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Journal articles on the topic 'Monte Carlo Metropolis'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Owen, A. B., and S. D. Tribble. "A quasi-Monte Carlo Metropolis algorithm." Proceedings of the National Academy of Sciences 102, no. 25 (June 13, 2005): 8844–49. http://dx.doi.org/10.1073/pnas.0409596102.

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2

Makarova, K. V., A. G. Makarov, M. A. Padalko, V. S. Strongin, and K. V. Nefedev. "Multispin Monte Carlo Method." Dal'nevostochnyi Matematicheskii Zhurnal 20, no. 2 (November 25, 2020): 212–20. http://dx.doi.org/10.47910/femj202020.

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The article offers a Monte Carlo cluster method for numerically calculating a statistical sample of the state space of vector models. The statistical equivalence of subsystems in the Ising model and quasi-Markov random walks can be used to increase the efficiency of the algorithm for calculating thermodynamic means. The cluster multispin approach extends the computational capabilities of the Metropolis algorithm and allows one to find configurations of the ground and low-energy states.

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3

da Silva, Cesar R. S. "Optimizing Metropolis Monte Carlo simulations of semiconductors." Computer Physics Communications 153, no. 3 (July 2003): 392–96. http://dx.doi.org/10.1016/s0010-4655(03)00225-x.

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4

Rensburg, E. J. Janse van, and N. Madras. "Metropolis Monte Carlo simulation of lattice animals." Journal of Physics A: Mathematical and General 30, no. 23 (December 7, 1997): 8035–66. http://dx.doi.org/10.1088/0305-4470/30/23/007.

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5

Mathé, Peter, and Erich Novak. "Simple Monte Carlo and the Metropolis algorithm." Journal of Complexity 23, no. 4-6 (August 2007): 673–96. http://dx.doi.org/10.1016/j.jco.2007.05.002.

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6

Müller, Christian, Fabian Weysser, Thomas Mrziglod, and Andreas Schuppert. "Markov-Chain Monte-Carlo methods and non-identifiabilities." Monte Carlo Methods and Applications 24, no. 3 (September 1, 2018): 203–14. http://dx.doi.org/10.1515/mcma-2018-0018.

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Abstract We consider the problem of sampling from high-dimensional likelihood functions with large amounts of non-identifiabilities via Markov-Chain Monte-Carlo algorithms. Non-identifiabilities are problematic for commonly used proposal densities, leading to a low effective sample size. To address this problem, we introduce a regularization method using an artificial prior, which restricts non-identifiable parts of the likelihood function. This enables us to sample the posterior using common MCMC methods more efficiently. We demonstrate this with three MCMC methods on a likelihood based on a complex, high-dimensional blood coagulation model and a single series of measurements. By using the approximation of the artificial prior for the non-identifiable directions, we obtain a sample quality criterion. Unlike other sample quality criteria, it is valid even for short chain lengths. We use the criterion to compare the following three MCMC variants: The Random Walk Metropolis Hastings, the Adaptive Metropolis Hastings and the Metropolis adjusted Langevin algorithm.

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7

Petrila, Iulian, and Vasile Manta. "Metropolis Monte Carlo analysis of all-optical switching." Computer Physics Communications 185, no. 11 (November 2014): 2874–78. http://dx.doi.org/10.1016/j.cpc.2014.07.008.

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8

Kamatani, K. "Ergodicity of Markov chain Monte Carlo with reversible proposal." Journal of Applied Probability 54, no. 2 (June 2017): 638–54. http://dx.doi.org/10.1017/jpr.2017.22.

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Abstract We describe the ergodic properties of some Metropolis–Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually analyzed under a subgeometric ergodic framework, but we prove that the mixed preconditioned Crank–Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed target distributions. This useful property comes from the fact that, under a suitable transformation, the MpCN algorithm becomes a random-walk Metropolis algorithm.

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9

SCHULTE, MELANIE, and CAROLINE DROPE. "3D ISING NONUNIVERSALITY: A MONTE CARLO STUDY." International Journal of Modern Physics C 16, no. 08 (August 2005): 1217–24. http://dx.doi.org/10.1142/s0129183105007844.

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We investigate as a member of the Ising universality class the Next-Nearest Neighbor Ising model without external field on a simple cubic lattice by using the Monte Carlo Metropolis Algorithm. The Binder cumulant and the susceptibility ratio, which should be universal quantities at the critical point, were shown to vary for small negative next-nearest neighbor interactions.

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10

DILGER, H. "TOPOLOGICAL ZERO MODES IN MONTE CARLO SIMULATIONS." International Journal of Modern Physics C 06, no. 01 (February 1995): 123–34. http://dx.doi.org/10.1142/s0129183195000101.

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We present an improvement of global Metropolis updating steps, the instanton hits, used in a hybrid Monte Carlo simulation of the two-flavor Schwinger model with staggered fermions. These hits are designed to change the topological sector of the gauge field. In order to match these hits to an unquenched simulation with pseudofermions, the approximate zero mode structure of the lattice Dirac operator has to be considered explicitly.

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11

IBA, YUKITO. "EXTENDED ENSEMBLE MONTE CARLO." International Journal of Modern Physics C 12, no. 05 (June 2001): 623–56. http://dx.doi.org/10.1142/s0129183101001912.

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"Extended Ensemble Monte Carlo" is a generic term that indicates a set of algorithms, which are now popular in a variety of fields in physics and statistical information processing. Exchange Monte Carlo (Metropolis-Coupled Chain, Parallel Tempering), Simulated Tempering (Expanded Ensemble Monte Carlo) and Multicanonical Monte Carlo (Adaptive Umbrella Sampling) are typical members of this family. Here, we give a cross-disciplinary survey of these algorithms with special emphasis on the great flexibility of the underlying idea. In Sec. 2, we discuss the background of Extended Ensemble Monte Carlo. In Secs. 3, 4 and 5, three types of the algorithms, i.e., Exchange Monte Carlo, Simulated Tempering, Multicanonical Monte Carlo, are introduced. In Sec. 6, we give an introduction to Replica Monte Carlo algorithm by Swendsen and Wang. Strategies for the construction of special-purpose extended ensembles are discussed in Sec. 7. We stress that an extension is not necessary restricted to the space of energy or temperature. Even unphysical (unrealizable) configurations can be included in the ensemble, if the resultant fast mixing of the Markov chain offsets the increasing cost of the sampling procedure. Multivariate (multicomponent) extensions are also useful in many examples. In Sec. 8, we give a survey on extended ensembles with a state space whose dimensionality is dynamically varying. In the appendix, we discuss advantages and disadvantages of three types of extended ensemble algorithms.

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12

Potter, Christopher C. J., and Robert H. Swendsen. "Guaranteeing total balance in Metropolis algorithm Monte Carlo simulations." Physica A: Statistical Mechanics and its Applications 392, no. 24 (December 2013): 6288–99. http://dx.doi.org/10.1016/j.physa.2013.08.059.

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13

Suksmono, A. B., and A. Hirose. "Interferometric SAR image restoration using Monte Carlo metropolis method." IEEE Transactions on Signal Processing 50, no. 2 (2002): 290–98. http://dx.doi.org/10.1109/78.978384.

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14

Mezei, Mihaly. "A Near-neighbour Algorithm for Metropolis Monte Carlo Simulations." Molecular Simulation 1, no. 3 (March 1988): 169–71. http://dx.doi.org/10.1080/08927028808080940.

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15

Eisele, Sebastian, and Steffen Grieshammer. "MOCASSIN : Metropolis and kinetic Monte Carlo for solid electrolytes." Journal of Computational Chemistry 41, no. 31 (September 24, 2020): 2663–77. http://dx.doi.org/10.1002/jcc.26418.

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16

Chapman, W., and N. Quirke. "Metropolis Monte Carlo simulation of fluids with multiparticle moves." Physica B+C 131, no. 1-3 (August 1985): 34–40. http://dx.doi.org/10.1016/0378-4363(85)90137-8.

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17

Moskovkin, P., and M. Hou. "Metropolis Monte Carlo predictions of free Co–Pt nanoclusters." Journal of Alloys and Compounds 434-435 (May 2007): 550–54. http://dx.doi.org/10.1016/j.jallcom.2006.08.178.

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18

Anderson, Joshua A., M. Eric Irrgang, and Sharon C. Glotzer. "Scalable Metropolis Monte Carlo for simulation of hard shapes." Computer Physics Communications 204 (July 2016): 21–30. http://dx.doi.org/10.1016/j.cpc.2016.02.024.

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19

Qin, Zhaohui S., and Jun S. Liu. "Multipoint Metropolis Method with Application to Hybrid Monte Carlo." Journal of Computational Physics 172, no. 2 (September 2001): 827–40. http://dx.doi.org/10.1006/jcph.2001.6860.

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20

Khrushcheva, O., E. E. Zhurkin, L. Malerba, C. S. Becquart, C. Domain, and M. Hou. "Copper precipitation in iron: a comparison between metropolis Monte Carlo and lattice kinetic Monte Carlo methods." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 202 (April 2003): 68–75. http://dx.doi.org/10.1016/s0168-583x(02)01830-x.

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21

Betancourt, Michael. "The Convergence of Markov Chain Monte Carlo Methods: From the Metropolis Method to Hamiltonian Monte Carlo." Annalen der Physik 531, no. 3 (March 23, 2018): 1700214. http://dx.doi.org/10.1002/andp.201700214.

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22

Liang, Faming, and Ick-Hoon Jin. "A Monte Carlo Metropolis-Hastings Algorithm for Sampling from Distributions with Intractable Normalizing Constants." Neural Computation 25, no. 8 (August 2013): 2199–234. http://dx.doi.org/10.1162/neco_a_00466.

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Simulating from distributions with intractable normalizing constants has been a long-standing problem in machine learning. In this letter, we propose a new algorithm, the Monte Carlo Metropolis-Hastings (MCMH) algorithm, for tackling this problem. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. It replaces the unknown normalizing constant ratio by a Monte Carlo estimate in simulations, while still converges, as shown in the letter, to the desired target distribution under mild conditions. The MCMH algorithm is illustrated with spatial autologistic models and exponential random graph models. Unlike other auxiliary variable Markov chain Monte Carlo (MCMC) algorithms, such as the Møller and exchange algorithms, the MCMH algorithm avoids the requirement for perfect sampling, and thus can be applied to many statistical models for which perfect sampling is not available or very expensive. The MCMH algorithm can also be applied to Bayesian inference for random effect models and missing data problems that involve simulations from a distribution with intractable integrals.

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23

Siems, Tobias. "Markov Chain Monte Carlo on finite state spaces." Mathematical Gazette 104, no. 560 (June 18, 2020): 281–87. http://dx.doi.org/10.1017/mag.2020.51.

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We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically coherent, yet simple and understandable way. To this end, we prove a pivotal convergence theorem for finite Markov chains and a minimal version of the Perron-Frobenius theorem. Subsequently, we briefly discuss two fundamental MCMC methods, the Gibbs and Metropolis-Hastings sampler. Only very basic knowledge about matrices, convergence of real sequences and probability theory is required.

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24

Roberts, Gareth O., and Jeffrey S. Rosenthal. "Complexity bounds for Markov chain Monte Carlo algorithms via diffusion limits." Journal of Applied Probability 53, no. 2 (June 2016): 410–20. http://dx.doi.org/10.1017/jpr.2016.9.

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Abstract We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC) algorithms to the computer science notion of algorithm complexity. Our main result states that any weak limit of a Markov process implies a corresponding complexity bound (in an appropriate metric). We then combine this result with previously-known MCMC diffusion limit results to prove that under appropriate assumptions, the random-walk Metropolis algorithm in d dimensions takes O(d) iterations to converge to stationarity, while the Metropolis-adjusted Langevin algorithm takes O(d1/3) iterations to converge to stationarity.

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25

Xiong, Haoyi, Kafeng Wang, Jiang Bian, Zhanxing Zhu, Cheng-Zhong Xu, Zhishan Guo, and Jun Huan. "SpHMC: Spectral Hamiltonian Monte Carlo." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 5516–24. http://dx.doi.org/10.1609/aaai.v33i01.33015516.

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Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) methods have been widely used to sample from certain probability distributions, incorporating (kernel) density derivatives and/or given datasets. Instead of exploring new samples from kernel spaces, this piece of work proposed a novel SGHMC sampler, namely Spectral Hamiltonian Monte Carlo (SpHMC), that produces the high dimensional sparse representations of given datasets through sparse sensing and SGHMC. Inspired by compressed sensing, we assume all given samples are low-dimensional measurements of certain high-dimensional sparse vectors, while a continuous probability distribution exists in such high-dimensional space. Specifically, given a dictionary for sparse coding, SpHMC first derives a novel likelihood evaluator of the probability distribution from the loss function of LASSO, then samples from the high-dimensional distribution using stochastic Langevin dynamics with derivatives of the logarithm likelihood and Metropolis–Hastings sampling. In addition, new samples in low-dimensional measuring spaces can be regenerated using the sampled high-dimensional vectors and the dictionary. Extensive experiments have been conducted to evaluate the proposed algorithm using real-world datasets. The performance comparisons on three real-world applications demonstrate the superior performance of SpHMC beyond baseline methods.

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26

CODDINGTON, P. D. "ANALYSIS OF RANDOM NUMBER GENERATORS USING MONTE CARLO SIMULATION." International Journal of Modern Physics C 05, no. 03 (June 1994): 547–60. http://dx.doi.org/10.1142/s0129183194000726.

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Monte Carlo simulation is one of the main applications involving the use of random number generators. It is also one of the best methods of testing the randomness properties of such generators, by comparing results of simulations using different generators with each other, or with analytic results. Here we compare the performance of some popular random number generators by high precision Monte Carlo simulation of the 2-d Ising model, for which exact results are known, using the Metropolis, Swendsen-Wang, and Wolff Monte Carlo algorithms. Many widely used generators that perform well in standard statistical tests are shown to fail these Monte Carlo tests.

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27

TAKAISHI, TETSUYA. "BAYESIAN INFERENCE OF STOCHASTIC VOLATILITY MODEL BY HYBRID MONTE CARLO." Journal of Circuits, Systems and Computers 18, no. 08 (December 2009): 1381–96. http://dx.doi.org/10.1142/s0218126609005733.

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The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we compute parameters of the SV model by using the artificial financial data and compare the results from the HMC algorithm with those from the Metropolis algorithm. We find that the HMC algorithm decorrelates the volatility variables faster than the Metropolis algorithm. Second we make an empirical study for the time series of the Nikkei 225 stock index by the HMC algorithm. We find the similar correlation behavior for the sampled data to the results from the artificial financial data and obtain a ϕ value close to one (ϕ ≈ 0.977), which means that the time series has the strong persistency of the volatility shock.

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28

Sucharitakul, Sukrit, Rattikorn Yimnirun, and Yongyut Laosiritaworn. "Acceptor-Doped Ferroelectric Modeling via Monte Carlo Simulation." Key Engineering Materials 421-422 (December 2009): 231–34. http://dx.doi.org/10.4028/www.scientific.net/kem.421-422.231.

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A 2D Monte Carlo simulation was done as an approach to get further insight of acceptor-doped ferroelectric material. By utilizing vector model allowing 14 directions of orientation for ferroelectric systems, Metropolis algorithm was applied on DIFFOUR Hamiltonian to obtain hysteresis profiles. Subjected to different concentration of acceptor dopants, power law scaling of hysteresis properties were obtained as functions of external parameters such as temperature, external field amplitude and frequency. The hysteresis loop shape and properties agreed well with those obtained experimentally.

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29

JOHN, GEORGE C., and VIJAY A. SINGH. "MONTE CARLO EVALUATION OF THE AHARONOV-BOHM EFFECT." International Journal of Modern Physics C 06, no. 01 (February 1995): 67–76. http://dx.doi.org/10.1142/s012918319500006x.

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The electron propagator in the Aharonov-Bohm effect is investigated using the Feynman path integral formalism. The calculation of the propagator is effected using a variation of the Metropolis Monte Carlo algorithm. Unlike “exact” calculations, our approach permits us to include a nonvanishing solenoid radius. We investigate the dependence of the resulting interference pattern on the magnetic field as well as the solenoid radius. Our results agree with the exact case in the limit of an infinitesimally small solenoid radius.

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30

Medina-Aguayo, Felipe, Daniel Rudolf, and Nikolaus Schweizer. "Perturbation bounds for Monte Carlo within Metropolis via restricted approximations." Stochastic Processes and their Applications 130, no. 4 (April 2020): 2200–2227. http://dx.doi.org/10.1016/j.spa.2019.06.015.

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31

Zhurkin, Evgeny E., Dmitry Terentyev, Marc Hou, Lorenzo Malerba, and Giovanni Bonny. "Metropolis Monte-Carlo simulation of segregation in Fe–Cr alloys." Journal of Nuclear Materials 417, no. 1-3 (October 2011): 1082–85. http://dx.doi.org/10.1016/j.jnucmat.2010.12.191.

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32

Tsuda, N., A. Fujitsu, and T. Yukawa. "Note on the Metropolis Monte Carlo method on random lattices." Computer Physics Communications 87, no. 3 (June 1995): 372–74. http://dx.doi.org/10.1016/0010-4655(94)00129-p.

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33

Barbuzza, R., and A. Clausse. "Metropolis Monte Carlo for tomographic reconstruction with prior smoothness information." IET Image Processing 5, no. 2 (2011): 198. http://dx.doi.org/10.1049/iet-ipr.2010.0124.

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34

Atchadé, Yves F., Gareth O. Roberts, and Jeffrey S. Rosenthal. "Towards optimal scaling of metropolis-coupled Markov chain Monte Carlo." Statistics and Computing 21, no. 4 (July 3, 2010): 555–68. http://dx.doi.org/10.1007/s11222-010-9192-1.

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35

Zinchenko, O., H. A. De Raedt, E. Detsi, P. R. Onck, and J. T. M. De Hosson. "Nanoporous gold formation by dealloying: A Metropolis Monte Carlo study." Computer Physics Communications 184, no. 6 (June 2013): 1562–69. http://dx.doi.org/10.1016/j.cpc.2013.02.004.

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36

CODDINGTON, P. D. "TESTS OF RANDOM NUMBER GENERATORS USING ISING MODEL SIMULATIONS." International Journal of Modern Physics C 07, no. 03 (June 1996): 295–303. http://dx.doi.org/10.1142/s0129183196000235.

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Large-scale Monte Carlo simulations require high-quality random number generators to ensure correct results. The contrapositive of this statement is also true — the quality of random number generators can be tested by using them in large-scale Monte Carlo simulations. We have tested many commonly-used random number generators with high precision Monte Carlo simulations of the 2-d Ising model using the Metropolis, Swendsen-Wang, and Wolff algorithms. This work is being extended to the testing of random number generators for parallel computers. The results of these tests are presented, along with recommendations for random number generators for high-performance computers, particularly for lattice Monte Carlo simulations.

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37

Pawig, S. Große, and K. Pinn. "Monte Carlo Algorithms for the Fully Frustrated XY Model." International Journal of Modern Physics C 09, no. 05 (July 1998): 727–36. http://dx.doi.org/10.1142/s0129183198000637.

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We investigate local update algorithms for the fully frustrated XY model on a square lattice. In addition to the standard updating procedures like the Metropolis or heat bath algorithm we include overrelaxation sweeps, implemented through single spin updates that preserve the energy of the configuration. The dynamical critical exponent (of order two) stays more or less unchanged. However, the integrated autocorrelation times of the algorithm can be significantly reduced.

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38

BAILLIE, CLIVE F. "LATTICE SPIN MODELS AND NEW ALGORITHMS — A REVIEW OF MONTE CARLO COMPUTER SIMULATIONS." International Journal of Modern Physics C 01, no. 01 (April 1990): 91–117. http://dx.doi.org/10.1142/s0129183190000050.

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We review Monte Carlo computer simulations of spin models — both discrete and continuous. We explain the phenomenon of critical slowing which seriously degrades the efficiency of standard local Monte Carlo algorithms such as the Metropolis algorithm near phase transitions. We then go onto describe in detail the new algorithms which ameliorate the problem of critical slowing down, and give their dynamical critical exponent values.

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39

STANICA, NICOLAE, GIANINA DOBRESCU, LUMINITA PATRON, SOONG-HYUCK SUH, FANICA CIMPOESU, and LUCIAN POSTELNICU. "A MONTE CARLO SIMULATION OF MAGNETIC ORDERING IN ISING FERRITES OF FORMULA 5Fe2O3.3Y2O3 WITH GARNET STRUCTURE." Journal of Theoretical and Computational Chemistry 05, no. 02 (June 2006): 151–61. http://dx.doi.org/10.1142/s0219633606002192.

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The magnetic properties simulation of extended networks containing quantum spins, by original FORTRAN code "MCIsing", is presented. The computer code is based on Ising model and uses Monte Carlo-Metropolis (MCM) algorithm. The results of magnetic Monte Carlo studies on a garnet type lattice, Ising model ferrimagnet, provide insights into the exchange interactions involved in the Ferrites of Formula 5 Fe 2 O 3.3 Y 2 O 3 with Garnet Structure.

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40

Jones, Galin L., Gareth O. Roberts, and Jeffrey S. Rosenthal. "Convergence of Conditional Metropolis-Hastings Samplers." Advances in Applied Probability 46, no. 02 (June 2014): 422–45. http://dx.doi.org/10.1017/s0001867800007151.

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We consider Markov chain Monte Carlo algorithms which combine Gibbs updates with Metropolis-Hastings updates, resulting in aconditional Metropolis-Hastings sampler(CMH sampler). We develop conditions under which the CMH sampler will be geometrically or uniformly ergodic. We illustrate our results by analysing a CMH sampler used for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon discrete observations.

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41

Jones, Galin L., Gareth O. Roberts, and Jeffrey S. Rosenthal. "Convergence of Conditional Metropolis-Hastings Samplers." Advances in Applied Probability 46, no. 2 (June 2014): 422–45. http://dx.doi.org/10.1239/aap/1401369701.

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We consider Markov chain Monte Carlo algorithms which combine Gibbs updates with Metropolis-Hastings updates, resulting in a conditional Metropolis-Hastings sampler (CMH sampler). We develop conditions under which the CMH sampler will be geometrically or uniformly ergodic. We illustrate our results by analysing a CMH sampler used for drawing Bayesian inferences about the entire sample path of a diffusion process, based only upon discrete observations.

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42

Fiedler, K., and B. Grauert. "Monte Carlo Calculation: Thermodynamic Functions in Zeolites. I. Theoretical Fundamentals." Adsorption Science & Technology 3, no. 3 (September 1986): 181–87. http://dx.doi.org/10.1177/026361748600300308.

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A Monte Carlo method for calculating thermodynamic functions of zeolitic adsoption systems is presented, which is different from the method of Metropolis et al. (1949; 1953). The method is based on emphasizing sampling strategy for representing the canonical measure by means of a trajectory averaging. The method allows the calculation of free energy, energy and other derived thermodynamic functions directly from the histogram as well as the calculation of the empirical dispersion and the bias.

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43

Hareli, Chen, and Maytal Caspary Toroker. "Water Oxidation Catalysis for NiOOH by a Metropolis Monte Carlo Algorithm." Journal of Chemical Theory and Computation 14, no. 5 (April 3, 2018): 2380–85. http://dx.doi.org/10.1021/acs.jctc.7b01214.

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44

Caracciolo, Sergio, Andrea Pelissetto, and Alan D. Sokal. "A general limitation on Monte Carlo algorithms of the Metropolis type." Physical Review Letters 72, no. 2 (January 10, 1994): 179–82. http://dx.doi.org/10.1103/physrevlett.72.179.

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45

Mazars, Martial. "Communications: The Metropolis Monte Carlo finite element algorithm for electrostatic interactions." Journal of Chemical Physics 132, no. 12 (March 28, 2010): 121101. http://dx.doi.org/10.1063/1.3367886.

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46

Blundell, Jamie R., and Eugene M. Terentjev. "Semiflexible filaments subject to arbitrary interactions: a Metropolis Monte Carlo approach." Soft Matter 7, no. 8 (2011): 3967. http://dx.doi.org/10.1039/c0sm01322f.

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47

Boghosian, Bruce M. "Generalization of Metropolis and heat-bath sampling for Monte Carlo simulations." Physical Review E 60, no. 2 (August 1, 1999): 1189–94. http://dx.doi.org/10.1103/physreve.60.1189.

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48

De Vos, Dirk, Emil De Borger, Jan Broeckhove, and Gerrit T. S. Beemster. "Simulating leaf growth dynamics through Metropolis-Monte Carlo based energy minimization." Journal of Computational Science 9 (July 2015): 107–11. http://dx.doi.org/10.1016/j.jocs.2015.04.026.

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49

Detz, Hermann, and Gottfried Strasser. "Metropolis Monte Carlo based Relaxation of Atomistic III-V Semiconductor Models." IFAC-PapersOnLine 48, no. 1 (2015): 550–55. http://dx.doi.org/10.1016/j.ifacol.2015.05.074.

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50

Altekar, G., S. Dwarkadas, J. P. Huelsenbeck, and F. Ronquist. "Parallel Metropolis coupled Markov chain Monte Carlo for Bayesian phylogenetic inference." Bioinformatics 20, no. 3 (January 22, 2004): 407–15. http://dx.doi.org/10.1093/bioinformatics/btg427.

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