Results 1  10
of
87
Exact Sampling with Coupled Markov Chains and Applications to Statistical Mechanics
, 1996
"... For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has ..."
Abstract

Cited by 406 (13 self)
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For many applications it is useful to sample from a finite set of objects in accordance with some particular distribution. One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M sufficiently large, the distribution governing the state of the chain approximates the desired distribution. Unfortunately it can be difficult to determine how large M needs to be. We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution. The method uses couplings, which have also played a role in other sampling schemes; however, rather than running the coupled chains from the present into the future, one runs from a distant point in the past up until the present, where the distance into the past that one needs to go is determined during the running of the al...
Generalizing SwendsenWang to Sampling Arbitrary Posterior Probabilities
 PAMI
, 2005
"... Many vision tasks can be formulated as graph partition problems that minimize energy functions. For such problems, the Gibbs... ..."
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Cited by 53 (12 self)
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Many vision tasks can be formulated as graph partition problems that minimize energy functions. For such problems, the Gibbs...
The RandomCluster Model
, 2006
"... Abstract. The class of randomcluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the theory of certain random combinatorial structures, an ..."
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Cited by 43 (18 self)
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Abstract. The class of randomcluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the theory of certain random combinatorial structures, and of electrical networks. Much (but not all) of the physical theory of Ising/Potts models is best implemented in the context of the randomcluster representation. This systematic summary of randomcluster models includes accounts of the fundamental methods and inequalities, the uniqueness and specification of infinitevolume measures, the existence and nature of the phase transition, and the structure of the subcritical and supercritical phases. The theory for twodimensional lattices is better developed than for three and more dimensions. There is a rich collection of open problems, including some of substantial significance for the general area of disordered systems, and these are highlighted when encountered. Amongst the major open questions, there is the problem of ascertaining the exact nature of the phase transition for general values of the clusterweighting factor q, and the problem of proving that the critical randomcluster model in two
Markov Chain Monte Carlo Simulations and Their Statistical Analysis, World Scientific
, 2004
"... ..."
Statistical Mechanics: Entropy, Order Parameters, and Complexity
 Oxford Master Series in Physic
, 2006
"... The author provides this version of this manuscript with the primary intention of making the text accessible electronically—through web searches and for browsing and study on computers. Oxford University Press retains ownership of the copyright. Hardcopy printing, in particular, is subject to the s ..."
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Cited by 31 (2 self)
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The author provides this version of this manuscript with the primary intention of making the text accessible electronically—through web searches and for browsing and study on computers. Oxford University Press retains ownership of the copyright. Hardcopy printing, in particular, is subject to the same copyright rules as they would be for a printed book. CLARENDON PRESS. OXFORD
Mixing Properties of the SwendsenWang Process on the Complete Graph and Narrow Grids
 IN PROCEEDINGS OF DIMACS WORKSHOP ON STATISTICAL PHYSICS METHODS IN DISCRETE PROBABILITY, COMBINATORICS AND THEORETICAL COMPUTER SCIENCE
, 2000
"... We consider the mixing properties o the SwendsenWang process or the 2state Potts model or Ising model, on the complete n vertex graph Kn and for the Qstate model on an a x n grid where a is bounded as n  . ..."
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Cited by 28 (0 self)
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We consider the mixing properties o the SwendsenWang process or the 2state Potts model or Ising model, on the complete n vertex graph Kn and for the Qstate model on an a x n grid where a is bounded as n  .
The Computational Complexity of Generating Random Fractals
 J. Stat. Phys
, 1996
"... In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several widely used algorithms for equilibrating the Ising model ar ..."
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Cited by 16 (6 self)
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In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential; it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation that can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics. Keywords: Cluster algorithms, computational complexity, diffusion limited aggregation, Ising model, Metropolis algorithm, Pcompleteness 1
Invaded cluster algorithm for Potts models, Phys
 Rev. E
, 1996
"... The invaded cluster algorithm, a method for simulating phase transitions, is described in detail. Theoretical, albeit nonrigorous, justification of the method is presented and the algorithm is applied to Potts models in two and three dimensions. The algorithm is shown to be useful for both firstord ..."
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Cited by 14 (3 self)
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The invaded cluster algorithm, a method for simulating phase transitions, is described in detail. Theoretical, albeit nonrigorous, justification of the method is presented and the algorithm is applied to Potts models in two and three dimensions. The algorithm is shown to be useful for both firstorder and continuous transitions and evidently provides an efficient way to distinguish between these possibilities. The dynamic properties of the invaded cluster algorithm are studied. Numerical evidence suggests that the algorithm has no critical slowing for Ising models. �S1063651X�96�092082� PACS number�s�: 05.50.�q, 64.60.Fr, 75.10.Hk, 02.70.Lq I.
Invaded cluster algorithm for equilibrium critical points
 Phys. Rev. Lett
, 1995
"... A new cluster algorithm based on invasion percolation is described. The algorithm samples the critical point of a spin system without a priori knowledge of the critical temperature and provides an efficient way to determine the critical temperature and other observables in the critical region. The m ..."
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Cited by 11 (4 self)
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A new cluster algorithm based on invasion percolation is described. The algorithm samples the critical point of a spin system without a priori knowledge of the critical temperature and provides an efficient way to determine the critical temperature and other observables in the critical region. The method is illustrated for the two and threedimensional Ising models. The algorithm equilibrates spin configurations much faster than the closely related SwendsenWang algorithm. Typeset using REVTEX 1 Enormous improvements in simulating systems near critical points have been achieved by using cluster algorithms [1,2]. In the present paper we describe a new cluster method which has the additional property of ‘selforganized criticality. ’ In particular, the method can be used to sample the critical region of various spin models without the need to fine tune any parameters (or know them in advance). Here, as in other cluster algorithms, bond clusters play a pivotal role in a Markov process where successive spin configurations