Talk:Kriging

Unclear phrasing of a sentence

I think the sentence

This means that, when the samples are farther away from {\displaystyle x_{0}}x_{0}, the worse the estimation.

sounds a bit strange.

It should be either:

This means that, when the samples are farther away from {\displaystyle x_{0}}x_{0}, the estimation becomes worse.

or:

This means that, the farther the samples are away from {\displaystyle x_{0}}x_{0}, the worse the estimation. — Preceding unsigned comment added by Lehnekbn (talk • contribs) 19:50, 19 June 2020 (UTC)

Lehnekbn (talk) 19:52, 19 June 2020 (UTC)

Geostatistical estimator: correlation or covariance?

In section "Geostatistical estimator" prior to the first set of equations of the section, the article says: "the correlation between two random variables solely depends on the spatial distance...", and then proceeds to introduce several expressions in terms of $C(Z(x_{1}),Z(x_{2}))$, giving the impression that $C$ refers to correlation. Going further with the explanation, however, one finds that the formula:

$C(\mathbf {h} )={\frac {1}{N(\mathbf {h} )}}\sum _{i=1}^{N(\mathbf {h} )}\left(Z(x_{i})Z(x_{i}+\mathbf {h} )\right)-m(x_{i})m(x_{i}+\mathbf {h} )$

is more related to the covariance, as defined in Covariance, than to Correlation. Though both concepts are related, but since there is no explanation as to what the symbol $C$ means, this section is confusing to someone novel in the matter as me.

--JulioSergio (talk) 05:53, 28 November 2013 (UTC)

I second this opinion. This section is confusing in several places as it doesn't define symbols. $C(Z(x_{1}),Z(x_{2}))$ is not defined, $\gamma (Z(x_{1}),Z(x_{2}))$ neither, $N(\mathbf {h} )$ neither ($N$ is supposed to be a constant, the number of samples, and not a function of $\mathbf {h}$). $C(\mathbf {h} )$ and $\gamma (\mathbf {h} )$ are said to be variograms and co-variograms, but these are not the same as $C(Z(x_{1}),Z(x_{2}))$ and $\gamma (Z(x_{1}),Z(x_{2}))$. Also, $C$ cannot be the covariance since a few equations later, $C$ appears at the same time as $Cov$ (in the expression of $Var(\epsilon (x_{0}))$).

Nbonneel (talk) 15:50, 9 May 2017 (UTC)

Explanation of the use of random processes

"The fact that these models incorporate uncertainty in their conceptualization doesn't mean that the phenomenon - the forest, the aquifer, the mineral deposit - has resulted from a random process, but solely allows to build a methodological basis for the spatial inference of quantities in unobserved locations and to the quantification of the uncertainty associated with the estimator."

This sentence, while admirably attempting to explain the concept in simple English, adds nothing pertinent; in my opinion, it adds confusion. The idea that something results from a random process or not is ambiguous, given the many different definitions of randomness. Surement (talk) 17:31, 26 March 2014 (UTC)

Kriging for use in interpolation needs improvement

I think the explanation given in the Dakota User Manual version 6, chapter 8.4.3.5 is a bit better than the wiki article's. For instance equation 8.20 in the user manual is insightful from the background of function approximation. This wiki article lacks anything as clear and simple as the explanation given in the user manual. The manual is available from http://dakota.sandia.gov/index.html, and may be cited similar to

Adams, B.M., Bauman, L.E., Bohnhoff, W.J., Dalbey, K.R., Ebeida, M.S., Eddy, J.P., Eldred, M.S., Hough, P.D., Hu, K.T., Jakeman, J.D., Swiler, L.P., and Vigil, D.M., "DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 5.4 User's Manual," Sandia Technical Report SAND2014-4633, July 2014. — Preceding unsigned comment added by 67.1.255.84 (talk) 02:21, 8 August 2014 (UTC)

modulation --> modeling?

This article says, "The first step in geostatistical modulation is to create a random process that best describes the set of observed data."

What does "modulation" here mean? Is this supposed to say "geostatistical modeling"?

Capitalisation

Both the capitalised 'Kriging' and non-capitalised 'kriging' words are found in the literature, however I have found the non-capitalisation instance more widespread in primary publications. Therefore it seems appropriate to restore this to what the article had pre-March 2016. Feel free to jump in and discuss more, if needed. +mt 21:49, 11 January 2017 (UTC)

Kriging v.s. Gaussian Process Regression

It is not appropriate to redirect Gaussian Process Regression (GPR) to Kriging. When the random field is stationary Gaussian, Kriging and GPR have similarities, but Kriging (OK and its variants) is in general builts on the top of intrinsically stationary random fields (not Gaussian random fields).

can look at D. Myers' responds on researchgate

https://www.researchgate.net/post/Why_should_data_follow_normal_distribution_for_ordinary_kriging_analysis

Also a suggestion regarding the structure:

1. Background

2. Theory

2.1 Intrinsic Stationarity

2.2 Spatial BLUP

3. Algorithm

3.1 OK (with SK as a special case)

3.2 Variants (UK, CoK, DK/IK)

3.3 Hybrid (regression-K, Bayesian K)

4. Proprieties

5. Application (potentially with R/ArcGIS/Python modules) — Preceding unsigned comment added by Kyle YKS (talk • contribs) 17:24, 19 October 2018 (UTC)

Pioneering plotter

The theoretical basis for the method was developed by the French mathematician Georges Matheron in 1960, based on the Master's thesis of Danie G. Krige, the pioneering plotter of distance-weighted average gold grades at the Witwatersrand reef complex in South Africa.

First, the tack-on is unclear whether it references Krige or his thesis. Second, is "pioneering plotter of" merely an elegant variation of the staid "which considers the"? If so, I prescribe woodshed, bullet, gun, hasty grave. I think "pioneering" is already implied here. — MaxEnt 21:05, 30 May 2019 (UTC)

Convoluted, inaccessible language

Article needs to be rewritten for clarity. — Preceding unsigned comment added by Archimedes of Syracuse (talk • contribs) 16:05, 16 June 2019 (UTC)

Pronunciation

We need to add a pronunciation of this word as I have heard in the industry three different pronunciations. Danie G. Krige was South African. So, Krige is pronounced Kreeg-a, Therefore, the correct pronunciation for Kriging is Kreeg-ing not Kryg-ing nor Kry-jing.

From Danie G. Krige, Krige (ˈkriχə). (2 syllables like Kreeg-a).

Proposal

• Remove this sentence "The English verb is to krige and the most common noun is kriging; both are often pronounced with a hard "g", following an Anglicized pronunciation of the name "Krige"."
• Add pronunciation (ˈkriχ:ɪŋ) in first line after first instance of kriging. (Please note that I'm not an expert on IPA but I think this is correct)
• Add footnote: To honor Danie G. Krige (ˈkriχə), the pronunciation of the process named after him should be consistent with the pronunciation of his name. - Mrdvt92 (talk) 13:23, 13 May 2021 (UTC)

Based on the discussion at https://languagehat.com/kriging/ I plan to update the pronunciation to /kri:gɪŋ/ which is KREE-ging - Mrdvt92 (talk) 15:11, 24 October 2022 (UTC)

Wiktionary https://en.wiktionary.org/wiki/kriging has the IPA pronunciation as /ˌˈkɹiːɡɪŋ/ - Mrdvt92 (talk) 20:21, 20 June 2023 (UTC)

Sum of weights equals one proof is wrong

The proof that in simple kriging the sum of weights equals 1 is wrong. It implicitly assumes that the means are non zero. If the means are zero, the equation can't be divided by it. I'm not a professional so I don't know what the right thing to do is. 46.123.253.62 (talk) 15:58, 25 June 2022 (UTC)