Talk:Metropolis–Hastings algorithm

From Wikipedia, the free encyclopedia

Hello. A comment on the title -- I've never seen the method in question called by "Metropolis-Hastings Markov Chain Monte Carlo Sampling". A google search finds only two instances of the words in the title ([1] and [2]), excluding many Wikipedia copies. I think the shorter names "Metropolis-Hastings algorithm" and "Markov chain Monte Carlo" are more common. I'm inclined to rename the article to "Markov chain Monte Carlo" and make "Metropolis-Hastings algorithm" redirect to that. Any comments? Happy editing, Wile E. Heresiarch 22:59, 6 Mar 2004 (UTC)

I think "Markov chain Monte Carlo" is often used for more general class of algorithms, including Metropolis-Hastings and other algorithms. So, it might be better to rename this article "Metropolis-Hastings algorithm". Andris 23:06, 6 Mar 2004 (UTC)

OK, thanks for your input. I am going to rename the article to "Metropolis-Hastings algorithm" now. Wile E. Heresiarch 03:18, 7 Mar 2004 (UTC)

Shouldn't there be a separate entry for just the Metropolis algorithm? I don't think the extensions by Hastings are widely-known (Google: 34,300 vs. 9,310). 21:18, 26 Aug 2004 (UTC)

I agree. I am writing an article on the "plain" Metropolis algorithm which I certainly believe to be more commonly used (at least it is in my field). Will add to wikipedia when its a more properly formulated Jackliddle 03:33, 20 Nov 2004 (UTC)

I think it would be clearer to say that if the proposed value is rejected then x^{t+1}=x^t. I got confused because I assumed that the algorithm was repeated (without stepping the time) until a proposed value was accepted.

I found this very confusing as well. The article should say exactly what happens when the proposed value is rejected. I don't know so I can't edit it. Dlakelan

The N function needs to be defined. It seems to be a sum of gaussians? The way it is written, it appears to be a single gaussian in a high dimensional space. --72.33.96.204 19:23, 16 May 2006 (UTC)

Contents

[edit] x prime or x_t?

Here are two conflicting comments on the case a>1, which I have cut and pasted for readability. --Rinconsoleao 15:12, 16 July 2007 (UTC)

There seems to be a typo in the last display. If a>1, we would accept the proposal, x', not x_t. --Youyifong 06:38, 28 July 2006 (UTC)
Hi, is there a mistake here? In the step-by-step instructions,
x^{t+1} = \left \{ \begin{matrix} x'(x(t)?) & \mbox{if }a > 1 \\ x'\mbox{ with probability }a, & \mbox{if }a < 1 \end{matrix} \right.
(Postdoc 02:30, 16 July 2007 (UTC))

The algorithm always accepts if a>1. That is, xt + 1 = x' when a>1. Notice that this is consistent with the statements about the uniform random variable u in the previous paragraph. I have rewritten the "step-by-step instructions" to make this clearer. --Rinconsoleao 15:12, 16 July 2007 (UTC)

Please check the page again. The pages mis-typed x' as x_t, as Youyifong mentioned again. Also, should it be "a >= 1" ? (Postdoc 05:38, 30 July 2007 (UTC))
Thanks! --Rinconsoleao 15:44, 31 July 2007 (UTC)

[edit] Gibbs sampling

The article says that the Gibbs-sampler is a special case of the MH-algorithm. As far as I know it is a complementary MCMC-method which works quite differently. --Smeyen 01:07, 24 February 2007 (UTC)


In Gibbs sampler, its proposal distribution is the full conditional distribution of some part of parameter space conditional on the rest, which always resultes in a acceptance probability of 1. See [http:://www.stat.purdue.edu/~lebanon/notes/metropolis.pdf] (Postdoc 05:46, 30 July 2007 (UTC))

[edit] Subscripts instead of superscripts?

Shouldn't this article be using subscripts like xt instead of superscripts like xt? SteveWitham 05:10, 7 May 2007 (UTC)

[edit] Q confusion

The notation for Q is not consistent. Sometimes it is called Q(x'|x^t) and sometimes Q(x';x^t).

Also, with the present parameter order (other articles on the web calls it Q(x^t, y), i.e. swaps the parameters), I think the text is wrong when it talks about Q(x'|x^t) being independent of x'. I think it should be Q(x'|x^t) not depending on x^t - makes more sense. -- BjarkeDahlEbert (talk) 22:30, 8 December 2007 (UTC)


[edit] Multiple-try Metropolis

I have created an article called the Multiple-Try Metropolis algorithm, which describes how to sample more efficiently from high dimensional distributions. Hope it's useful :) Velocidex (talk) 02:49, 3 May 2008 (UTC)

I've moved it to Multiple-try Metropolis, with a lower-case t, as required by WP:MOS. In Wikipedia article titles, the first letter of the title, unlike the later letters, is case-insensitive in links and appears as a capital at the top of the article; later initial letters are to be lower case except when there's some special reason to capitalize them. Metropolis is in this case a person's name, so it has a capital M. Michael Hardy (talk) 16:47, 4 May 2008 (UTC)