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Cited by 2 (1 self)
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Many approaches to analog performance parameter macro modeling have been investigated by the research community. These models are typically derived from discrete data obtained from circuit simulation using numerous input combinations of component sizes for a given circuit topology. The simulations are computationally intensive, therefore it is advantageous to reduce the number of simulations necessary to build an accurate macro model. We present a new algorithm for adaptively sampling multidimensional black box functions based on Duchon pseudocubic splines. The splines readily and accurately model high dimensional functions based on discrete unstructured data and require no tuning of parameters as seen in many other interpolation methods. The adaptive sampler, in conjunction with pseudocubic splines, is used to accurately model various analog performance parameters for an operational amplifier topology using fewer sample points than traditional gridded and quasirandom sampling methodologies.