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Books on the topic 'Markov chain Monte Carlo samplers'

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Published: 6 September 2023

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1

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

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2

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

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3

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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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

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

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6

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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7

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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8

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

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9

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

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10

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

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11

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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12

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

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13

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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14

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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15

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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16

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

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17

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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18

Markov chain Monte Carlo simulations and their statistical analysis: With web-based Fortran code. Hackensack, NJ: World Scientific, 2004.

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19

Markov chain Monte Carlo simulations and their statistical analysis: With web-based fortran code. Singapore: World Scientific Publishing, 2004.

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20

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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21

Limit Theory for Spatial Processes, Bootstrap Quantile Variance Estimators, and Efficiency Measures for Markov Chain Monte Carlo. [New York, N.Y.?]: [publisher not identified], 2014.

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22

Coolen, A. C. C., A. Annibale, and E. S. Roberts. Markov Chain Monte Carlo sampling of graphs. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0006.

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This chapter looks at Markov Chain Monte Carlo techniques to generate hard- and soft-constrained exponential random graph ensembles. The essence is to define a Markov chain based on ergodic randomization moves acting on a network with transition probabilities which satisfy detailed balance. This is sufficient to ensure that the Markov chain will sample from the ensemble with the desired probabilities. This chapter studies several commonly seen randomization move sets and carefully defines acceptance probabilities for a range of different ensembles using both the Metropolis–Hastings and the Glauber prescription. Particular care is paid to describe and avoid the pitfalls that can occur in defining randomization moves for hard-constrained ensembles, and applying them without introducing inadvertent bias (i.e. defining and comparing protocols including switch-and-hold and mobility).

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23

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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24

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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25

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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26

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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27

Gamerman, Dani, and Hedibert F. Lopes. Markov Chain Monte Carlo. Chapman and Hall/CRC, 2006. http://dx.doi.org/10.1201/9781482296426.

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28

Brooks, Steve, Andrew Gelman, Galin Jones, and Xiao-Li Meng, eds. Handbook of Markov Chain Monte Carlo. Chapman and Hall/CRC, 2011. http://dx.doi.org/10.1201/b10905.

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29

Gilks, W. R., S. Richardson, and David Spiegelhalter, eds. Markov Chain Monte Carlo in Practice. Chapman and Hall/CRC, 1995. http://dx.doi.org/10.1201/b14835.

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30

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

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31

Brooks, Steve, Andrew Gelman, Xiao-Li Meng, and Galin L. Jones. Handbook of Markov Chain Monte Carlo. Taylor & Francis Group, 2011.

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32

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

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33

Brooks, Steve, Andrew Gelman, Xiao-Li Meng, and Galin Jones. Handbook of Markov Chain Monte Carlo. Taylor & Francis Group, 2011.

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34

Brooks, Steve, Andrew Gelman, Xiao-Li Meng, and Galin Jones. Handbook of Markov Chain Monte Carlo. Taylor & Francis Group, 2011.

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35

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

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36

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

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37

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

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38

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

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39

Coolen, A. C. C., A. Annibale, and E. S. Roberts. Graphs with hard constraints: further applications and extensions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0007.

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This chapter looks at further topics pertaining to the effective use of Markov Chain Monte Carlo to sample from hard- and soft-constrained exponential random graph models. The chapter considers the question of how moves can be sampled efficiently without introducing unintended bias. It is shown mathematically and numerically that apparently very similar methods of picking out moves can give rise to significant differences in the average topology of the networks generated by the MCMC process. The general discussion in complemented with pseudocode in the relevant section of the Algorithms chapter, which explicitly sets out some accurate and practical move sampling approaches. The chapter also describes how the MCMC equilibrium probabilities can be purposely deformed to, for example, target desired correlations between degrees of connected nodes. The mathematical exposition is complemented with graphs showing the results of numerical simulations.

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40

Jones, Galin L. Convergence rates and Monte Carlo standard errors for Markov chain Monte Carlo Algorithms. 2001.

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41

Tweedie, Richard L., and Gareth O. Roberts. Understanding Monte Carlo Markov Chain (Springer Series in Statistics). Springer, 2008.

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42

Cheng, Russell. Finite Mixture Examples; MAPIS Details. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0018.

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Two detailed numerical examples are given in this chapter illustrating and comparing mainly the reversible jump Markov chain Monte Carlo (RJMCMC) and the maximum a posteriori/importance sampling (MAPIS) methods. The numerical examples are the well-known galaxy data set with sample size 82, and the Hidalgo stamp issues thickness data with sample size 485. A comparison is made of the estimates obtained by the RJMCMC and MAPIS methods for (i) the posterior k-distribution of the number of components, k, (ii) the predictive finite mixture distribution itself, and (iii) the posterior distributions of the component parameters and weights. The estimates obtained by MAPIS are shown to be more satisfactory and meaningful. Details are given of the practical implementation of MAPIS for five non-normal mixture models, namely: the extreme value, gamma, inverse Gaussian, lognormal, and Weibull. Mathematical details are also given of the acceptance-rejection importance sampling used in MAPIS.

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43

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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44

Pinto, Ruxandra L. Improving markov chain monte carlo estimators using overrelaxation and coupling techniques. 2002.

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45

Pinto, Ruxandra L. Improving Markov chain Monte Carlo estimations using overrelaxing and coupling techniques. 2002, 2002.

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46

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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47

Matsuura, So, and Masanori Hanada. MCMC from Scratch: A Practical Introduction to Markov Chain Monte Carlo. Springer, 2022.

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48

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

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49

Laver, Michael, and Ernest Sergenti. Systematically Interrogating Agent-Based Models. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691139036.003.0004.

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This chapter develops the methods for designing, executing, and analyzing large suites of computer simulations that generate stable and replicable results. It starts with a discussion of the different methods of experimental design, such as grid sweeping and Monte Carlo parameterization. Next, it demonstrates how to calculate mean estimates of output variables of interest. It does so by first discussing stochastic processes, Markov Chain representations, and model burn-in. It focuses on three stochastic process representations: nonergodic deterministic processes that converge on a single state; nondeterministic stochastic processes for which a time average provides a representative estimate of the output variables; and nondeterministic stochastic processes for which a time average does not provide a representative estimate of the output variables. The estimation strategy employed depends on which stochastic process the simulation follows. Lastly, the chapter presents a set of diagnostic checks used to establish an appropriate sample size for the estimation of the means.

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50

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

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