Extended Ensemble Monte Carlo

Iba, Yukito

doi:10.1142/s0129183101001912

Cited by 200 publications

(176 citation statements)

References 110 publications

(326 reference statements)

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“…[6][7][8] A recent review of these methods can be found in the literature. 9 In parallel tempering, several independent replicas of a system are simulated simultaneously. Each replica ͑or simulation box͒ can experience different thermodynamic-state conditions ͑e.g., temperature, pressure, or chemical potential͒.…”

Section: Introductionmentioning

confidence: 99%

Multicanonical parallel tempering

Faller¹,

Yan²,

Pablo³

2002

The Journal of Chemical Physics

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We present a novel implementation of the parallel tempering Monte Carlo method in a multicanonical ensemble. Multicanonical weights are derived by a self-consistent iterative process using a Boltzmann inversion of global energy histograms. This procedure gives rise to a much broader overlap of thermodynamic-property histograms; fewer replicas are necessary in parallel tempering simulations, and the acceptance of trial swap moves can be made arbitrarily high. We demonstrate the usefulness of the method in the context of a grand-multicanonical ensemble, where we use multicanonical simulations in energy space with the addition of an unmodified chemical potential term in particle-number space. Several possible implementations are discussed, and the best choice is presented in the context of the liquid-gas phase transition of the Lennard-Jones fluid. A substantial decrease in the necessary number of replicas can be achieved through the proposed method, thereby providing a higher efficiency and the possibility of parallelization.

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Section: Introductionmentioning

confidence: 99%

Multicanonical parallel tempering

Faller¹,

Yan²,

Pablo³

2002

The Journal of Chemical Physics

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“…Improved numerical ergodicity is usually achieved compared to direct Monte Carlo or molecular dynamics simulations by allowing the system to circumvent barriers between metastable basins or even to cross them when, for instance, the external parameter is associated with inverse temperature and takes small values. Because of its popularity and versatility, the expanded ensemble method has been the subject of numerous studies [15][16][17][18][19][20][21] over recent years. To evaluate the thermodynamic expectations, several estimators have been proposed, namely, the (standard) binning estimator, 6 a standard reweighting estimator 21 , a self-consistent reweighting estimator 17 called simulated tempering weighted histogram analysis method (STWHAM), a histogram reweighting estimator 22 called corrected z-averaged restraints (CZAR) and an adiabatic reweighting (AR) estimator.…”

Section: -4mentioning

confidence: 99%

Estimating thermodynamic expectations and free energies in expanded ensemble simulations: Systematic variance reduction through conditioning

Athènes

Terrier

2017

The Journal of Chemical Physics

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Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more accurate estimates are obtained by combining Monte Carlo integration and integration by numerical quadrature along particular coordinates. We show that this variance reduction technique, referred to as conditioning in probability theory, can be advantageously implemented in expanded ensemble simulations. These simulations aim at estimating thermodynamic expectations as a function of an external parameter that is sampled like an additional coordinate. Conditioning therein entails integrating along the external coordinate by numerical quadrature. We prove variance reduction with respect to alternative standard estimators and demonstrate the practical efficiency of the technique by estimating free energies and characterizing a structural phase transition between two solid phases.

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“…We refer the reader to Iba (2001) for the details and to Goswami & Liu (2006) (unpublished technical report) for an alternative approach.…”

Section: Exchange Perform the Delayed Rejection Exchange Movementioning

confidence: 99%

Population-Based Reversible Jump Markov Chain Monte Carlo

Jasra¹,

Stephens²,

Holmes³

2007

Biometrika

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In this paper we present an extension of population-based Markov chain Monte Carlo (MCMC) to the trans-dimensional case. One of the main challenges in MCMC-based inference is that of simulating from high and trans-dimensional target measures. In such cases, MCMC methods may not adequately traverse the support of the target; the simulation results will be unreliable. We develop population methods to deal with such problems, and give a result proving the uniform ergodicity of these population algorithms, under mild assumptions. This result is used to demonstrate the superiority, in terms of convergence rate, of a population transition kernel over a reversible jump sampler for a Bayesian variable selection problem. We also give an example of a population algorithm for a Bayesian multivariate mixture model with an unknown number of components. This is applied to gene expression data of 1000 data points in six dimensions and it is demonstrated that our algorithm out performs some competing Markov chain samplers.

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Extended Ensemble Monte Carlo

Cited by 200 publications

References 110 publications

Multicanonical parallel tempering

Multicanonical parallel tempering

Estimating thermodynamic expectations and free energies in expanded ensemble simulations: Systematic variance reduction through conditioning

Population-Based Reversible Jump Markov Chain Monte Carlo

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