Evan
Noel Cressie's book, first published in 1994, details the complete lognormal backtransform which includes the difference between the variance of the estimates and the variance of the 'true' values in the log space. My own papers of the late 1990s carried practical verifications of this transform in various applications. These can be downloaded free by following links at http://uk.geocities.com/drisobelclark/resume or I can email to anyone without a stable web link ;-)
One advantage I did not mention in my previous email is that a parametric backtransform allows for change of support between sample and estimated entity. For example, borehole data being used to estimated mining blocks. I left this out as being more relevant to geological and mining applications, which is a limited interest group (I think). Adding the change of support
problem complicates checking of back transforms except in cases like mining where immense numbers of previous sampling data can be used to emulate larger volumes.
As you say, any transform - by definition - requires a stable backtransform verified by both theory and practice. My own view is simple: try it, check it, check it again, check it somewhere else, get someone else to check it. If all that passes muster, then forge ahead gayly!!
Isobel
[EMAIL PROTECTED] wrote:
Gregoire,
Isobel noted that "The parametric backtransform for lognormal kriging,
for example, includes components to ensure that the backtransform
produces unbiassed estimates in the original data space."
A significant finding in Weber and Englund (Math Geol 24-4 1992) was
that this does NOT ensure unbiasedness, confirming the advice in Journel
and Huijbregts to use an additional bias correction. (All of the geostat
literature uses a kriging variance term in the "unbiased" back
transform. But in classical statistics, the variance term in the back
transform is the population or sample variance. Have we got it wrong?)
Perhaps more important if you choose to use normal score kriging, is
that you have the same bias correction problem. We did not test
normal-score kriging but we did test rank kriging. As Isobel pointed
out, these are minor variants of the same theme. Without a
Journel-Huijbregts bias correction, rank kriging performed poorly; with
it, it performed well.
Evan Englund
Gregoire Dubois@jrc.it> To
Sent by: ai-geostats@jrc.it
owner-ai-geostat cc
[EMAIL PROTECTED] 'Isobel Clark'
<[EMAIL PROTECTED]>,
'Anatoly Saveliev'
08/10/2006 04:16 <[EMAIL PROTECTED]>
AM Subject
RE: AI-GEOSTATS: Log versus
nscore transform
Please respond
to
Gregoire Dubois@jrc.it>
Dear list
In addition to the excellent points made by Isobel, others from Anatoly
are given below. I went through the archives of ai-geostats and found
back very interesting discussions on this point (I apparently asked a
similar question in 2001, and 2003, ... I definitely have a poor
memory). As pointed here again, the nscore transform is probably
interesting only if the are many data, enough at least to draw a clear
histogram.
Having in mind a paper of Evan Englund in which 6 back-transforms are
compared in a case study involving lognormal kriging, I would personally
be tempted to go directly for a nscore transform to avoid myself asking
questions on the consequences of the back transform (I also most
frequently deal with datasets with so called "hot spots", i.e. very
skewed datasets for which the lognormal transform may not be
sufficient). I admit the nscore back-transform remains almost at the
level of a magic button to me and that I am discarding warnings like
those made in Saito and Goovaerts (Geostatistical interpolation of
positively skewed and censored data in a dioxin contaminated site.
Environmental Science & Technology, 2000, vol.34, No.19: 4228-4235) in
which a straight back-transform of the nscore estimates would lead to
biased estimates.
Still, I suspect the "lognormal kriging" reflex to be some behaviour
conditioned by the mining field while other disciplines focusing on
extreme values may be less receptive to the approach and go directly for
the more appealing (at first sight) nscore transform.
Best regards,
Gregoire
PS: Speaking now as the moderator of ai-geostats, please send replies to
the list, not to the author of the question. This should further
contribute to letting the archives grow.
__________________________________________
Gregoire Dubois (Ph.D.)
European Commission (EC)
Joint Research Centre Directorate (DG JRC)
WWW: http://www.ai-geostats.org
"The views expressed are purely those of the writer and may not in any
circumstances be regarded as stating an official position of the
European Commission."
-----Original Message-----
From: Anatoly Saveliev [mailto:[EMAIL PROTECTED]
Sent: 10 August 2006 11:42
To: [EMAIL PROTECTED]
Subject: Re: AI-GEOSTATS: Log versus nscore transform
Dear Gregoire,
>
> I am puzzled about the use of logarithmic and nscore transforms in
geostatistics.
>
> Given the apparent advantages in using nscore transforms over the
logarithmic transform (nscore has no problem when dealing with 0 values
and is "managing" the tails of the distribution very (more?)
efficiently), why would one still want to use log-normal kriging?
Because of the mathematical elegance of using a model only?
not only ...
- a lot of the known variables in geology, ecology and more widely in
the Earth science have log-normal distribution: they are limited by the
zero (or phone values) at the left end, and are unlimited at the right
end of the domain.
- nscore is histogram-based, and as that it need a lot of data for the
robust histogram estimation.
- I'm not agree that nscore ""managing" the tails of the distribution
very (more?) efficiently". As a rule, we haven't enough data at the left
and especialy at the righ sides of the values domain, so we need to
guess the tails (two guesses instead of one for the log()).
- log-transfom have a close form, so all the data are used in the
transform fit. Zeros are not a problem since Y'=log(a+b*Y) or
Y'=sign(Y)*log(a+b*|Y|) is used. nscore is locally interpolated (and
extrapolated at the sides), so it is less robust.
> Moreover, one can frequently not be "sure" about the lognormality of
the analysed dataset, so why would one still take the risk of using
log-normal kriging?
what means "not sure"??? Pearson and Kolmogorov-Smirnov tests will be
used :-))
> Thank you in advance for any feedback on this issue.
Best regards,
Anatoly Saveliev,
Kazan State University, Russia
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