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I barely know what a markov chain is (I had a terrible teacher) and I probably have an idea of what a stationary distribution is... but I don't know how a Monte Carlo method works and I don't know how a Markov Chain Monte Carlo algorithm works.

Can someone please explain it to me in plain English and very simple terms?

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Downvoters might also explain here why they think this question is ill-formed. Not writing anything and downvoting is like assuming you didn't understand the question because you know nothing about the subject. –  Marco Aug 21 '13 at 16:01
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I did not downvote. But I guess, the question is too broad and can be locked as Not a real question. If I were you, I would do more self study and ask specific question. –  edit Aug 21 '13 at 16:15
    
Thanks, you're probably right. I can't find proper material unfortunately, this stuff seems quite hard to find as a well-explained thing. –  Marco Aug 21 '13 at 16:18
    
"I can't find proper material" Seriously? Skimming through one or two wikipedia pages then using the search engine of MSE would already bring you a lot. –  Did Aug 21 '13 at 16:37
    
If you're able to study on wikipedia go ahead. I can not. –  Marco Aug 21 '13 at 17:36
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1 Answer

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This is a question that requires your efforts starting to read diligently through a matter that is abbreviated MCMC (Markov Chain Monte Carlo). In this context the Monte Carlo Method provides a random sampling technique (algorithm) to obtain relevant information from observations on a system which we can theoretically model by a Markov Chain. In layman terms one obtains from a system, which can be described by a Markov Chain, per-sample observations by randomly playing roulette. See for basic introduction here>>>.

Reference to books find here>>>

and here>>>

Generally there are lots of diverse other references on the topic on MSE: http://math.stackexchange.com/search?q=markov+chain+monte+carlo

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MCMC, not MMC please. –  Did Aug 21 '13 at 16:38
    
thanks was just confused by the Roman Numbers. –  al-Hwarizmi Aug 21 '13 at 16:39
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