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73
NonUniform Random Variate Generation
, 1986
"... This is a survey of the main methods in nonuniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorith ..."
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Cited by 1006 (25 self)
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This is a survey of the main methods in nonuniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorithms, before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods.
Continuous Random Variate Generation by Fast Numerical Inversion
, 2002
"... The inversion method for generating... In this paper we demonstrate that with Hermite interpolation of the inverse CDF we can obtain very small error bounds close to machine precision. Using our adaptive interval splitting method this accuracy is reached with moderately sized tables that allow for a ..."
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Cited by 24 (8 self)
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The inversion method for generating... In this paper we demonstrate that with Hermite interpolation of the inverse CDF we can obtain very small error bounds close to machine precision. Using our adaptive interval splitting method this accuracy is reached with moderately sized tables that allow for a fast and simple generation procedure.
Graph Annotations in Modeling Complex Network Topologies
"... The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in such a graph possess some nontrivial internal structure that ..."
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Cited by 21 (2 self)
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The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in such a graph possess some nontrivial internal structure that varies across and differentiates among distinct types of links or nodes. In this work, we abstract such additional information as network annotations. We introduce a network topology modeling framework that treats annotations as an extended correlation profile of a network. Assuming we have this profile measured for a given network, we present an algorithm to rescale it in order to construct networks of varying size that still reproduce the original measured annotation profile. Using this methodology, we accurately capture the network properties essential for realistic simulations of network applications and protocols, or any other simulations involving complex network topologies, including modeling and simulation of network evolution. We apply our approach to the Autonomous System (AS) topology of the Internet annotated with business relationships between ASs. This topology captures the largescale structure of the Internet. In depth understanding of this structure and tools to model it are cornerstones of research on future Internet architectures and designs. We find that our techniques are able to accurately capture the structure of annotation correlations within this topology, thus reproducing a number of its important properties in syntheticallygenerated random graphs.
Random variate generation for exponentially and polynomially tilted stable distributions
 ACM Transactions on Modeling and Computer Simulation 19, Article
, 2009
"... Abstract. We develop exact random variate generators for the polynomially and exponentially tilted unilateral stable distributions. The algorithms, which generalize Kanter’s method, are uniformly fast over all choices of the tilting and stable parameters. The key to the solution is a new distributio ..."
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Cited by 16 (2 self)
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Abstract. We develop exact random variate generators for the polynomially and exponentially tilted unilateral stable distributions. The algorithms, which generalize Kanter’s method, are uniformly fast over all choices of the tilting and stable parameters. The key to the solution is a new distribution which we call Zolotarev’s distribution. We also present a novel double rejection method that is useful whenever densities have an integral representation involving an auxiliary variable.
Inverting the symmetrical beta distribution
 ACM Trans. Math. Software. Forthcoming
, 2004
"... We propose a fast algorithm for computing the inverse symmetrical beta distribution. Four series (two around x = 0 and two around x = 1/2) are used to approximate the distribution function and its inverse is found via Newton’s method. This algorithm can be used to generate beta random variates by in ..."
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Cited by 10 (0 self)
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We propose a fast algorithm for computing the inverse symmetrical beta distribution. Four series (two around x = 0 and two around x = 1/2) are used to approximate the distribution function and its inverse is found via Newton’s method. This algorithm can be used to generate beta random variates by inversion and is much faster than currently available general inversion methods for the beta distribution. It turns out to be very useful for generating gamma processes efficiently via bridge sampling.
2010. “Random variate generation by numerical inversion when only the density is known
 ACM Transactions on Modeling and Computer Simulation
"... ePubWU, the institutional repository of the WU Vienna University of Economics and Business, is provided by the University Library and the ITServices. The aim is to enable open access to the scholarly output of the WU. ..."
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Cited by 9 (3 self)
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ePubWU, the institutional repository of the WU Vienna University of Economics and Business, is provided by the University Library and the ITServices. The aim is to enable open access to the scholarly output of the WU.
On the Behavior of the Weighted Star Discrepancy Bounds for Shifted Lattice
"... Abstract We examine the question of constructing shifted lattice rules of rank one with an arbitrary number of points n, an arbitrary shift, and small weighted star discrepancy. An upper bound on the weighted star discrepancy, that depends on the lattice parameters and is easily computable, serves a ..."
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Cited by 3 (1 self)
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Abstract We examine the question of constructing shifted lattice rules of rank one with an arbitrary number of points n, an arbitrary shift, and small weighted star discrepancy. An upper bound on the weighted star discrepancy, that depends on the lattice parameters and is easily computable, serves as a figure of merit. It is known that there are lattice rules for which this upper bound converges as O(n −1+δ) for any δ> 0, uniformly over the shift, and lattice rules that achieve this convergence rate can be found by a componentbycomponent (CBC) construction. In this paper, we examine practical aspects of these bounds and results, such as: What is the shape of the probability distribution of the figure of merit for a random lattice with a given n? Is the CBC construction doing much better than just picking the best out of a few random lattices, or much better than using a randomized CBC construction that tries only a small number of random values at each step? How does the figure of merit really behave as a function of n for the best lattice, and on average for a random lattice, say for n under a million? Do we observe a convergence rate near O(n −1) in that range of values of n? Finally, is the figure of merit a tight bound on the true discrepancy, or is there a large gap between the two? 1
Automatic Markov Chain Mont Carlo Procedures . . .
, 2006
"... Generating samples from multivariate distributions efficiently is an important task in Monte Carlo integration and many other stochastic simulation problems. Markov chain Monte Carlo has been shown to be very efficient compared to “conventional methods”, especially when many dimensions are involved. ..."
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Cited by 3 (1 self)
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Generating samples from multivariate distributions efficiently is an important task in Monte Carlo integration and many other stochastic simulation problems. Markov chain Monte Carlo has been shown to be very efficient compared to “conventional methods”, especially when many dimensions are involved. In this article we propose a HitandRun sampler in combination with the RatioofUniforms method. We show that it is well suited for an algorithm to generate points from quite arbitrary distributions, which include all logconcave distributions. The algorithm works automatically in the sense that only the mode (or an approximation of it) and an oracle is required, i.e., a subroutine that returns the value of the density function at any point x. We show that the number of evaluations of the density increases slowly with dimension.
Reparameterized and Marginalized Posterior and Predictive Sampling for Complex Bayesian Geostatistical Models
, 2007
"... This paper proposes a fourpronged approach to efficient Bayesian estimation and prediction for complex Bayesian hierarchical Gaussian models for spatial and spatiotemporal data. The method involves reparameterizing the variance/covariance structure of the model, reformulating the means structure, ..."
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Cited by 3 (1 self)
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This paper proposes a fourpronged approach to efficient Bayesian estimation and prediction for complex Bayesian hierarchical Gaussian models for spatial and spatiotemporal data. The method involves reparameterizing the variance/covariance structure of the model, reformulating the means structure, marginalizing the joint posterior distribution, and applying a simplexbased slice sampling algorithm. The approach permits fusion of pointsource data and areal data measured at different resolutions and accommodates nonspatial correlation and variance heterogeneity as well as spatial and/or temporal correlation. The method produces Markov chain Monte Carlo samplers with low autocorrelation in the output, so that fewer iterations are needed for Bayesian inference than would be the case with other sampling algorithms.