Abstract
Markov Chain Monte Carlo is an innovative and widely used computational methodology for an accurate estimation of a distribution, whose direct numerical evaluation is intractable. The main idea is to construct an ergodic Markov chain which is simple to simulate and has the target distribution as its invariant probability. This technique has been indispensable in the estimation of posterior distribution in Bayesian inference.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Diaconis, P. (2009). The Markov Chain Monte Carlo revolution. Bulletin of the American Mathematical Society, 46(2), 179–20.
Gelfand, A. E., & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85(410), 398–409.
Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6(6), 721–741.
Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equations of state calculations by fast computing machines. Journal of Chemical Physics, 21(6), 1087–1092.
Robert, C., & Casella, G. (2004). Monte Carlo statistical methods. New York: Springer.
Wasserman, L. (2003). All of statistics: A concise course in statistical inference. New York: Springer.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag New York
About this chapter
Cite this chapter
Bhattacharya, R., Lin, L., Patrangenaru, V. (2016). Markov Chain Monte Carlo (MCMC) Simulation and Bayes Theory. In: A Course in Mathematical Statistics and Large Sample Theory. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-4032-5_14
Download citation
DOI: https://doi.org/10.1007/978-1-4939-4032-5_14
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-4030-1
Online ISBN: 978-1-4939-4032-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)