1019Re: AI-GEOSTATS: Log normal kriging (2)
- May 14, 2003Gregoire Dubois wrote:
>What I did for mapping groundwater quality variables during my PhD research
> I also saw case studies where the back transformation did not take the
> Lagrange parameter into account. How can this be justified and how much would
> such an approach affect the transformation?
1. estimate block mean concentrations on the log scale, and std.errors
2. calculate approximate 95% predictions intervals by est +/- 2 * std.err
3. back-transform both sides of the interval by taking the exponent.
What results is not an interval estimate of the block mean value (which
may be outside this interval!) but an estimate of the block geometric
mean value. When, on the log scale block mean and block median coincide
(e.g. when log-concentrations within a block are symmetrically distributed)
this value coincides with the block median value. The full story is in
Journal of Hydrology 200, p. 364-386; reprints available from me.
Now what I wonder is how much it matters if you ignore the lagrange
parameter but only use the kriging variance: isn't this parameter usually
much smaller than the kriging variance? Isobel?
>I try to explain kriging usually as prediction using regression models
> PS: as a colleague told me, geostatistics is often closer to black magic than
> to any scientific discipline...
with spatially correlated errors (modelled as stationary random functions).
In this context, you are practically in the field of statistics. Authors
to read are: Cressie, Christensen, Diggle, M. Stein, Ribeiro, and probably
A good friend of mine who already was in this area before I was even born
once told me that his impression was that geostatistics suffers from
"boosterism" by a number of important authors: each small step is
sold with many new names, new jargon, exclamation marks, and so on. This
puts off many scientists who are interested from the outside, but who are
not in the main stream, like statisticians. I, for example, cannot read
the BME papers.
Two days ago I had a discussion with a PhD student here. He had been
studying Goovaerts' 1997 reference book, and came to the conclusion that
the difference between simple and ordinary kriging was that simple
kriging uses global neighbourhoods, whereas ordinary kriging uses
local neighbouhoods. I apologized, and had to admit that I'd advised
him to read the wrong book, at least for this issue.
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