[ai-geostats] Positive Definite Problems
I have a sub-set of data that does not appear to be anisotropic, nor does it contain “bad” outliers; however, my kriging of this data errors out the system by saying the covariance matrix is not positive definite. How do you fix a problem such as this? What might be some common causes of this problem?
Thanks in advance,
OSU Environmental Sciences
Couple of possible explanations. Try these for size:
(1) you may have points which are very close together
if not with identical co-ordinates. Bear in mind that
'close together' depends on the precision of your
software. Most software works to around 8 significant
figures. If you co-ordinates are in the millions, the
computer will not be able to see the difference
between two samples at a distance less than (say) 1.
First check your data for duplicate samples (most
(2) you may be using one of the semi-variogram models
which is not terribly stable, like the 'hole effect'
or the gaussian. The above problem intensifies if you
use a gaussian, because 'too close' now means the
whole of the initial curve on the model.
(3) you may have an equation solving routine which
loses precision very fast and be using too many
If none of these does it for you, I'll try to think of