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Books on the topic 'Markov chain Monte Carlo (MCMC)'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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1

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

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2

1961-, Robert Christian P., ed. Discretization and MCMC convergence assessment. New York: Springer, 1998.

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3

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

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4

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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5

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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6

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

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7

Cowles, Mary Kathryn. Possible biases induced by MCMC convergence diagnostics. Toronto: University of Toronto, Dept. of Statistics, 1997.

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8

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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9

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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10

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

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11

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

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12

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

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13

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

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14

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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15

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

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16

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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17

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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18

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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19

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

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20

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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21

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

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22

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

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23

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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24

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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25

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

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26

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

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27

Cheng, Russell. Finite Mixture Models. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198505044.003.0017.

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Fitting a finite mixture model when the number of components, k, is unknown can be carried out using the maximum likelihood (ML) method though it is non-standard. Two well-known Bayesian Markov chain Monte Carlo (MCMC) methods are reviewed and compared with ML: the reversible jump method and one using an approximating Dirichlet process. Another Bayesian method, to be called MAPIS, is examined that first obtains point estimates for the component parameters by the maximum a posteriori method for different k and then estimates posterior distributions, including that for k, using importance sampling. MAPIS is compared with ML and the MCMC methods. The MCMC methods produce multimodal posterior parameter distributions in overfitted models. This results in the posterior distribution of k being biased towards high k. It is shown that MAPIS does not suffer from this problem. A simple numerical example is discussed.

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28

Martin, Andrew D. Bayesian Analysis. Edited by Janet M. Box-Steffensmeier, Henry E. Brady, and David Collier. Oxford University Press, 2009. http://dx.doi.org/10.1093/oxfordhb/9780199286546.003.0021.

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This article surveys modern Bayesian methods of estimating statistical models. It first provides an introduction to the Bayesian approach for statistical inference, contrasting it with more conventional approaches. It then explains the Monte Carlo principle and reviews commonly used Markov Chain Monte Carlo (MCMC) methods. This is followed by a practical justification for the use of Bayesian methods in the social sciences, and a number of examples from the literature where Bayesian methods have proven useful are shown. The article finally provides a review of modern software for Bayesian inference, and a discussion of the future of Bayesian methods in political science. One area ripe for research is the use of prior information in statistical analyses. Mixture models and those with discrete parameters (such as change point models in the time-series context) are completely underutilized in political science.

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29

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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30

Henderson, Daniel A., R. J. Boys, Carole J. Proctor, and Darren J. Wilkinson. Linking systems biology models to data: A stochastic kinetic model of p53 oscillations. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.7.

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This article discusses the use of a stochastic kinetic model to study protein level oscillations in single living cancer cells, using the p53 and Mdm2 proteins as examples. It describes the refinement of a dynamic stochastic process model of the cellular response to DNA damage and compares this model to time course data on the levels of p53 and Mdm2. The article first provides a biological background on p53 and Mdm2 before explaining how the stochastic kinetic model is constructed. It then introduces the stochastic kinetic model and links it to the data and goes on to apply sophisticated MCMC methods to compute posterior distributions. The results demonstrate that it is possible to develop computationally intensive Markov chain Monte Carlo (MCMC) methods for conducting a Bayesian analysis of an intra-cellular stochastic systems biology model using single-cell time course data.

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31

Quintana, José Mario, Carlos Carvalho, James Scott, and Thomas Costigliola. Extracting S&P500 and NASDAQ Volatility: The Credit Crisis of 2007–2008. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.13.

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This article demonstrates the utility of Bayesian modelling and inference in financial market volatility analysis, using the 2007-2008 credit crisis as a case study. It first describes the applied problem and goal of the Bayesian analysis before introducing the sequential estimation models. It then discusses the simulation-based methodology for inference, including Markov chain Monte Carlo (MCMC) and particle filtering methods for filtering and parameter learning. In the study, Bayesian sequential model choice techniques are used to estimate volatility and volatility dynamics for daily data for the year 2007 for three market indices: the Standard and Poor’s S&P500, the NASDAQ NDX100 and the financial equity index called XLF. Three models of financial time series are estimated: a model with stochastic volatility, a model with stochastic volatility that also incorporates jumps in volatility, and a Garch model.

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32

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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33

Lopes, Hedibert, and Nicholas Polson. Analysis of economic data with multiscale spatio-temporal models. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.12.

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This article discusses the use of Bayesian multiscale spatio-temporal models for the analysis of economic data. It demonstrates the utility of a general modelling approach for multiscale analysis of spatio-temporal processes with areal data observations in an economic study of agricultural production in the Brazilian state of Espìrito Santo during the period 1990–2005. The article first describes multiscale factorizations for spatial processes before presenting an exploratory multiscale data analysis and explaining the motivation for multiscale spatio-temporal models. It then examines the temporal evolution of the underlying latent multiscale coefficients and goes on to introduce a Bayesian analysis based on the multiscale decomposition of the likelihood function along with Markov chain Monte Carlo (MCMC) methods. The results from agricultural production analysis show that the spatio-temporal framework can effectively analyse massive economics data sets.

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34

Rubin, Donald, Xiaoqin Wang, Li Yin, and Elizabeth Zell. Bayesian causal inference: Approaches to estimating the effect of treating hospital type on cancer survival in Sweden using principal stratification. Edited by Anthony O'Hagan and Mike West. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198703174.013.24.

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This article discusses the use of Bayesian causal inference, and more specifically the posterior predictive approach of Rubin’s causal model (RCM) and methods of principal stratification, in estimating the effects of ‘treating hospital type’ on cancer survival. Using the Karolinska Institute in Stockholm, Sweden, as a case study, the article investigates which type of hospital (large patient volume vs. small volume) is superior for treating certain serious conditions. The study examines which factors may reasonably be considered ignorable in the context of covariates available, as well as non-compliance complications due to transfers between hospital types for treatment. The article first provides an overview of the general Bayesian approach to causal inference, primarily with ignorable treatment assignment, before introducing the proposed approach and motivating it using simple method-of-moments summary statistics. Finally, the results of simulation using Markov chain Monte Carlo (MCMC) methods are presented.

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35

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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36

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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37

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

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38

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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39

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

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40

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

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41

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

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42

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

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43

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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44

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

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45

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

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46

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

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47

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

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48

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

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49

Simulation and Monte Carlo: With applications in finance and MCMC. Wiley, 2007.

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50

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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