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Journal articles on the topic 'Markov chain Monte Carlo methods'

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Published: 4 June 2021
Last updated: 25 May 2024

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1

Athreya, K. B., Mohan Delampady, and T. Krishnan. "Markov Chain Monte Carlo methods." Resonance 8, no. 12 (December 2003): 18–32. http://dx.doi.org/10.1007/bf02839048.

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2

Athreya, K. B., Mohan Delampady, and T. Krishnan. "Markov chain Monte Carlo methods." Resonance 8, no. 10 (October 2003): 8–19. http://dx.doi.org/10.1007/bf02840702.

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3

Athreya, K. B., Mohan Delampady, and T. Krishnan. "Markov chain Monte Carlo methods." Resonance 8, no. 7 (July 2003): 63–75. http://dx.doi.org/10.1007/bf02834404.

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4

Athreya, K. B., Mohan Delampady, and T. Krishnan. "Markov Chain Monte Carlo methods." Resonance 8, no. 4 (April 2003): 17–26. http://dx.doi.org/10.1007/bf02883528.

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5

Andrieu, Christophe, Arnaud Doucet, and Roman Holenstein. "Particle Markov chain Monte Carlo methods." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72, no. 3 (June 2010): 269–342. http://dx.doi.org/10.1111/j.1467-9868.2009.00736.x.

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6

Gelman, Andrew, and Donald B. Rubin. "Markov chain Monte Carlo methods in biostatistics." Statistical Methods in Medical Research 5, no. 4 (December 1996): 339–55. http://dx.doi.org/10.1177/096228029600500402.

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7

Brockwell, Anthony, Pierre Del Moral, and Arnaud Doucet. "Sequentially interacting Markov chain Monte Carlo methods." Annals of Statistics 38, no. 6 (December 2010): 3387–411. http://dx.doi.org/10.1214/09-aos747.

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8

Jones, Galin L., and Qian Qin. "Markov Chain Monte Carlo in Practice." Annual Review of Statistics and Its Application 9, no. 1 (March 7, 2022): 557–78. http://dx.doi.org/10.1146/annurev-statistics-040220-090158.

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Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of probability distributions commonly encountered in modern applications. For MCMC simulation to produce reliable outcomes, it needs to generate observations representative of the target distribution, and it must be long enough so that the errors of Monte Carlo estimates are small. We review methods for assessing the reliability of the simulation effort, with an emphasis on those most useful in practically relevant settings. Both strengths and weaknesses of these methods are discussed. The methods are illustrated in several examples and in a detailed case study.
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9

Jones, Galin L., and Qian Qin. "Markov Chain Monte Carlo in Practice." Annual Review of Statistics and Its Application 9, no. 1 (March 7, 2022): 557–78. http://dx.doi.org/10.1146/annurev-statistics-040220-090158.

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Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of probability distributions commonly encountered in modern applications. For MCMC simulation to produce reliable outcomes, it needs to generate observations representative of the target distribution, and it must be long enough so that the errors of Monte Carlo estimates are small. We review methods for assessing the reliability of the simulation effort, with an emphasis on those most useful in practically relevant settings. Both strengths and weaknesses of these methods are discussed. The methods are illustrated in several examples and in a detailed case study.
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10

Montanaro, Ashley. "Quantum speedup of Monte Carlo methods." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2181 (September 2015): 20150301. http://dx.doi.org/10.1098/rspa.2015.0301.

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Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.
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11

Klauenberg, Katy, and Clemens Elster. "Markov chain Monte Carlo methods: an introductory example." Metrologia 53, no. 1 (January 13, 2016): S32—S39. http://dx.doi.org/10.1088/0026-1394/53/1/s32.

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12

Eberle, Andreas, and Carlo Marinelli. "Stability of sequential Markov Chain Monte Carlo methods." ESAIM: Proceedings 19 (2007): 22–31. http://dx.doi.org/10.1051/proc:071905.

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13

Kamatani, Kengo. "Local degeneracy of Markov chain Monte Carlo methods." ESAIM: Probability and Statistics 18 (2014): 713–25. http://dx.doi.org/10.1051/ps/2014004.

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14

Jacob, Pierre E., John O’Leary, and Yves F. Atchadé. "Unbiased Markov chain Monte Carlo methods with couplings." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 82, no. 3 (May 6, 2020): 543–600. http://dx.doi.org/10.1111/rssb.12336.

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15

Chib, Siddhartha, and Edward Greenberg. "Markov Chain Monte Carlo Simulation Methods in Econometrics." Econometric Theory 12, no. 3 (August 1996): 409–31. http://dx.doi.org/10.1017/s0266466600006794.

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We present several Markov chain Monte Carlo simulation methods that have been widely used in recent years in econometrics and statistics. Among these is the Gibbs sampler, which has been of particular interest to econometricians. Although the paper summarizes some of the relevant theoretical literature, its emphasis is on the presentation and explanation of applications to important models that are studied in econometrics. We include a discussion of some implementation issues, the use of the methods in connection with the EM algorithm, and how the methods can be helpful in model specification questions. Many of the applications of these methods are of particular interest to Bayesians, but we also point out ways in which frequentist statisticians may find the techniques useful.
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16

Bercu, Bernard, Pierre Del Moral, and Arnaud Doucet. "Fluctuations of interacting Markov chain Monte Carlo methods." Stochastic Processes and their Applications 122, no. 4 (April 2012): 1304–31. http://dx.doi.org/10.1016/j.spa.2012.01.001.

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17

Matthew Richey. "The Evolution of Markov Chain Monte Carlo Methods." American Mathematical Monthly 117, no. 5 (2010): 383. http://dx.doi.org/10.4169/000298910x485923.

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18

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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19

Verhofen, Michael. "Markov Chain Monte Carlo Methods in Financial Econometrics." Financial Markets and Portfolio Management 19, no. 4 (December 2005): 397–405. http://dx.doi.org/10.1007/s11408-005-6459-1.

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20

Kamatani, Kengo. "Local consistency of Markov chain Monte Carlo methods." Annals of the Institute of Statistical Mathematics 66, no. 1 (April 11, 2013): 63–74. http://dx.doi.org/10.1007/s10463-013-0403-3.

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21

Daw, E. W., J. Kumm, G. L. Snow, E. A. Thompson, and E. M. Wijsman. "Monte carlo markov chain methods for genome screening." Genetic Epidemiology 17, S1 (1999): S133—S138. http://dx.doi.org/10.1002/gepi.1370170723.

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22

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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23

Koike, Takaaki, and Marius Hofert. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations." Risks 8, no. 1 (January 15, 2020): 6. http://dx.doi.org/10.3390/risks8010006.

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In this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo (MC) methods often provide inefficient estimates due to the rare-event character of the crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as the Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. The efficiency of the MCMC estimators is demonstrated in a series of numerical experiments.
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24

Luangkesorn, K. L., and Z. F. Eren-Doğu. "Markov Chain Monte Carlo methods for estimating surgery duration." Journal of Statistical Computation and Simulation 86, no. 2 (January 23, 2015): 262–78. http://dx.doi.org/10.1080/00949655.2015.1004065.

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25

HEATH, S. C. "Markov Chain Monte Carlo Methods for Radiation Hybrid Mapping." Journal of Computational Biology 4, no. 4 (January 1997): 505–15. http://dx.doi.org/10.1089/cmb.1997.4.505.

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26

Han, Cong, and Bradley P. Carlin. "Markov Chain Monte Carlo Methods for Computing Bayes Factors." Journal of the American Statistical Association 96, no. 455 (September 2001): 1122–32. http://dx.doi.org/10.1198/016214501753208780.

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27

Mau, Bob, Michael A. Newton, and Bret Larget. "Bayesian Phylogenetic Inference via Markov Chain Monte Carlo Methods." Biometrics 55, no. 1 (March 1999): 1–12. http://dx.doi.org/10.1111/j.0006-341x.1999.00001.x.

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28

Chib, Siddhartha, Federico Nardari, and Neil Shephard. "Markov chain Monte Carlo methods for stochastic volatility models." Journal of Econometrics 108, no. 2 (June 2002): 281–316. http://dx.doi.org/10.1016/s0304-4076(01)00137-3.

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29

Liechty, J. C. "Markov chain Monte Carlo methods for switching diffusion models." Biometrika 88, no. 2 (June 1, 2001): 299–315. http://dx.doi.org/10.1093/biomet/88.2.299.

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30

Robert, Christian P. "Convergence Control Methods for Markov Chain Monte Carlo Algorithms." Statistical Science 10, no. 3 (August 1995): 231–53. http://dx.doi.org/10.1214/ss/1177009937.

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31

Livingstone, Samuel, and Mark Girolami. "Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions." Entropy 16, no. 6 (June 3, 2014): 3074–102. http://dx.doi.org/10.3390/e16063074.

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32

Carlin, Bradley P., and Siddhartha Chib. "Bayesian Model Choice Via Markov Chain Monte Carlo Methods." Journal of the Royal Statistical Society: Series B (Methodological) 57, no. 3 (September 1995): 473–84. http://dx.doi.org/10.1111/j.2517-6161.1995.tb02042.x.

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33

Thomas, Duncan C. "Introduction: Bayesian Models and Markov Chain Monte Carlo Methods." Genetic Epidemiology 21, S1 (2001): S660—S661. http://dx.doi.org/10.1002/gepi.2001.21.s1.s660.

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34

Derakhshanian, N., P. Risse, T. Ježo, M. Klasen, K. Kovařík, A. Kusina, F. I. Olness, and I. Schienbein. "Nuclear PDF Determination Using Markov Chain Monte Carlo Methods." Acta Physica Polonica B Proceedings Supplement 16, no. 7 (2023): 1. http://dx.doi.org/10.5506/aphyspolbsupp.16.7-a33.

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35

Finke, Axel, Arnaud Doucet, and Adam M. Johansen. "Limit theorems for sequential MCMC methods." Advances in Applied Probability 52, no. 2 (June 2020): 377–403. http://dx.doi.org/10.1017/apr.2020.9.

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AbstractBoth sequential Monte Carlo (SMC) methods (a.k.a. ‘particle filters’) and sequential Markov chain Monte Carlo (sequential MCMC) methods constitute classes of algorithms which can be used to approximate expectations with respect to (a sequence of) probability distributions and their normalising constants. While SMC methods sample particles conditionally independently at each time step, sequential MCMC methods sample particles according to a Markov chain Monte Carlo (MCMC) kernel. Introduced over twenty years ago in [6], sequential MCMC methods have attracted renewed interest recently as they empirically outperform SMC methods in some applications. We establish an $\mathbb{L}_r$ -inequality (which implies a strong law of large numbers) and a central limit theorem for sequential MCMC methods and provide conditions under which errors can be controlled uniformly in time. In the context of state-space models, we also provide conditions under which sequential MCMC methods can indeed outperform standard SMC methods in terms of asymptotic variance of the corresponding Monte Carlo estimators.
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36

Grana, Dario, Leandro de Figueiredo, and Klaus Mosegaard. "Markov chain Monte Carlo for petrophysical inversion." GEOPHYSICS 87, no. 1 (November 12, 2021): M13—M24. http://dx.doi.org/10.1190/geo2021-0177.1.

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Stochastic petrophysical inversion is a method used to predict reservoir properties from seismic data. Recent advances in stochastic optimization allow generating multiple realizations of rock and fluid properties conditioned on seismic data. To match the measured data and represent the uncertainty of the model variables, many realizations are generally required. Stochastic sampling and optimization of spatially correlated models are computationally demanding. Monte Carlo methods allow quantifying the uncertainty of the model variables but are impractical for high-dimensional models with spatially correlated variables. We have developed a Bayesian approach based on an efficient implementation of the Markov chain Monte Carlo (MCMC) method for the inversion of seismic data for the prediction of reservoir properties. Our Bayesian approach includes an explicit vertical correlation model in the proposal distribution. It is applied trace by trace, and the lateral continuity model is imposed by using the previously simulated values at the adjacent traces as conditioning data for simulating the initial model at the current trace. The methodology is first presented for a 1D problem to test the vertical correlation, and it is extended to 2D problems by including the lateral correlation and comparing two novel implementations based on sequential sampling. Our method is applied to synthetic data to estimate the posterior distribution of the petrophysical properties conditioned on the measured seismic data. The results are compared with an MCMC implementation without lateral correlation and demonstrate the advantage of integrating a spatial correlation model.
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37

Sagamiko, Thadei, Nyimvua Shaban, and Isambi Mbalawata. "Sensitivity Analysis and Uncertainty Parameter Quantification in a Regression Model: The Case of Deforestation in Tanzania." Tanzania Journal of Science 46, no. 3 (October 30, 2020): 673–83. http://dx.doi.org/10.4314/tjs.v46i3.9.

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Sep 2020, Published Oct 2020AbstractIn this paper a multiple regression model for the economic factors and policy that influence therate of deforestation in Tanzania is formulated. Sensitivity analysis for parameters of explanatoryvariables using one-at-a time and direct methods is carried out and the model is fitted by classicalleast square (LSQ) and Markov Chain Monte Carlo (MCMC) methods. Uncertainty quantificationof parameters by adaptive Markov Chain Monte Carlo methods is performed. The coefficient ofdetermination indicates that 87% of deforestation rate is explained by explanatory variablescaptured in the model. Household poverty rate is found to be the most sensitive factor todeforestation, while purchasing power is the least sensitive in both methods. Model validationindicates a good agreement between the collected data and the predicted data by the model andMarkoc Chain Monte Carlo method yielded a good sample mix. Thus, the study recommends thatsince economic activities tend to increase the rate of deforestation, then policy and decisionmakingprocesses should link the country’s desire for economic growth and environmentalmanagement. Keywords: deforestation; economic factors; Markov Chain Monte Carlo methods; regressionmodel; sensitivity;
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38

Shadare, A. E., M. N. O. Sadiku, and S. M. Musa. "Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions." Advanced Electromagnetics 8, no. 5 (December 17, 2019): 29–36. http://dx.doi.org/10.7716/aem.v8i5.1255.

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The advent of the Monte Carlo methods to the field of EM have seen floating random walk, fixed random walk and Exodus methods deployed to solve Poisson’s equation in rectangular coordinate and axisymmetric solution regions. However, when considering large EM domains, classical Monte Carlo methods could be time-consuming because they calculate potential one point at a time. Thus, Markov Chain Monte Carlo (MCMC) is generally preferred to other Monte Carlo methods when considering whole-field computation. In this paper, MCMC has been applied to solve Poisson’s equation in homogeneous and inhomogeneous axisymmetric regions. The MCMC results are compared with the analytical and finite difference solutions.
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39

MacEachern, Steven N., and Mario Peruggia. "Importance Link Function Estimation for Markov Chain Monte Carlo Methods." Journal of Computational and Graphical Statistics 9, no. 1 (March 2000): 99. http://dx.doi.org/10.2307/1390615.

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40

Croll, Bryce. "Markov Chain Monte Carlo Methods Applied to Photometric Spot Modeling." Publications of the Astronomical Society of the Pacific 118, no. 847 (September 2006): 1351–59. http://dx.doi.org/10.1086/507773.

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41

Puolamäki, Kai, Mikael Fortelius, and Heikki Mannila. "Seriation in Paleontological Data Using Markov Chain Monte Carlo Methods." PLoS Computational Biology 2, no. 2 (February 10, 2006): e6. http://dx.doi.org/10.1371/journal.pcbi.0020006.

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42

Ginting, V., F. Pereira, and A. Rahunanthan. "Multi-physics Markov chain Monte Carlo methods for subsurface flows." Mathematics and Computers in Simulation 118 (December 2015): 224–38. http://dx.doi.org/10.1016/j.matcom.2014.11.023.

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43

Fitzgerald, W. J. "Markov chain Monte Carlo methods with applications to signal processing." Signal Processing 81, no. 1 (January 2001): 3–18. http://dx.doi.org/10.1016/s0165-1684(00)00187-0.

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44

Maceachern, Steven N., and Mario Peruggia. "Importance Link Function Estimation for Markov Chain Monte Carlo Methods." Journal of Computational and Graphical Statistics 9, no. 1 (March 2000): 99–121. http://dx.doi.org/10.1080/10618600.2000.10474868.

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45

Proppe, Carsten. "Markov Chain Monte Carlo Simulation Methods for Structural Reliability Analysis." Procedia Engineering 199 (2017): 1122–27. http://dx.doi.org/10.1016/j.proeng.2017.09.226.

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46

Battle, David. "Applications of Markov chain Monte Carlo methods in ocean acoustics." Journal of the Acoustical Society of America 119, no. 5 (May 2006): 3343. http://dx.doi.org/10.1121/1.4786445.

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47

Del Moral, Pierre, and Arnaud Doucet. "A new class of interacting Markov chain Monte Carlo methods." Comptes Rendus Mathematique 348, no. 1-2 (January 2010): 79–83. http://dx.doi.org/10.1016/j.crma.2009.11.006.

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48

Berzuini, Carlo, Nicola G. Best, Walter R. Gilks, and Cristiana Larizza. "Dynamic Conditional Independence Models and Markov Chain Monte Carlo Methods." Journal of the American Statistical Association 92, no. 440 (December 1997): 1403–12. http://dx.doi.org/10.1080/01621459.1997.10473661.

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49

Higdon, David M. "Auxiliary Variable Methods for Markov Chain Monte Carlo with Applications." Journal of the American Statistical Association 93, no. 442 (June 1998): 585–95. http://dx.doi.org/10.1080/01621459.1998.10473712.

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50

Giudici, Paolo. "Markov chain Monte Carlo methods for probabilistic network model determination." Journal of the Italian Statistical Society 7, no. 2 (August 1998): 171–83. http://dx.doi.org/10.1007/bf03178927.

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