I'm looking for some papers or books with practical and theoretical examples about basic MCMC for Bayesian Statistics (With R). I've never studied about simulation, and that's why I'm looking for "basic" information. Can you give me some recommendations or advice?
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$\begingroup$ I strongly advise you to study some basic simulation before trying to tackle MCMC. $\endgroup$ – Glen_b Jan 15 '17 at 13:28
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$\begingroup$ Given the pedigree of some of the recommendations below, I hesitate to post this here, but if you really want "basic", I have some notes on the use of MCMC for parameter inference in physically-based models here (using Python rather than R). The other references given below are far more rigorous, so please use with caution, but I'd like to think they might one day be useful to someone other than me :-) $\endgroup$ – JamesS Jan 16 '17 at 9:31
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Besides the above titles, there are books specifically targeting R, like
- Jim Albert's Bayesian Computation with R
- our book Bayesian Essentials with R with a solution manual on arXiv
- our book Introduction to Monte Carlo Methods with R which is a beginner's version of our more comprehensive Monte Carlo Statistical Methods and also has an arXived solution manual
- Richard McElreath's Statistical Rethinking with Examples in R and STAN which I reviewed on my blog
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1$\begingroup$ Christian, I want to congratulate you because TBC! as a beginner at Bayesian stats, your book has helped me a lot! $\endgroup$ – Red Noise Jan 15 '17 at 21:11
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$\begingroup$ @user135273: thank you. The Bayesian Choice may sometimes be harsh for a beginner...! $\endgroup$ – Xi'an Jan 15 '17 at 21:13
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people often highly recommend Kruschke's Doing Bayesian Data Analysis as a great intro book.
From there maybe try Gelman's Bayesian Data Analysis.
Then finish it off with the excellent Monte Carlo Statistical Methods
Without more information on what specifically you are looking for this is probably best I can do.
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When I started to learn statistics I found Gelman's book on Bayesian data analysis very difficult to understand , it may be a bit overwhelming for someone new to statistics !.
I recommend you to start with Peter Hoff's book A First Course in Bayesian Statistical Methods .
It is not a comprehensive book for advanced statistical topics but it contains a large number of statistical models and examples and R-codes are provided either throughout the text or from the website for this book.
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If you ask about introductory papers, you can check the following:
Casella, G., & George, E. I. (1992). Explaining the Gibbs sampler. The American Statistician, 46(3), 167-174.
Andrieu, C., de Freitas, N., Doucet, A. & Jordan, M.I. (2003). An introduction to MCMC for machine learning. Machine Learning, 50, 5-43.
Tierney, L. (1994). Markov chains for exploring posterior distributions. The Annals of Statistics, 1701-1728.
Hartig, F., Calabrese, J.M., Reineking, B., Wiegand, T., & Huth, A. (2011). Statistical inference for stochastic simulation models – theory and application. Ecology Letters, 14, 816–827.
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1$\begingroup$ Historically, the American Statistician paper by George and Ed should have been entitled Gibbs for kids, but the editors did not like it. It took an animal breeder, Dan Gianola, to recycle the title into Gibbs for pigs and get his review published. $\endgroup$ – Xi'an Jan 15 '17 at 20:18
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Bayes theory always made sense to me, but Bayesian analysis was always very confusing. Things really started to click when I read this blog post about the 8 Schools example: http://andrewgelman.com/2014/01/21/everything-need-know-bayesian-statistics-learned-eight-schools/
I actually think the example could be more meaningful with a better example, the metric described in the 8 Schools is some abstract "coaching" result.
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Great graphical explanation of MCMC from Stata
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