Talk:Geostatistics

message: Geostatistics is a fundamentally flawed variant of classical statistics because it violates the requirement of functional independence and ignores the concept of degrees of freedom. It is a scientific fact that each distance-weighted average has its own variance. Changing its name to "kriged estimate" does not alter the fact that each kriged estimate, too, has its own variance. In addition, Fisher's F-test for spatial dependence cannot be applied because kriging variances and covariances of sets of kriged estimates are simply voodoo variances. —Preceding unsigned comment added by 66.183.14.73 (talk) 22:12, December 14, 2003
:Could the person who wrote these comments identify himself or herself? Michael Hardy 00:12, 15 Dec 2003 (UTC)
replies: text: I think more needs to be said than what is said above, before it can be taken seriously by anyone except those knowledgeable in the theory of geostatistics.  Say enough, for example, so that anyone with a PhD in statistics can understand it.  Then I might help rephrase it for a broader audience than that and incorporate it into the article. Michael Hardy 22:27, 29 March 2006 (UTC)

text: Geostatistics  is a fundamentally flawed variant of mathematical statistics because it violates the requirement of functional independence and ignores the concept of degrees of freedom. It is a scientific fact that each distance-weighted average had its own variance before it became a kriged estimate. Its rebirth as an honorific kriged estimate does not make its variance vanish without a trace. As a result, Fisher's F-test for spatial dependence cannot be applied because the variance of a subset of some infinite set of distance-weighted average is as invalid a measure for variability, precision and risk as its covariance is for spatial dependence. Not surprisingly because an infinite set of distance-weighted averages gives exactly zero degrees of freedom.--Iconoclast 20:42, 16 April 2006 (UTC)
replies: text: Yeah, this is completely wrong. I just completed a Quantitative Methods in Geography course and there definitely was like 2 chapters about degrees of freedom. Sorry. —Preceding unsigned comment added by 130.85.149.221 (talk) 20:50, June 7, 2006
=======================================================================
The person who made the rude remarks may not have expressed himself very well, and I 
agree with all of you about the lack of references.  A lack of references always
invalidates criticism.  There was also a bit of confusion about the difference between
empirical measurement of spatial patterns (what most geostatistics is designed for)
and statistical tests of the patterns.  Geostatistics are perfectly valid for empirical
measurement, it is when we want to make statistical inferences about some of them
that we run into a few problems.  
I have just begun to worry about this myself (I study geographic variation in 
animals and genes).  However I can explain the main problem and give some
references to get around them.  The critical references (for how to avoid it!) 
are:
Benjamini, Y. and D. Yekutieli.  2001.  The control of the
false discovery rate in multiple testing under
dependency.  Annals of Statistics 29, 1165-1188.
Efron, B.  2007.   Size, power and false discovery rates.
Annals of Statistics 35, 1351-1377.
Romano, J.P. and M. Wolf.  1007.  Control of generalized
error rates in multiple testing.  Annals of Statistics
35, 1378-1408.
Li, Y., N. Wang, M. Hong, N.D. Turner, J.R. Lupton and
R.J. Carroll.  Nonparametric estimation of correlation
functions in longitudinal and spatial data, with
application to colon carcinogenesis experiments.
Annals of Statistics 35, 1608-1643.
Storey, J.D. 2002.  A direct approach to false
discovery rates.  Journal of the Royal Statistical 
Society 64, 479-498.
Briefly, unlike other kinds of data, geographical (or other spatial) data
are not independent because what happens at one location is likely to
happen at adjacent locations.  This can happen for a variety of reasons
including causes which operate over a larger spatial scale than a single
sampling unit (e.g. operating over several of your sample locations), and
effects which spread in space.  This results in a high correlation between
sample values close together, but a decreasing correlation with distance.
There is a large literature on measuring this, under the term 'spatial
autocorrelation' as well as under the term 'geostatistics'.  Statistically 
it is a nuisance becuase most statistical tests assume each sample is independent--manifestly not true for spatial data.  The references I 
gave above get at this problem.  I also like the Baysian approach that 
one of you suggested, and this may be able to avoid the spatial 
autocorrelation problem with suitable design.  We need to find a good 
statistician to describe for us the exact way to do this!  As I said, 
I'm just learning this myself, but I thought I would share the references 
with you anyway.
Oddly enough the first people to attack this seem to be medical researchers
because phenomena in one body or tissue location can affect adjacent cells
and tissues.  So don't be put off by the non-standard applications in the
above references!
Chlamydera 17:48, 30 November 2007 (UTC)
thread_title:  "Geostatistics is a fundamentally flawed …"

message: The person who made the rude remarks may not have expressed himself very well, and I 
agree with all of you about the lack of references.  A lack of references always
invalidates criticism.  There was also a bit of confusion about the difference between
empirical measurement of spatial patterns (what most geostatistics is designed for)
and statistical tests of the patterns.  Geostatistics are perfectly valid for empirical
measurement, it is when we want to make statistical inferences about some of them
that we run into a few problems.  
I have just begun to worry about this myself (I study geographic variation in 
animals and genes).  However I can explain the main problem and give some
references to get around them.  The critical references (for how to avoid it!) 
are:
Benjamini, Y. and D. Yekutieli.  2001.  The control of the
false discovery rate in multiple testing under
dependency.  Annals of Statistics 29, 1165-1188.
Efron, B.  2007.   Size, power and false discovery rates.
Annals of Statistics 35, 1351-1377.
Romano, J.P. and M. Wolf.  1007.  Control of generalized
error rates in multiple testing.  Annals of Statistics
35, 1378-1408.
Li, Y., N. Wang, M. Hong, N.D. Turner, J.R. Lupton and
R.J. Carroll.  Nonparametric estimation of correlation
functions in longitudinal and spatial data, with
application to colon carcinogenesis experiments.
Annals of Statistics 35, 1608-1643.
Storey, J.D. 2002.  A direct approach to false
discovery rates.  Journal of the Royal Statistical 
Society 64, 479-498.
Briefly, unlike other kinds of data, geographical (or other spatial) data
are not independent because what happens at one location is likely to
happen at adjacent locations.  This can happen for a variety of reasons
including causes which operate over a larger spatial scale than a single
sampling unit (e.g. operating over several of your sample locations), and
effects which spread in space.  This results in a high correlation between
sample values close together, but a decreasing correlation with distance.
There is a large literature on measuring this, under the term 'spatial
autocorrelation' as well as under the term 'geostatistics'.  Statistically 
it is a nuisance becuase most statistical tests assume each sample is independent--manifestly not true for spatial data.  The references I 
gave above get at this problem.  I also like the Baysian approach that 
one of you suggested, and this may be able to avoid the spatial 
autocorrelation problem with suitable design.  We need to find a good 
statistician to describe for us the exact way to do this!  As I said, 
I'm just learning this myself, but I thought I would share the references 
with you anyway.
Oddly enough the first people to attack this seem to be medical researchers
because phenomena in one body or tissue location can affect adjacent cells
and tissues.  So don't be put off by the non-standard applications in the
above references!
Chlamydera 17:48, 30 November 2007 (UTC)
thread_title: ===========================================================

message: To user(s) who have been editing this page recently: Please be civil in the editing of wikis. If you don't agree with the principles of geostats that's fine, but wikipedia is not the place for direct attacks. Thank you.
S lyster 02:35, 29 March 2006 (UTC)
thread_title: "To user(s) who have been editing this page"

message: Bringing knowledge of the pseudo science of assuming, kriging, smoothing and rigging he rules of mathematical statistics to the world.--Iconoclast 20:37, 16 April 2006 (UTC)
thread_title: All Wikipedians and all Krige's men cannot put the distance-weighted average and its variance together again.

message: This business is not totally quack. Not all geostats depend on Gaussian or Bayesian analyses - one can screw up stats and make a mess of it in any field. Yes, Geostatistics as a reasonably new field has its share of screw-ups I am sure. But that is not to say it is all pseudo-science. Criminology for one makes great, successful use of it (Crime mapping). The argument here could apply to medicine - "some doctors do stupid things, therefore Western medicine is pseudoscience". That "History" piece needs total rewrite, though - very unencyclopedic the way it looks right now; I would suggest pulling it out altogether until it's tweaked.Bridesmill 05:05, 30 June 2006 (UTC)
thread_title: From RfC

message: I found the previous version of this page very difficult to follow, so for the sake of readability, I've refactored the page. In particular I have organized the discussions chronologically as is the established WP talk page practice. I also broke separate discussions into sections with section headings, indented comments to indicate a change of writer and signed unsigned comments. If you think I have somehow misrepresented anyones comments —I apologize — please correct as you see fit, but please try to follow standard WP practice for talkpage discussions. Thanks — Paul August ☎ 17:50, 1 July 2006 (UTC)
thread_title:  Page refactor 

message: Hello SCmurky and other interested Wikipedians, Here’s a simple question that would get geostatistics going again. To have or not to have a variance, that’s the question! The rest are details!! Does or doesn’t every distance-weighted average have its own variance? Mutually exclusive responses are yes or no but geostatisticians may have conditional responses.
If the answer is YES, complete: Yes but ... and fill in the blanks. 
If the answer is NO , complete: No because ... and fill in the blanks.
If the answer is conditional, study the properties of variances in Volk’s "Applied Statistics for Engineers" before responding. For example, the distance-weighted average does have a variance but the kriged estimate doesn't is a cute but scientifically nonsensical response. IAMG’s brass and JMG’s brains should be requested not only to respond to the same question but also to assign the most gifted geostatistical mind to complete geostatistics. JWM--Iconoclast 18:42, 1 July 2006 (UTC)
thread_title:  Just one simple question 

message: The question under dispute is whether every distance-weighted average had its own variance before it was reborn as an honorific but variance-deprived kriged estimate. The seminal work that led to the loss of the variance of the distance-weighted average can be condensed as follows: Professor D G Krige discovered at the Witwatersrand gold reef complex in South Africa in the early 1950s that two or more gold assays, determined in samples selected at positions with different coordinates in a finite sample space, define an infinite set of distance-weighted averages. Professor Dr G Matheron was so taken with Krige’s aptitude in augmenting small sets of measured data in large samples spaces with subsets of infinite sets of distance-weighted averages that he conferred on Krige the ubiquitous krige eponym. Krige and Matheron did not know that one-to-one correspondence between distance-weighted averages and variances is inviolable in mathematical statistics, which explains why pioneering geostatisticians replaced the true variance of the distance-weighted average with the false variance of a set of distance-weighted averages. In time, kriging variances and kriging covariances of sets of kriged estimates became the cornerstones of geostatistics. However, the false variance of a set of kriged estimates is as meaningless a measure for variability, precision and risk as its false covariance is for spatial dependence. Geostatistics is an invalid variant of mathematical statistics because it violates the requirement of functional independence and ignores the concept of degrees of freedom. JanWMerks --Iconoclast 21:33, 3 July 2006 (UTC)
thread_title:  Cut from article 

message: Visit ai-geostats and open Clark and the Kriging Game. Clark’s hypothetical uranium data can be found in her 1979 Practical Geostatistics, Chapter 4. Estimation, Figure 4.1 and Table 4.1. Clark has posted this third geostatistics texbook on her website, and a retro-review is posted on mine.    
Step 1. Go to Cells E10 and E11 on Sheet Kriging game and replace Clark’s coordinates of 1,265 m Easting and 713 m Northing within her sample space with 4,500 m Easting and 4,500 m Northing beyond this sample space. Observe that the distance-weighted average and arithmetic mean are numerically identical at 366 ppm, and that the variance of the weighted average and the variance of the arithmetic mean are numerically identical at 896 ppm^2.  Go to Sheet xy=0-5000 and look at the distance between Clark’s sample space and the distance-weighted average of 366 ppm for the entered coordinates. Cells G42.46 show that all weighting factors converge on 1/n=0.2 whereas Cells E33 and F33 show that the degrees of freedom converge on df=n-1.
Step 2. Go to Cells E10 and E11 on Sheet Kriging game and re-enter Clark’s coordinates of 1,265 m Easting and 713 m Northing. Go to Sheet xy=0-5000 and observe the distance-weighted average of 371 ppm for this point  within Clark’s sample space! Go to Sheet x=725 y=1300 and take another look! The distance-weighted average still has its own variance and confidence limits!! 
Step 3. It’s easy to enter more coordinates because there’re infinite pairs to work with! Those beyond Clark’s sample space give distance-weighted averages numerically identical to the arithmetic mean of 366 ppm, and variances numerically identical to the Central Limit Theorem (896 ppm^2). Yet, didn't the variance of the distance-weighted average disappear somewhere in Clark’s sample space? It did so in Krige’s Witwatersrand complex, didn’t it? What’s wrong with this spreadsheet?
Step 4. Go to Fisher’s F-test for spatial dependence and look at Cells E5.E17. This test is applied to the variance of a random walk and the variance of a systematic walk, both of which visit each hypothetically sampled position only once. Given that the calculated value of F=4,480/2,161=2.07 is below the tabulated value of F0.05;4;8=3.84 at 5% probability, it follows that Clark’s hypothetical uranium data do no display a significant degree of spatial dependence in her sample space. Hence, the distance-weighted average of  371 ppm at Clark’s coordinates is not necessarily an unbiased estimate. Therefore, interpolation within Clark's sample space is impermissible and extrapolation beyond it is a scientific fraud. 
I’ve worked with area-, count-, density-, distance-, length-, mass- and volume-weighted averages. Each of these weighted averages has its own variance. In early 1990s, we found out that the true variance of the distance-weighted average was replaced with the false kriging variance of some set of kriged estimates. The formula for the variance of a set of measured values with variable weights is also posted on the above website. It is simple to show that this formula converges on the Central Limit Theorem as all weighting factors converge on 1/n. Print out the read me file and do read it because my case against geostatistics is ongoing! Start thinking about unbiased statistical inferences such as confidence limits.
Geostatistics with its pseudo kriging variances and covariances is beyond salvation. Give each distance-weighted average its own variance and mathematical statistics is back. JWM --Iconoclast 22:48, 8 July 2006 (UTC)
thread_title:  Clark and the Kriging Game 

message: Y'know, Ive tried to be accomodating, but I find that this article is going nowhere. I have said before that geostatistics is a broader category than kriging, Ive also attempted to clarify your comments so that they may be comprehended by readers, but you persist with a singular, argumentative, and non-referenced POV statements. In any case, I shall remove any reference to kriging within this article, I believe that this argument will be better placed in the Kriging page than here, and I will not interfere with that page; but as for geostatistics, I will begin to explore statistical problem solving in geography. SCmurky 02:55, 13 July 2006 (UTC)
thread_title: I'm Over It

message: What about Krige? Did he really not know (ie. implies that he is ignorant), or did he choose to ignore this rule; given the reserved tone of your recent edits, I wont delete this outright, but I still need clarification to make this statement NPOV. Keep in mind however, that the majority of this controversy section should be in the kriging article, with only a short summary in the geostats article. SCmurky 00:16, 27 July 2006 (UTC)
thread_title: Start over

message: The criticism by Merks in the section "Criticism" was original research, and as such, cannot be part of Wikipedia. HOWEVER, the fact that Merks criticizes geostatistics *is* verifiable, notable, and as such can be reported by Wikipedia. I wrote the text so that it conveys (as well as I could) the criticism, without violating WP:V, WP:OR, and WP:NPOV. Renato (talk) 14:35, 17 August 2008 (UTC)
thread_title:  Turning original research into criticism that observes Wikipedia policies 

message: The article as of now 2. July 2009 the article makes the impression that geostatistics is a vague collection of statistical methods in geography. Hart (1954) Central tendency in areal distributions, Economic Geography, 30, 48-59 might have coid the term in that way. However to my understanding the modern meaning of the the word is something like "statistical theory and application for processes with continues spatial index" (Cressie 1993 Statistics of spatial data, Wiley) and looking at the citations list of the article with the word geostatistics in it, which I know and contain geostatistics in the title:
   4. Clark I, 1979, Practical Geostatistics, Applied Science Publishers, London
   5. David, M, 1977, Geostatistical Ore Reserve Estimation, 
                       Elsevier Scientific Publishing Company, Amsterdam
   7. Chilès, J.P., Delfiner, P. 1999. Geostatistics: modelling spatial uncertainty, 
                        Wiley Series in Probability and Mathematical Statistics, 695 pp.
   8. Deutsch, C.V., Journel, A.G, 1997. GSLIB: Geostatistical Software Library 
               and User's Guide (Applied Geostatistics Series), Second Edition, 
               Oxford University Press, 369 pp., http://www.gslib.com/
   9. Deutsch, C.V., 2002. Geostatistical Reservoir Modeling, 
                Oxford University Press, 384 pp., http://www.statios.com/WinGslib/index.html
  10. Isaaks, E.H., Srivastava R.M.: Applied Geostatistics. 1989.
  12. Journel, A G and Huijbregts, 1978, Mining Geostatistics, Academic Press
  14. Lantuéjoul, C. 2002. Geostatistical simulation: models and algorithms. Springer, 256 pp.
  16. Matheron, G. 1962. Traité de géostatistique appliquée. Tome 1, Editions Technip, Paris, 334 pp.
  19. Merks, J W, 1992, Geostatistics or voodoo science, The Northern Miner, May 18
  21. Myers, Donald E.; "What Is Geostatistics?
  22. Philip, G M and Watson, D F, 1986, Matheronian Geostatistics; 
                 Quo Vadis?, Mathematical Geology, Vol 18, No 1
  26. Wackernagel, H. 2003. Multivariate geostatistics, 
                   Third edition, Springer-Verlag, Berlin, 387 pp.
all understand geostatistics in as something that solves or are related to the Problem of interpolating and (to a minor degree) analysing a random function (process) with a continues index observed at some locations, coming from the geological definition of Matheron of geostatistics focusing of inferring ore reserves. The same hold true of 
Modern spatiotemporal Geostatistics by G. Christakos
or
 Nonparametric Geostatistics von S. Henley
  
Applied Geostatistics with SGeMS: A User's Guide von Nicolas Remy, Alexandre Boucher, und Jianbing Wu von Cambridge University Press (Gebundene Ausgabe - 22. Januar 2009)
An Introduction to Applied Geostatistics von Edward H. Isaaks, Isaaks, und R. Mohan Srivastava von Oxford Univ Pr (Taschenbuch - 11. Januar 1990)
 Basic Linear Geostatistics von Margaret Armstrong von Springer, Berlin (Taschenbuch - November 1997)
In the same way spatial statistics is not a part of geostatistics but the other way round geostatistics a spatial case of spatial statistics.  However the article totally misinterprets the term:
Going the through the current TOC: 
    * 1 Background
          o 1.1 Role of statistics in geography (As said, geography is not the background of geostatistcs, 
                   even though Toblers law of geography is of the cited in this context. The typical background is (mineral resource) geology.)
    * 2 Spatial data and descriptive statistics
          o 2.1 Boundary delineation (that spatial statistics)
          o 2.2 Modifiable areal units (thats spatial statistics)
          o 2.3 Spatial aggregation/scale problem (The upscaling problem is a topic in geostatistics, but not as aggregation of political units, 
                                        but as mean values over (e.g. mining) blocks) 
    * 3 Descriptive spatial statistics (point pattern analysis is a part of spatial statistics but not of geostatistics, 
                   see e.g. Cressie 1993 as cited above)
          o 3.1 Spatial measures of central tendency (thats related to districts and not random fields)
          o 3.2 Spatial measures of dispersion (this part is completely uninformative)
    * 4 Topology (topology is not statistics, not even geostatistics, its merily a geospatial problem)
          o 4.1 Topology rules (still not statistics)
    * 5 Computational Geometry (computational geometry is not even statistics) 
    * 6 Topography (might be interpolated with geostatistics, but that is not mentioned here)
    * 7 Sampling methodology (geospatial sampling seams to be the first word after the first chapter actually related to the subject of geostatistics)
    * 8 Criticism (This is clearly a paragraph criticizing kriging which is a major subject of geostatistics. 
                          Although I disagree with the cited work by Merks, it is the first part acutally related to geostatistics. 
                                 Strictly speaking however this chapter belongs to Kriging and not here.)
    * 9 Related software (this are all real geostatistical software packages and should stay here)
    * 10 Notes (Should go to references and it is fully sufficient to cite Mr. Merks once)
    * 11 References (Most of them are really good references on geostatistics, but most of them are not cited above)
    * 12 See also (Only the kriging link seams appropriate)
    * 13 External links (quite ok)
In conclusion, the article is talking about the wrong thing, although in a previous age somebody knowing the subject seamed to have added references, software and web-sites. 
In my view a current article must explain the main purpose: interpolation, conditional simulation, the main methodology: analysing spatial dependence, and the main methods of geostatistics: Variograms, Kriging (Matheronian Geostatistics), Baysian Maximum Entropy (following the works of George Christakos, e.g. http://www.unc.edu/depts/case/BMElab/), Multiple point methods like SNESIM and FILTERSIM (following the works of Journel, Strebell and Caers,e.g. http://pangea.stanford.edu/groups/iamg/workshop1.pdf ).  
I propose is to remove chapters 1-7 and to rewrite the whole article in that sense.
Any comments. 
Boostat (talk) 15:58, 2 July 2009 (UTC)
thread_title:  Geostatistics is not "Statistics in Geography" and not "Spatial Statistics" 

message: I have made a start by moving some blocks of text to statistical geography, given that there seems to be aggreement above. At present everything that was present is in either article. I think it would be best to delete the sections still here which have essentially no content (i.e. Computational Geometry, Topography, Statistical sampling) and to concentrate on what needs to be said about geostatistics. At present the photo which was here is in both articles, as I don't know whether it really is relevant to "geostatistics". Melcombe (talk) 11:33, 13 August 2009 (UTC)
replies: text: I found some awesome images on the NRCAN site. I have downloaded them, and have asked for permission to publish them on Wikipedia. SCmurky (talk) 22:58, 13 August 2009 (UTC)

text: Regarding your edits. While I believe that they are likely for the best, I can't get over the feeling that the article now offers nothing. It is little more than a short intro, with a rant about kriging at the end. SCmurky (talk) 00:36, 14 August 2009 (UTC)
thread_title:  Moving text to statistical geography 

message: Dear Wikipedia authors,
I write this note in the name of a group of scientists from various universities in North America and Europe specialised in the domain of geostatistics and its application in hydrology, petroleum engineering and mining.
We have the project of providing to the public a wikipedia page that has an encyclopedic character, describing history, methods and tools currently used in geostatistics.
In our opinion, the current content of the "geostatistics" page is poorly informative, subjectively written and controversial. We think Dr Merks has a right to have his voice heard and to claim his opinions, but if those opinions are not supported by peer-reviewed publications, wikipedia is not the place for this. There are thousands of other scientists, with peer-reviewed publications, who need to have their work made available to the public through Wikipedia.
We are currently working on a new structure of the page and content that will be more informative. When we will update the current page, we will sent to the broad geostatistical community invitations to review and modify this content.  —Preceding unsigned comment added by Gregoire.mariethoz (talk • contribs) 19:07, 21 April 2010 (UTC)
replies: text: That's great news. I'm not from this community, but have been following things here, and I'm very glad that experts on this area are remodeling the page. Renato (talk) 20:21, 21 April 2010 (UTC)
thread_title:  Remodeling of this page 

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