Talk:Spatial dependence

See Talk:Kriging or Talk:Geostatistics for NPOV debate -- hike395 11:39, 16 April 2006 (UTC)

All Wikipedians and all Krige's men cannot put the distance-weighted average and its variance together again!

How utterly ridiculous for those who want to bring knowledge to the world.--Iconoclast 19:48, 16 April 2006 (UTC)

Wikipedians may well do what Krige's men failed to do! JWM.--Iconoclast 21:13, 29 July 2006 (UTC)

Why dont you add an article on stochastic simulation in geography? The letter you refer to seems to indicate that this is the correct approach, at least for reproduction of spatial variability. My question would then be whether kriging is in fact an estimation of spatial variability. SCmurky 02:49, 29 July 2006 (UTC)

What should be done first of all is verify spatial dependence between measured values in the ordered set for the stochastic variable of interest. If the set does not display a significant degree of spatial dependence, then it is impossible to obtain unbiased distance-weighted averages and variances. If it does, however, any set of coordinates within the validated sample space gives an unbiased distance-weighted average, a variance and 95% confidence limits. In this case, stochastic simulation would give more but statistically identical stats. I've applied stochastic simulation for complex stochastic systems such as recoveries in metallurgical balances in mineral processing plants. I need to know what you propose to do before we take the next step. JWM. --Iconoclast 21:13, 29 July 2006 (UTC)

Accuracy

The article as it is today 31 Jan 2008 is not accurate. I will cite the article and discusse the problem:

In mathematical statistics, spatial dependence is a measure for the degree of associative dependence between independently measured values in a temporally or in situ ordered set, determined in samples selected at positions with different coordinates in a sample space or a sampling unit. In this context, independently measured implies that neither the primary sample selection stage, nor the sample preparation stage or the analytical stage in the measurement hierarchy add uncertainties to any contiguous subset of the complete set of measured values.

Dependence and an independece are defined by probability theory and not by mathematical statistics. Spatial dependence is not a measure, but a quality. In mathematical statistics and probability theory degree is typically the degrees of freedom or degree of a polynomial and not associative dependence. There is no dependence between independent things. The words "in situ" (here saying in space) "ordered" (for arranged) "sample space" (here for sampling area and not for set of possible values). In any case uncertainty will added by any measurement procedure. This is what measurement error is all about. The discription with "contiguous" is far from any mathematical definition of spatial dependence.

Spatial dependence is verified by applying analysis of variance to the variance of a set and the first variance term of the ordered set (closest/shortest lag) and comparing the observed F-value between these variances with tabulated F-values at 5% or 1% probability and applicable degrees of freedom. Testing additional variance terms of the ordered set for spatial dependence makes it possible to chart a sampling variogram.

The author of the passage is here citing his own work. Which is not allowed by the rules of Wikipedia. Anyway, the wording should least say that it "can" be verified in this way, since as the author of this passage well knows, it is in most cases not done in this way.

A significant degree of spatial dependence gives a higher degree of precision for the central value of a set of measured values. Therefore, testing for spatial dependence makes scientific sense in many applications in mineral exploration, mining, mineral processing, smelting and refining, and in a broad range of engineering and scientific disciplines.

The first sentence should read: The stronger the spatial dependence the smaller the kriging error. However again words are confusing: Significance e.g. of the above mentioned test, does not change the precision of something. It might change the validity of the analysis, but not its precision. "The central value of a set of measured values" seams to be a long way of saying mean. However the precision of the mean as an estimator for the expected value is typically decreased if there is a strong spatial dependence. So written the sentence is wrong. It does make sense to test for spatial dependence, but this is not implied by the sentence before, neighther in corrected reading nor in written sense. So the "therefore" is misleading.

Boostat (talk) 09:05, 31 January 2008 (UTC)

Personal point of view

As it is standing, this artiocle id not documenting "spatial dependence", but mr. Merks personal view on spatial dependence. It should either be removed or totally rewritten. It has no information value for a reader not knowing about the controversy mr. Merks is stirring up. Kjetil Halvorsen 18:39, 24 August 2010 (UTC) —Preceding unsigned comment added by Kjetil1001 (talk • contribs)

I agree, at least as far as the Controversy section goes. I'll remove that now. --Avenue (talk) 19:48, 25 August 2010 (UTC)