Talk:Gibbs algorithm: Difference between revisions

This page mentions two things: The Gibbs Algorithm and the Gibbs Distribution. In my opinion, both are important and should be separated. According to various Markov Random Field literature, the Gibbs distribution takes the form of:

$P(f)=Z^{-1}\times e^{-{\frac {1}{T}}U(f)}$

where

$Z=\sum _{f\in F}e^{-{\frac {1}{T}}U(f)}$

is a normalizing factor. T is a constant called the temperature, and U(f) is an energy function. For a specific choice of U(f), this leads to the (Gaussian) Normal_distribution.

Gibbs Algorithm vs Gibbs Sampler

This article states that the Gibbs Algorithm is different from the Gibbs Sampler. But I encountered various interpretations of Markov Random Fields in terms of maximizing the Entropy, which is often defined as

$H=-\sum _{i}p_{i}\log p_{i}$

This makes the Gibbs algorithm probably a special case of Markov chain Monte Carlo iterations. For an interpretation of Markov Random Fields in terms of Entropy see for example here [1] op page 5/6.