Talk:Markov chain Monte Carlo

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the first paragraph needs to be dumbed down for the naive reader. what is this exactly? :) Kingturtle 07:27 30 May 2003 (UTC)

I'll work on it. Note that I didn't actually write it -- it was moved from Monte Carlo method. -- Tim Starling 07:36 30 May 2003 (UTC)

This still needs to be simplified so that someone unversed in statistics, or whatever this is, can understand it. Patadragon 20:47, 27 November 2006 (UTC)

[edit] "rejections sampling" is no random walk algorithm

The list of random walk algorithms at the bottom of the page lists "rejection sampling" as the first entry. Is this really correct? As far as I know "rejection sampling" is just a technique to sample from a given distribution and is typically not connected to random walk methods.

-- Jochen

I think what is described here as Rejection sampling is in fact correctly described as Importance sampling, and it is a key component of MCMC.

Blaise F Egan

But does this make it a "random walk algorithm"? Where is the random walk? Ok, I see that it was modified to be a little bit close to random walks. Then the most suspicious one would be "slice sampling"? Is this somehow a "random walk algorithm", too? --Jochen 16:51, 27 Feb 2005 (UTC)

Slice sampling is a Markov Chain Monte Carlo method: it defines a Markov chain which leaves a desired distribution invariant; successive steps are correlated but assymptotically come from the correct distribution. Rejection sampling draws independent, exact samples. There is no dependence on the previous state, so it isn't really a "walk". Adaptive rejection sampling (ARS) has this property also, although it may be used within an MCMC method. For example ARS is an important part of the BUGS Gibbs sampling package, but this would be better put on the Gibbs sampling page. 128.40.213.241 13:43, 23 August 2005 (UTC)

Rejection sampling, Importance sampling, and MCMC algorithms are all different things. They are all Monte Carlo sampling techniques, nevertheless. See:

C. Andrieu, N. De Freitas, A. Doucet, M. I. Jordan. "An Introduction to MCMC for Machine Learning". Machine Learning, 50, 5-43, 2003. --129.82.47.113 20:33, 3 November 2005 (UTC)