# Gibbs random field

1. Oct 10, 2012

### pamparana

Hello everyone,

I am trying to understand markov random fields and how it is related to the Gibbs measure and basically trying to understand the Gibbs-MRF equivalancy.

Anyway, while browsing Wikipedia documents, I was looking at the page on MRFs and when I came across the following line;

I got confused with this. Aren't probabilities supposed to be positive. Why would be a probability distribution be negative? What does a negative probability distribution even mean? Would one use it in any possible case? So, are not ALL probability distributions gibbs random field?

Thanks,
/L

2. Oct 10, 2012

### chiro

Hey pamparana.

I do recall hearing about this once before in the context of Dirac, but I never really gave it much thought, however the wiki page is probably a good place to start on learning this:

http://en.wikipedia.org/wiki/Negative_probability

The above says that a guy named M.S. Bartlett did the mathematical and logical consistency analysis of these kinds of distributions, so that would be a good place to start if you can't get something immediate on google.

3. Oct 10, 2012

### chiro

You've got me interesting in this, and a quick search came up with the following:

http://cs5824.userapi.com/u11728334/docs/8db4cf52c20c/Khrennikov_Interpretations_of_probability_34766.pdf [Broken]

Last edited by a moderator: May 6, 2017
4. Oct 11, 2012

### pamparana

Wow, thanks! Crazy stuff!

Would need a lot of time to process this. In any case, it seems most of the probability distributions we encounter most of the time are Gibbs fields.