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Books on the topic 'Gaussian; Markov chain Monte Carlo methods'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

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

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2

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

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3

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

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4

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

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5

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

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6

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

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7

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

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8

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 o

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9

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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10

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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11

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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12

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 discu

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13

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 the

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14

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

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15

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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16

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 infer

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17

Geweke, John, Gary Koop, and Herman Van Dijk, eds. The Oxford Handbook of Bayesian Econometrics. Oxford University Press, 2011. http://dx.doi.org/10.1093/oxfordhb/9780199559084.001.0001.

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Bayesian econometric methods have enjoyed an increase in popularity in recent years. Econometricians, empirical economists, and policymakers are increasingly making use of Bayesian methods. The Oxford Handbook of Bayesian Econometrics is a single source about Bayesian methods in specialized fields. It contains articles by leading Bayesians on the latest developments in their specific fields of expertise. The volume provides broad coverage of the application of Bayesian econometrics in the major fields of economics and related disciplines, including macroeconomics, microeconomics, finance, and

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18

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

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19

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 sampli

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20

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 chapte

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21

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 temp

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22

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 fo

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23

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-

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24

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

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