17

I am having a hard time understanding what is the difference between kriging and gaussian processes. I mean wiki says they are the same but their formulas for prediction are so different.

I am a bit confused why they are called similar. Clarifications?

user34790
  • 6,049
  • 6
  • 42
  • 64

3 Answers3

7

There are some subtle differences between ordinary and simple kriging, maybe that confuses you. GP regression in the way it is usually presented is analogous to simple kriging. In the Gaussian process Wikipedia entry it says that the article refers explicitly to a "zero-meaned distribution"; that is the same assumption found in simple kriging.

Also generally speaking kriging is usually performed in a 2 or 3 dimensional spaces, (eg. pollutant concentration along some given area) while most GPR toy examples are one dimensional (eg. $CO_2$ concentration in the atmosphere against time).

Ultimately kriging/GPR is an interpolation technique and most (not all) of the difference among the variants of it lays on the assumption about the mean trend $\mu(X)$ (or E[$X_t$] if you like this notation better).

usεr11852
  • 33,608
  • 2
  • 75
  • 117
  • 4
    This isn't really true. Often you see in the GP literature that without loss of generality they use zero mean assumptions but then add the structure of the mean into the kernel (for example with the addition of a linear kernel etc). GPs are certainly not used in only one dimension as can be seen in pretty much any paper on the subject. The 1D scenario is used only for intuition purposes in introductory texts. In fact in most 1D cases you can encode the GP into a Kalman filter which is computationally more efficient. – j__ Nov 09 '15 at 08:15
  • @j__ For the first part of your comment: I agree partially but unfortunately it is mostly a terminology issue that people tend to abuse it at times. I present the canonical distinction I have seen in books. For the second part: Allow me to disagree. I have seen multiple applications of GPR 1D cases (eg. [in FX rates modelling](http://arxiv.org/pdf/1402.3085.pdf), [in Phylogenetics](http://arxiv.org/pdf/1004.4668v3.pdf), and [in ODE solutions](http://arxiv.org/pdf/1306.2365v3.pdf) - these just doing a quick Google search). i appreciate your comment that generally a statistical framework (cont.) – usεr11852 Nov 09 '15 at 09:31
  • comes into its own when applied in multivariate settings but that does not discredit 1D applications. – usεr11852 Nov 09 '15 at 09:33
  • 1
    well I do see where you are coming from. I guess I would say it is more common for GPs to act in general N dimensional spaces as opposed to being restricted to 2/3 which is the case with Kriging. A special case is the 1D setting. That may be a good middle ground we can agree on ;) – j__ Nov 09 '15 at 09:40
  • 2
    Yes, 1-D cases tend to be *unique*. (Awful pun) – usεr11852 Nov 09 '15 at 09:58
2

GPs are known as kriging in geostatistics. To learn about the history of Gaussian Processes watch this video http://youtu.be/4r463NLq0jU?t=26s

pushkar
  • 169
  • 1
  • 6
0

Kriging is a type of Gaussian process that uses a spatial covariance function or kernel.

These are some helpful resources :

https://arxiv.org/pdf/1708.02663.pdf - talks about gradient enhanced Kriging with PLS but the formulas are the same as Kriging.

https://distill.pub/2019/visual-exploration-gaussian-processes/ - explains Gaussian processes and shows effect of various kernels on the covariance matrix.

Vikram N
  • 1
  • Hi, welcome to CV. Can you please add the reference of the paper you cite in case the link dies in the future? – Antoine Feb 01 '22 at 07:21
  • Most standard Kriging formulations do not assume the processes are Gaussian. The usual assumptions are either the "intrinsic" property or second-order stationary. The [Wikipedia article](https://en.wikipedia.org/wiki/Kriging) is confusing in this respect: although it explicitly states that Kriging is "gaussian process regression," nothing in its description of Kriging, or even the subsequent analyses assumes gaussianity. *Everything* is based entirely on consideration of the mean and covariance functions. – whuber Feb 01 '22 at 15:49