AI-GEOSTATS: Lognormal Kriging Revisited
- Dear all,
Even after learning geostats for couple of years, I am not sure I got
the concepts right. (My lame excuse, "Since I am a statistician, I have
to understand a lot" does not help) Hence, pardon me if/since my
questions are very fundamental to this group. Whenever I have
geostatistical concept and implementation issues, I explore the
ai-geostats (old & new) archives at yahoo!groups to clear clouds over my
head. However, I haven't found any relevant threads deeply addressing on
the following questions. Thus, I am posting here.
1. Having normality in data always bothers me; I see the text books and
papers comment on this issue, mostly saying, "Normality is not necessary
for kriging, but having normal data distribution makes the prediction
better." I am yet to understand this statement.
2. On Lognormal kriging, I have two questions.
2.1. If my (original) data shows a second order polynomial trend, while
fitting a lognormal distribution, how to proceed further along variogram
fitting & kriging?
Removing the trend from the original data and fitting the variogram to
the 'residual'? or, can this second order polynomial trend be directly
incorporated into the lognormal OK or lognormal KT?
[In the archives, I saw a post by Prof. Donald Myers touched this issue;
'Dioxin contaminated site' paper by Dr. Goovaerts has touched the
comparative studies among different types of kriging]
Prof. Cressie's book ("Statistics for Spatial Data", pp. 135-137)
discusses the lognormal kriging to an extent. However, I do not
understand well how the 'Mean' discussed in the lognormal kriging is
connected to the trend in the original data.
2.2. How to do the lognormal cokriging? (as a matter of fact, is it
anything called 'lognormal cokriging'?) I haven't seen any lognormal
cokriging models in the books.
I have to cokrige in two ways. In the first case, both cokriging data
sets are lognormal. In the second case, while one is lognormal, the
other is normally distributed. I would appreciate if anyone can give a
short statistical methodology on how these problems can be approched.
Even giving citations may be helpful for my reference. I am also
searching for papers that talk about principal component kriging on
non-normally distributed data & handling anisotropy in lognormal
3. As the result of the complexity wrapped with the lognormal & the
transgaussian transformations, is it alright "getting away" with the
traditional OK/KT keeping a "blind eye" on the normality? [I do not know
how scientific this question is. However, I could not resist the
of asking it]
Thank you very much.
Department of Civil & Environmental Engineering
New Orleans, LA
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