Simone
Not so banal a question. 34 years ago my supervisor
gave me some papers to read which said exactly that.
Even with a Master's in applied statistics, I could
not make head-nor-tail of the explanation. So I went
on a three week short course at Fontainebleau and they
explained it around the middle of the third week!
A very simplistic explanation: when you calculate an
ordinary covariance you have two columns of figures,
say variable g and f. The covariance between g and f
is calculated (in practice) by multiplying the two
columns together, summing the results and then
subtracting the product of the two means. Difficult to
do in a text email but:
Sum(g x f)/n - mean(g) x mean(f)
This is exactly equivalent to:
Sum (g-mean(g)x(f-mean(f))/n
{leave out the whole n or (n-1) debate at this point)
In a geostatistical context, g would be the value of a
sample (any sample). f would be the value of another
sample a specified distance away. That is, specify one
particular distance (h), find pairs of samples that
distance apart, first sample in pair is g (first
column), second sample in pair is f (second column).
Calculate covariance as above with the modification
that the mean of g and the mean of f will be the same.
Repeat for many different distances and you end up
with a graph of how the covariance of the values
varies with the distance between the samples.
I, personally, prefer the semi-variogram approach
because it is a lot easier to explain! Also, you do
not need to know (or estimate) the mean. More
explanations in free downloadable Practical
Geostatistics 1979,
http://uk.geocities.com/drisobelclark/practica.htm.
If you have second order stationarity, the covariance
function is simply the sample value variance minus the
semi-variogram.
Does this help?
Isobel
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