Talk:Gaussian process

message: The introduction is pretty much impenetrable for a lay reader. The attempt to define simply what a stochastic process is, for example, says "a collection of random variables indexed by time or space". But what if the reader is not familiar with random variables? Or does not instantly grasp what indexing by time or space means? A real-world example would go a long way here, especially one where the random variables and space/time-indexing can be concretely and intuitively linked to something in everyday experience.
This theme continues throughout the whole article, as the reader is assumed to have a strong mathematical or statistical background. There is a distinct lack of non-specialist, non-abstract examples. The introductory text in the "Applications" section fails to identify a single concrete example of a problem that Gaussian Processes might be applied to. "Given any set of N points in the desired domain of your functions..." OK, but what might those points and functions represent in the real world? "Gaussian processes are thus useful as a powerful non-linear multivariate interpolation tool." OK, but what kind of real-world problem might require non-linear multivariate interpolation?
Etc.  — Preceding unsigned comment added by 2A02:6B6E:B8CD:0:7D5A:C359:DADB:4C38 (talk) 21:49, 30 December 2021 (UTC)
thread_title:  Inadequate material for non-technical readers 

message: Is the integral of a Gaussian process somehow also a Gaussian process?  Or is this just a common abuse of terminology?  I think it's the later, and made some changes to reflect that...  — Preceding unsigned comment added by 132.204.26.35 (talk) 21:33, 16 September 2014 (UTC)
thread_title: Gaussian Process vs. integral of Gaussian Process

message: Added cleanup tag: this article does not give someone in the field an adequate overview of what a Gaussian process is, and goes off on a tangent involving undefined math. —Preceding unsigned comment added by Ninjagecko (talk • contribs) 
: Perhaps it could be made accessible to a somewhat broader audience, but where does it go off on a tangent or get into "undefined math"?  It gives the definition and a simple characterization, and then it lists examples, with links. Michael Hardy 21:45, 4 December 2006 (UTC)
replies: text: Of course, any article can be improved in many ways, and surely this one can also. However, I have no idea what you mean by undefined math. In addition, I would have thought that for someone in the field, this article is rather banal and uninteresting, since surely its contents would be already familiar to such an individual. Do you mean someone not in the field? --CSTAR 03:54, 5 December 2006 (UTC)
replies: text:  Somehow my reply never went through. Michael-- Yes, you're right. Technically the indices were previously defined way at the top, thus I removed the cleanup tag. Nevertheless it wasn't very clear I thought, so I improved the article lots by categorizing all the glomped-up text, and making the definition abit clearer. CSTAR-- No, I meant what I said: "someone in the field". Even as a reference, it was hard to follow. I've already fixed it though. —The preceding unsigned comment was added by Ninjagecko (talk • contribs) 09:21, 6 December 2006 (UTC)

text:  Also CSTAR, I personally find it rather haughty, to imagine the only people who have any business reading this entry are people who've been working with this material for 4+ years. The point of a reference is to be a reference for someone who wants to learn or brush up on the material. No offense. Ninjagecko 09:24, 6 December 2006 (UTC)
replies: text:  I don't think your statement(the only people who have any business reading this entry are people who've been working with this material for 4+ years) paraphrases in any way what I said. In any case what I had intended to say was that the article was technicaly correct. --CSTAR 13:36, 6 December 2006 (UTC)
thread_title: Untitled

message: I have renamed the link to www.gaussianprocesses.com, to "The Gaussian Processes Research Group at the Australian Centre for Field Robotics".  The web site has a very general sounding name, but the home page is currently recruiting students to a lab, rather than explaining the theory of Gaussian processes, as the link description previously claimed to do.  I hope this avoids confusion. Mebden (talk) 08:26, 5 March 2009 (UTC)
thread_title:  Link to the Gaussian Processes Research Group at the Australian Centre for Field Robotics 

message: Is the i that appears in the second display formula of the section the Imaginary unit? If it is an index, it is not bound to any summation sign. Maybe a real-valued variable? I do not have a reference with me of the formula so I cannot fix it, but I guess that something is missing. I would be grateful if someone does fix it. Junkie.dolphin (talk) 15:49, 3 July 2012 (UTC)
replies: text: The fact that it is the imaginary unit is confirmed/implied by the equation being part of a sentence starting "Using characteristic functions ....". Melcombe (talk) 16:55, 3 July 2012 (UTC)
replies: text:  Thanks for the clarification, I had somehow failed to notice that detail. Junkie.dolphin (talk) 15:45, 24 July 2012 (UTC)
thread_title:  Alternative definition 

message: The current article says: "A Gaussian process is a statistical distribution Xt, t ∈ T, for which any finite linear combination of samples has a joint Gaussian distribution."  I think a "process" is an indexed collection of a random variable while a "distribution" is a function associated with a single random variable.   The notation apparently intends to convey the idea of "an indexed collection of distributions", so it would be better to use those words than the singular "a statistical distribution".
Tashiro~enwiki (talk) 18:15, 30 October 2015 (UTC)
replies: text: Yes, this must be wrong and it's confusing. It means you have to look somewhere else for the actual efinition (outside of Wikipedia). 76.118.180.76 (talk) 03:11, 15 December 2015 (UTC)

text: Hello. It is a distribution, but over an infinite dimensional space. Which makes it rather different from more common distributions, like e.g. the Gaussian distribution. I think the term "distribution" is more misleading than helpful here, so I have replaced it with plain "statistical model", since the text does then go on to define a GP. I hope that helps.  — Preceding unsigned comment added by Winterstein (talk • contribs) 09:09, 11 June 2016 (UTC)

text: Agreed. This is the first time ever that my opinion of Wikipedia as the definitive source for mathematics has ever taken a big hit. I can appreciate the fact that from the writer's perspective, that the first sentence, referenced just above in this discussion, looks simpler than to say  statement as written  — Preceding unsigned comment added by 156.40.216.3 (talk) 15:27, 17 August 2017 (UTC)
thread_title: "Process" is a "distribution"? 

message: The listed examples of covariance functions are really correlation functions (With exeption of the white noise one). I.e. they should be multiplied with sigma^2  — Preceding unsigned comment added by 188.113.80.156 (talk) 20:55, 30 May 2017 (UTC)
thread_title:  Covariance function/Correlation function 

message: They are the same ?  — Preceding unsigned comment added by 143.159.115.78 (talk) 14:01, 6 March 2017 (UTC)
replies: text: Gaussian process regression and Kriging are very similar(maybe the same except for formalism, but I don't know enough to say so). Gaussian Processes has uses outside of regression, though.  — Preceding unsigned comment added by 188.113.80.156 (talk) 21:02, 30 May 2017 (UTC)
thread_title: Merge with Kriging article?

message: About the recent edit by User:Kri: "Dubious|reason=The expected magnitude of a finite difference of a Wiener process divided by the step size approaches infinity as the step size approaches 0, but the expected magnitude of Gaussian noise is finite, so obviously this can't be true as is. So what is it that this (incorrect) statement actually means?"
The expected magnitude of a (usual) Gaussian process is finite, but the white noise is a generalized process; its expected magnitude (at a point) is infinite; only after integration is becomes finite. I'll add a link to white noise article.
Generalized processes are mentioned in : "Also the covariance \mathrm{E}(w(t_1)\cdot w(t_2)) becomes infinite when t_1=t_2; and the autocorrelation function \mathrm{R}(t_1,t_2) must be defined as N \delta(t_1-t_2), where N is some real constant and \delta is Dirac's "function"." See also : "it does not exist as a random height function. Instead, it is a random generalized function". Boris Tsirelson (talk) 06:55, 17 March 2019 (UTC)
replies: text: Okay, thank you for the clarification. Indeed, it makes more sense if you treat it as a generalized function. —Kri (talk) 15:10, 17 March 2019 (UTC)
thread_title:  Integral of a white noise 

message: The "simple example" given of 
:
\displaystyle X_{t}=\cos(at)\xi _{1}+\sin(at)\xi _{2}
suggests that each variable X_t can be the sum of two Gaussian-distributed variables.  But this can't be a Gaussian process, can it, because the sum of two Gaussians is not a Gaussian in general?  What am I missing? Fyedernoggersnodden (talk) 13:44, 7 May 2021 (UTC)
replies: text: Sum of Gaussians is another Gaussian (even for dependent RVs). See this Abs xyz (talk) 04:13, 25 October 2022 (UTC)
thread_title:  Simple cos/sin example is bimodal? 

message: A process is a family, not a set (mathematics)! Collection is to ambiguous.Sigma^2 (talk) 22:37, 28 July 2023 (UTC)
thread_title:  Collection? 

message: The linked Wikibook has some mistakes such as the claim "a stochastic process is a distribution". Another mistake in the Wikibook is for example in the section on operations on Gaussian variables. The user says: "For two correlated signals, the sum can be expressed by a scalar multiplication" which is false. The sum of two non-independent Gaussians is not necessarly Gaussian, it's only Gaussian if they are joint normal.--Tensorproduct (talk) 13:27, 8 September 2023 (UTC)
thread_title:  A word of caution regarding the "Wikibook"