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1

Liang, Faming, Chuanhai Liu, and Raymond J. Carroll. Advanced Markov Chain Monte Carlo Methods. Chichester, UK: John Wiley & Sons, Ltd, 2010. http://dx.doi.org/10.1002/9780470669723.

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2

S, Kendall W., Liang F. 1970-, and Wang J. S. 1960-, eds. Markov chain Monte Carlo: Innovations and applications. Singapore: World Scientific, 2005.

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3

R, Gilks W., Richardson S, and Spiegelhalter D. J, eds. Markov chain Monte Carlo in practice. London: Chapman & Hall, 1996.

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4

R, Gilks W., Richardson S, and Spiegelhalter D. J, eds. Markov chain Monte Carlo in practice. Boca Raton, Fla: Chapman & Hall, 1998.

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5

Liang, F. Advanced Markov chain Monte Carlo methods: Learning from past samples. Hoboken, NJ: Wiley, 2010.

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6

Joseph, Anosh. Markov Chain Monte Carlo Methods in Quantum Field Theories. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46044-0.

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7

Gerhard, Winkler. Image analysis, random fields and Markov chain Monte Carlo methods: A mathematical introduction. 2nd ed. Berlin: Springer, 2003.

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8

Winkler, Gerhard. Image Analysis, Random Fields and Markov Chain Monte Carlo Methods. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55760-6.

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9

Neal, Radford M. Markov chain Monte Carlo methods based on "slicing" the density function. Toronto: University of Toronto, Dept. of Statistics, 1997.

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10

Roberts, Gareth O. Markov chain Monte Carlo: Some practical implications of theoretical results. Toronto: University of Toronto, 1997.

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11

Gamerman, Dani. Markov chain Monte Carlo: Stochastic simulation for Bayesian inference. London: Chapman & Hall, 1997.

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12

Cowles, Mary Kathryn. A simulation approach to convergence rates for Markov chain Monte Carlo algorithms. [Toronto]: University of Toronto, Dept. of Statistics, 1996.

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13

1946-, Winkler Gerhard, ed. Image analysis, random fields and Markov chain Monte Carlo methods: A mathematical introduction. 2nd ed. Berlin: Springer, 2003.

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14

1947-, Gianola Daniel, ed. Likelihood, Bayesian and MCMC methods in quantitative genetics. New York: Springer-Verlag, 2002.

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15

Brémaud, Pierre. Markov chains: Gibbs fields, Monte Carlo simulation, and queues. New York: Springer, 1999.

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16

Mikhaĭlov, G. A. New Monte Carlo methods with estimating derivatives. Utrecht, The Netherlands: VSP, 1995.

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17

Freitas, Lopes Hedibert, ed. Markov chain Monte Carlo: Stochastic simulation for Bayesian inference. 2nd ed. Boca Raton: Taylor & Francis, 2006.

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18

Nicol, David M. Automated parallelization of discrete state-space generation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2000.

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19

Nicol, David M. Automated parallelization of discrete state-space generation. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 2000.

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20

George, Casella, and SpringerLink (Online service), eds. Introducing Monte Carlo Methods with R. New York, NY: Springer Science+Business Media, LLC, 2010.

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21

Suwa, Hidemaro. Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems. Tokyo: Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54517-0.

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22

Lunn, David Jonathan. The application of Markov chain Monte Carlo techniques to the study of population pharmacokinetics. Manchester: University of Manchester, 1995.

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23

Carroll, Raymond, Faming Liang, and Chuanhai Liu. Advanced Markov Chain Monte Carlo Methods. Wiley & Sons, Incorporated, John, 2010.

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24

Kamatani, Kengo. Stability of Markov Chain Monte Carlo Methods. Springer Japan, 2023.

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25

Handbook for Markov chain Monte Carlo. Boca Raton: Taylor & Francis, 2011.

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26

Richardson, S., David Spiegelhalter, and W. R. Gilks. Markov Chain Monte Carlo in Practice. Taylor & Francis Group, 1995.

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27

Richardson, S., David Spiegelhalter, and W. R. Gilks. Markov Chain Monte Carlo in Practice. Taylor & Francis Group, 1995.

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28

Markov chain Monte Carlo: Innovations and applications. Singapore: World Scientific, 2006.

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29

Carroll, Raymond, Faming Liang, and Chuanhai Liu. Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples. Wiley & Sons, Incorporated, John, 2011.

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30

Carroll, Raymond, Faming Liang, and Chuanhai Liu. Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples. Wiley & Sons, Incorporated, John, 2011.

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31

Carroll, Raymond, Faming Liang, and Chuanhai Liu. Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples. Wiley & Sons, Limited, John, 2010.

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32

Carroll, Raymond, Faming Liang, and Chuanhai Liu. Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples. Wiley & Sons, Incorporated, John, 2010.

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33

Allen, Michael P., and Dominic J. Tildesley. Monte Carlo methods. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803195.003.0004.

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The estimation of integrals by Monte Carlo sampling is introduced through a simple example. The chapter then explains importance sampling, and the use of the Metropolis and Barker forms of the transition matrix defined in terms of the underlying matrix of the Markov chain. The creation of an appropriately weighted set of states in the canonical ensemble is described in detail and the method is extended to the isothermal–isobaric, grand canonical and semi-grand ensembles. The Monte Carlo simulation of molecular fluids and fluids containing flexible molecules using a reptation algorithm is discussed. The parallel tempering or replica exchange method for more efficient exploration of the phase space is introduced, and recent advances including solute tempering and convective replica exchange algorithms are described.
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34

Boudreau, Joseph F., and Eric S. Swanson. Monte Carlo methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0007.

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Monte Carlo methods are those designed to obtain numerical answers with the use of random numbers . This chapter discusses random engines, which provide a pseudo-random pattern of bits, and their use in for sampling a variety of nonuniform distributions, for both continuous and discrete variables. A wide selection of uniform and nonuniform variate generators from the C++ standard library are reviewed, and common techniques for generating custom nonuniform variates are discussed. The chapter presents the uses of Monte Carlo to evaluate integrals, particularly multidimensional integrals, and then introduces the important method of Markov chain Monte Carlo, suitable for solving a wide range of scientific problems that require the sampling of complicated multivariate distributions. Relevant topics in probability and statistics are also introduced in this chapter. Finally, the topics of thermalization, autocorrelation, multimodality, and Gibbs sampling are presented.
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35

Markov Chain Monte Carlo in Practice (Interdisciplinary Statistics). Chapman & Hall/CRC, 1995.

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36

Joseph, Anosh. Markov Chain Monte Carlo Methods in Quantum Field Theories: A Modern Primer. Springer, 2020.

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37

Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spinphonon Complex Systems Springer Theses. Springer Verlag, Japan, 2013.

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38

Winkler, Gerhard. Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction. Springer London, Limited, 2012.

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39

Winkler, Gerhard. Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction. Springer Berlin / Heidelberg, 2012.

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40

Suwa, Hidemaro. Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-Phonon Complex Systems. Springer London, Limited, 2013.

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41

Lopes, Hedibert F., and Dani Gamerman. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition. Taylor & Francis Group, 2006.

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42

Lopes, Hedibert F., and Dani Gamerman. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition. Taylor & Francis Group, 2006.

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43

Markov Chain Monte Carlo: Innovations And Applications (Lecture Notes Series, Institute for Mathematical Sciences, N) (Lecture Note). World Scientific Publishing Company, 2005.

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44

Ciric, Aleksandar. A Guide to Monte Carlo and Quantum Monte Carlo methods : Quantum Monte Carlo: Variational and Diffusion; MC in general; Markov Chain; Statistics; Random number generators; Hidden Monte Carlo. Createspace Independent Publishing Platform, 2016.

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45

Uncoupling-Coupling Technique for Markov Chain Monte Carlo Methods, an - ZIB Report, September 2000. Konrad-Zuse-Zentrum, 2000.

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46

Hierarchical Modelling of Discrete Longitudinal Data: Applications of Markov Chain Monte Carlo. Munich, Germany: Herbert Witz Verlag, Wissenschaft, 1997.

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47

Sorensen, Daniel, and Daniel Gianola. Likelihood, Bayesian, and MCMC Methods in Quantitative Genetics. Springer London, Limited, 2006.

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48

Berg, Bernd A. Markov Chain Monte Carlo Simulations And Their Statistical Analysis: With Web-based Fortran Code. World Scientific Publishing Company, 2004.

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49

Lopes, Hedibert F., and Dani Gamerman. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition (Texts in Statistical Science Series). 2nd ed. Chapman & Hall/CRC, 2006.

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50

Winkler, Gerhard. Image Analysis, Random Fields and Markov Chain Monte Carlo Methods: A Mathematical Introduction (Stochastic Modelling and Applied Probability). 2nd ed. Springer, 2006.

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