Talk:Gibbs sampling

	This article is within the scope of WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.StatisticsWikipedia:WikiProject StatisticsTemplate:WikiProject StatisticsStatistics
???	This article has not yet received a rating on Wikipedia's content assessment scale.
???	This article has not yet received a rating on the importance scale.

Mathematics Start‑class Mid‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
Start	This article has been rated as Start-class on Wikipedia's content assessment scale.
Mid	This article has been rated as Mid-priority on the project's priority scale.

Stationary Distribution

I'm not an expert, but the phrase 'the stationary distribution' suggests uniqueness to me, but my intuition suggests there could be cases where it isn't unique. For example p(x,y)=0 unless |x-y|<1/2 and 1<|x-y|<2, in which case p(x,y)=1.

I think there is a typo in your example. If |x-y|<1/2 then it is never the case that |x-y|>1...

Anyway you are correct that for some distributions with inaccessible regions of state space, Gibbs sampling does not give a unique stationary distribution. In these cases Gibbs sampling by itself isn't a valid MCMC method. Here's a toy example of discrete x and y taking on values 0 and 1.

p(x=0,y=0)=0

p(x=0,y=1)=0.5

p(x=1,y=0)=0.5

p(x=1,y=1)=0

Gibbs sampling can never move out of (0,1) or (1,0). However, it does leave the distribution of interest invariant. So Gibbs sampling is always a valid MCMC operator that can be mixed with another operator that ensures ergodicity. Someone should add a lucid description of these issues at some point... 128.40.213.241 13:54, 6 September 2005 (UTC)[reply]

Proved vs. Proven

Isn't "proven" an adjective, with the more accepted past participle of "prove" being "proved"? Quantling (talk) 11:56, 12 October 2007

I made the change to "proved". Quantling (talk) 17:00, 14 May 2008 (UTC)[reply]

Deterministic

OK, Gibbs sampling is stochastic and produces a different result every time, vs. EM or variational approx. mathods. But the latter techniques generally use a random init, which make the result overall MORE sensitive to init that Gibbs sampling run for long enough.