Dear Isobel and all,
This is an interesting topic. I appreciate the ideas of the software "MIX", but have not tried it yet. If somebody finds it "really" useful, I may have a try. My main concern is that one needs to define subpopulations prior to “separate” mixed populations, but these subpopulations are in fact what we are looking for and thus they may not be pre-defined in many cases. This may be a “chicken and egg” dilemma in this case.
For the method of "probability
plot", I have some concerns. It is quite often declared that sub-populations can
be “separated” based on the "break points" or "kinks/inflexions". I feel this is
hard to prove. Whichever threshold values (e.g., break points) you choose to
separate a mixture, you can always say the low values are background and the
high ones are polluted, and you can always map them separately and explain them
with your geological/environmental knowledge in a very good way. Bearing my
doubt in mind, some time ago, I tried to use normal score values to produce
two perfect normal populations, say one with mean=0 and stddev=1 (n=10000,
min=-3.8361, max=3.8361), and the other with mean=8, and stddev=1 (n=10000,
min=4.1639, max=11.8361). The value "4" should be the separating point for the
two "sub-populations". The probability plot (specific method used was “Normal
Q-Q plot” which should be equivalent to others) of the mixed population showed
that the separating point of 4 was located in the middle of a "plateau", not on
the kinks. Reducing the mean value of the second "sub-population" just created
several kinks on the plot, and the expected separating points never appeared on
a kink. I also tried to use 3 normal subpopulations, and couldn't get the
"expected" results. Therefore, I don't think points of kinks can be used to
separate mixed populations into several subpopulations. Well, that was just an
experiment, but it did prove that my concern is real.
I'm looking for some constructive comments.:)
Cheers,
Chaosheng
>
> The common 'Normal Score' transform assumes one
> population. Transformations such as rank or logarithm
> do not assume one population.
>
> The best way to identify likely mixtures is with
> programs such as Peter MacDonald's Mix (cited in
> Ruben's email I think):
>
> http://www.math.mcmaster.ca/peter/mix/mix31.html
>
> or with probability plots. Many software packages have
> these and mixtures are easily identifiable by
> break-points or points of inflexion in the plot.
>
> For those (like myself) without easy access to
> libraries, there are a couple of papers which describe
> (geological) applications and using a combination of
> indicator and ordinary kriging to solve some problems.
>
>
> Papers can be found at
> http://uk.geocities.com/drisobelclark/resume
> follow the publications link. Look for my 1974 paper,
> now available in pdf format, the 1993 IMGC paper and
> the 1992 Troia paper with Jonathan Vieler.
>
> We have had good experience with this approach for 30
> years in fields as diverse as mineral resource
> estimation and seabird preservation.
>
> Isobel Clark
> http://geoecosse.bizland.com/courses.htm
>
>
>
>
>
>
>
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