Likelihood computation in spatial statistics requires accurate and efficient calculation of the normalizing constant (i.e. partition function) of the Gibbs distribution of the model. Two available methods to calculate...
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Likelihood computation in spatial statistics requires accurate and efficient calculation of the normalizing constant (i.e. partition function) of the Gibbs distribution of the model. Two available methods to calculate the normalizing constant by Markov chain Monte Carlo methods are compared by simulation experiments for an Ising model, a Gaussian Markov field model and a pairwise interaction point field model.
A new parallel algorithm for simulating Ising spin systems is presented. The sequential prototype is the n-fold way algorithm [2], which is efficient but is hard to parallelize using conservative methods. Our parallel...
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ISBN:
(纸本)076951104X;0769511058
A new parallel algorithm for simulating Ising spin systems is presented. The sequential prototype is the n-fold way algorithm [2], which is efficient but is hard to parallelize using conservative methods. Our parallel algorithm is optimistic. Unlike other optimistic algorithms, e.g., Time Warp, our algorithm is synchronous. It also belongs to the class of simulations known as "relaxation" [3];hence it is named "synchronous relaxation." We derive performance guarantees for this algorithm. If N is the number of PEs, then under weak assumptions we show that the number of correct events processed per unit of time is, on average, at least of order N/logN. All communication delays, processing time, and busy waits are taken into account.
A new parallel algorithm for simulating Ising spin systems is presented. The sequential prototype is the n-fold way algorithm [2], which is efficient but is hard to parallelize using conservative methods. Our parallel...
详细信息
ISBN:
(纸本)9780769511047
A new parallel algorithm for simulating Ising spin systems is presented. The sequential prototype is the n-fold way algorithm [2], which is efficient but is hard to parallelize using conservative methods. Our parallel algorithm is optimistic. Unlike other optimistic algorithms, e.g., Time Warp, our algorithm is synchronous. It also belongs to the class of simulations known as “relaxation” [3]; hence it is named “synchronous relaxation.” We derive performance guarantees for this algorithm. If N is the number of PEs, then under weak assumptions we show that the number of correct events processed per unit of time is, on average, at least of order N/ log N. All communication delays, processing time, and busy waits are taken into account.
Ln this paper we derive conditions for geometric ergodicity of the random-walk-based metropolis algorithm on R-k. We show that at least exponentially light tails of the target density is a necessity. This extends the ...
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Ln this paper we derive conditions for geometric ergodicity of the random-walk-based metropolis algorithm on R-k. We show that at least exponentially light tails of the target density is a necessity. This extends the one-dimensional result of Mengersen and Tweedle (1996, Arm. Statist. 24, 101-121). For super-exponential target densities we characterize the geometrically ergodic algorithms and we derive a practical sufficient condition which is stable under addition and multiplication. This condition is especially satisfied for the class of densities considered in Roberts and Tweedle (1996, Biometrika 83, 95-110). (C) 2000 Elsevier Science B.V. All rights reserved.
Given an everywhere positive probability measure pi on a finite state space E and the associated energy function H, this note gives convergence results for time-inhomogeneous metropolis chains which are used to simula...
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Given an everywhere positive probability measure pi on a finite state space E and the associated energy function H, this note gives convergence results for time-inhomogeneous metropolis chains which are used to simulate re or minimize H under some constraints. (C) 2000 Published by Elsevier Science B.V. All rights reserved.
This article describes a new metropolis-like transition rule, the multiple-try metropolis, for Markov chain Monte Carlo (MCMC) simulations. By using this transition rule together with adaptive direction sampling. we p...
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This article describes a new metropolis-like transition rule, the multiple-try metropolis, for Markov chain Monte Carlo (MCMC) simulations. By using this transition rule together with adaptive direction sampling. we propose a novel method for incorporating local optimization steps into a MCMC sampler in continuous state-space. Numerical studies show that the new method performs significantly better than the traditional metropolis-Hastings (M-H) sampler. With minor tailoring in using the rule, the multiple-try method can also be exploited to achieve the effect of a griddy Gibbs sampler without having to bear with griddy approximations, and the effect of a hit-and-run algorithm without having to figure out the required conditional distribution in a random direction.
A new recapture debugging model is suggested to estimate the number of faults in a system, nu, and the failure intensity of each fault, phi. The Gibbs sampler and the metropolis algorithm are used in this inference pr...
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A new recapture debugging model is suggested to estimate the number of faults in a system, nu, and the failure intensity of each fault, phi. The Gibbs sampler and the metropolis algorithm are used in this inference procedure. A numerical illustration suggests a notable improvement on the estimation of nu and phi compared with that of a removal debugging model.
For metropolis Monte Carlo simulations in statistical physics, efficient, easy-to-implement, and unbiased statistical estimators of thermodynamic properties are based on the transition dynamics. Using an Ising model e...
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For metropolis Monte Carlo simulations in statistical physics, efficient, easy-to-implement, and unbiased statistical estimators of thermodynamic properties are based on the transition dynamics. Using an Ising model example, we demonstrate (problem-specific) variance reductions compared to conventional histogram estimators. A proof of variance reduction in a microstate limit is presented.
A common approach to parallelizing simulated annealing is to generate several perturbations to the current solution simultaneously, requiring synchronization to guarantee correct evaluation of the cost function. The c...
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A common approach to parallelizing simulated annealing is to generate several perturbations to the current solution simultaneously, requiring synchronization to guarantee correct evaluation of the cost function. The cost of this synchronization may be reduced by allowing inaccuracies in the cost calculations. We provide a framework for understanding the theoretical implications of this approach based on a model of processor interaction under reduced synchronization that demonstrates how errors in cost calculations occur and how to estimate them. We show how bounds on error in the cost calculations in a simulated annealing algorithm can be translated into worst-case bounds on perturbations in the parameters which describe the behavior of the algorithm. (C) 2000 Elsevier Science B.V. All rights reserved.
We introduce a form of Rao-Blackwellization for Markov chains which uses the transition distribution for conditioning. We show that for reversible Markov chains, this form of Rao-Blackwellization always reduces the as...
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We introduce a form of Rao-Blackwellization for Markov chains which uses the transition distribution for conditioning. We show that for reversible Markov chains, this form of Rao-Blackwellization always reduces the asymptotic variance, and derive two explicit forms of the variance reduction obtained through repeated Rao-Blackwellization. The result applies to many Markov chain Monte Carlo methods used in practice. In particular, we discuss an application to data augmentation and give some simulation results for Ising model samplers. (C) 2000 Elsevier Science B.V. All rights reserved.
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