Good sources for learning Markov chain Monte Carlo (MCMC) Any suggestions for a good source to learn MCMC methods?
 A: 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
A: Gilks W.R., Richardson S., Spiegelhalter D.J. Markov Chain Monte Carlo in Practice. Chapman & Hall/CRC, 1996.
A relative oldie now, but still a goodie.
A: 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.
A: 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.
A: 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)
A: For online tutorials, there are

*

*A tutorial in MCMC, by Sahut (2000)

*Tutorial on Markov Chain Monte Carlo, by Hanson (2000)

*Markov Chain Monte Carlo for Computer Vision, by Zhu et al. (2005)

*Introduction to Markov Chain Monte Carlo simulations and their statistical analysis, by Berg (2004).

*A Tutorial on Markov Chain Monte-Carlo and Bayesian Modeling by Martin B. Haugh (2021).

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.
A: 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.
