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538
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 1019 (26 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.
The Markov chain Monte Carlo method: an approach to approximate counting and integration. in Approximation Algorithms for NPhard Problems, D.S.Hochbaum ed
, 1996
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Algebraic Algorithms for Sampling from Conditional Distributions
 Annals of Statistics
, 1995
"... We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so a ..."
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Cited by 268 (20 self)
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We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.
Iterated random functions
 SIAM Review
, 1999
"... Abstract. Iterated random functions are used to draw pictures or simulate large Ising models, among other applications. They offer a method for studying the steady state distribution of a Markov chain, and give useful bounds on rates of convergence in a variety of examples. The present paper surveys ..."
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Cited by 233 (3 self)
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Abstract. Iterated random functions are used to draw pictures or simulate large Ising models, among other applications. They offer a method for studying the steady state distribution of a Markov chain, and give useful bounds on rates of convergence in a variety of examples. The present paper surveys the field and presents some new examples. There is a simple unifying idea: the iterates of random Lipschitz functions converge if the functions are contracting on the average. 1. Introduction. The
General state space Markov chains and MCMC algorithm
 PROBABILITY SURVEYS
, 2004
"... This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform e ..."
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Cited by 177 (35 self)
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This paper surveys various results about Markov chains on general (noncountable) state spaces. It begins with an introduction to Markov chain Monte Carlo (MCMC) algorithms, which provide the motivation and context for the theory which follows. Then, sufficient conditions for geometric and uniform ergodicity are presented, along with quantitative bounds on the rate of convergence to stationarity. Many of these results are proved using direct coupling constructions based on minorisation and drift conditions. Necessary and sufficient conditions for Central Limit Theorems (CLTs) are also presented, in some cases proved via the Poisson Equation or direct regeneration constructions. Finally, optimal scaling and weak convergence results for MetropolisHastings algorithms are discussed. None of the results presented is new, though many of the proofs are. We also describe some Open Problems.
Generating Random Spanning Trees More Quickly than the Cover Time
 PROCEEDINGS OF THE TWENTYEIGHTH ANNUAL ACM SYMPOSIUM ON THE THEORY OF COMPUTING
, 1996
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Finite Markov Chains and Algorithmic Applications
 IN LONDON MATHEMATICAL SOCIETY STUDENT TEXTS
, 2001
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Markov Chain Algorithms for Planar Lattice Structures
, 1995
"... Consider the following Markov chain, whose states are all domino tilings of a 2n x 2n chessboard: starting from some arbitrary tiling, pick a 2 x 2 window uniformly at random. If the four squares appearing in this window are covered by two parallel dominoes, rotate the dominoes 90° in place. Repeat ..."
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Cited by 107 (11 self)
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Consider the following Markov chain, whose states are all domino tilings of a 2n x 2n chessboard: starting from some arbitrary tiling, pick a 2 x 2 window uniformly at random. If the four squares appearing in this window are covered by two parallel dominoes, rotate the dominoes 90° in place. Repeat many times. This process is used in practice to generate a random tiling, and is a widely used tool in the study of the combinatorics of tilings and the behavior of dimer systems in statistical physics. Analogous Markov chains are used to randomly generate other structures on various twodimensional lattices. This paper presents techniques which prove for the first time that, in many interesting cases, a small number of random moves suffice to obtain a uniform distribution.