Talk:Random field

Old Q
Xi in {0,1,...,G-1}? Shouldn't continuous variable and continuous fields also be allowed? fnielsen 11:21, 3 Mar 2005 (UTC)

hyperlinks missing
This article refers to Markov random field and Gibbs random field, neither of which exist in Wikipedia, however this article discussed MRF's and GRF's within itself. Shouldn't the other entries at least be stubbed-out with a short description? —Preceding unsigned comment added by 149.169.178.128 (talk • contribs)
 * Currently they do appear, but it seems that they are synonymous (the GRF entry redirects to MRF). If this is correct, one of the two should be removed from the list of examples.--AmitAronovitch (talk) 09:40, 1 November 2010 (UTC)

warning
This entry is incorrect. If there is a domain where such definition is used it is certainly not probability theory. The reference quoted treats a very special (although important) case of random fields. In modern probability theory the notion of random field is almost synonymous with stochastic process, except that the term "random field" is more often used if the underlying index set is a subset of $$\mathbb{R}^n$$. Slawekk 16:54, 14 March 2006 (UTC)

Expert attention needed
I agree. In current literature a random field is usually (in order of increasing abstraction) 1. collection of random variables (the "pointwise values" on its domain, a subset of $$\mathbb{R}^n$$) 2. a random variable with values in a functional space over that domain 3. a probability measure on that functional space. These concepts are equivalent in a suitable sense. The article ought to be completely rewritten. Jmath666 00:05, 19 March 2007 (UTC)

In need of complete rewrite
I totally agree that this needs a complete rewrite. The definition does not even make much mathematical sense, e.g., it starts with "let S = {X1, ..., Xn}", and then the variable S is never used again. —Preceding unsigned comment added by 84.208.147.123 (talk) 17:54, 10 March 2009 (UTC)

Need better illustrations
The article on Hidden Markov Models is an excellent example of how this topic should be written up. The current writeup is too concise and explains little if you don't already know the subject. Comment added by: Irenegoodnight. —Preceding unsigned comment added by Irenegoodnight (talk • contribs) 18:03, 6 October 2009 (UTC)

There is one fundamental point I have trouble to grasp relating to random fields. In stochastic calculus, I am used to encounter the notion of multidimensional stochastic process, that is a collection of time-indexed random variables taking values in a multidimensional space (e.g., $\mathbb{R}^n$). Given this notion, I have trouble to understand the difference between stochastic processes and random fields as stated in "A random field is a generalization of a stochastic process such that the underlying parameter need no longer be a simple real, but can instead be a multidimensional vector, space or even a manifold." Could you please advise on the following? —Preceding unsigned comment added by 212.184.196.214 (talk) 14:06, 7 October 2010 (UTC)


 * The "multidimensional vector" parameter replaces the real valued (one dimensional) "time" of the random process, not the (possibly mutidimensional) values. Indeed, the description was very confusing. I hope it is a little clearer now.--AmitAronovitch (talk) 13:07, 1 November 2010 (UTC)

OK, but...
Until someone takes up a major rewrite, I took some steps to upgrade the entry to a usable state. This included some corrections and clarifications, as well as replacing the definition with a new one (based on the def of "stochastic process"). Feedback and further improvements are needed.

p.s. I do not know what the original definition refered to, but surely it does not hold for some of the examples given in the references. It would be appreciated if the original author comes up with a reference, so we might add that as the definition of some specialized kind of field (an "X" random field is...). --AmitAronovitch (talk) 13:07, 1 November 2010 (UTC)

Unification?
Should "random field" be united with random function? --AmitAronovitch (talk) 13:07, 1 November 2010 (UTC)

Random fields vs. Stochastic processes
Stochastic process says that a "basic type of a stochastic process is a random field". But this articles states that it is a generalization of a stochastic process. Which is which? (I've also made this comment on Talk:Stochastic_process). Statisfactions (talk) 16:36, 23 January 2013 (UTC) Maybe you are wrong in my humble opinion, a stochastic process is different to a random field by the dimension of index set. Now I just want to know how to do a numerical study? Please help me, thanks.

Error on notation
On the section "Definitona and examples", when talking about the Markov field, there is a variable w which is not later defined. Maybe it was meant to mean a capital omega? — Preceding unsigned comment added by Serlack (talk • contribs) 18:04, 23 February 2014 (UTC)