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Any suggestions for a good source to learn MCMC methods?

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For online tutorials, there are

Practical Markov Chain Monte Carlo, by Geyer (Stat. Science, 1992), is also a good starting point, and you can look at the MCMCpack or mcmc R packages for illustrations.

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  • $\begingroup$ fyi : 2nd two links in the list are broken $\endgroup$ – still_learning Dec 8 '15 at 21:23
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I haven't read it (yet), but if you're into R, there is Christian P. Robert's and George Casella's book: Introducing Monte Carlo Methods with R (Use R)

I know of it from following his (very good) blog

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  • $\begingroup$ This book doesn't go in depth into MCMC. It actually have a page on it and skip MCMC theory in its entirety to go into Metropolist hashing. $\endgroup$ – Anthony Doan Apr 19 '17 at 5:57
  • $\begingroup$ While you are 100% entitled to your own opinion on our book, I beg to disagree with the notion that we do not go in depth into MCMC there. Judging from the question I do not think the OP was asking for the deep theory of MCMC algorithms (which is somehow covered in our earlier book). $\endgroup$ – Xi'an Nov 1 '17 at 11:27
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Handbook of Markov Chain Monte Carlo, Steve Brooks, Andrew Gelman, Galin Jones and Xiao-Li Meng, eds. 2011 CRC Press.

Chapter 4, 'Inference from simulations and monitoring convergence' by Gelman and Shirley, is available online.

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    $\begingroup$ Looks set to kick Gilks, Richardson & Spiegelhalter (1996) into the long grass when that comes it in May. $\endgroup$ – onestop Jan 3 '11 at 9:35
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Dani Gamerman & Hedibert F. Lopes. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference (2nd ed.). Boca Raton, FL: Champan & Hall/CRC, 2006. 344 pp. ISBN 0-412-81820-5.

-- a more recently updated book than Gilks, Richardson & Spiegelhalter. I haven't read it myself, but it was well reviewed in Technometrics in 2008, and the first edition also got a good review in The Statistician back in 1998.

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Another classic position (as accompanied to already mentioned Introducing Monte Carlo Methods with R):

Monte Carlo Statistical Methods by Robert and Casella (2004)

in the Use R! series there is also:

Introduction to Probability Simulation and Gibbs Sampling with R by Suess and Trumbo (2010)

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The text I have found most accessible is Bayesian Cognitive Modeling: A Practical Course. Very clear exposition. The book has great examples in BUGS, and they have been ported to Stan on its github examples page.

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