4
$\begingroup$

I have defined my gaussian variogram like this

$r(h) = \text{nugget} + \text{partial_sill}\cdot(1 - \exp(-\frac{3h^2}{\text{range}^2}))$

I set nugget = 0.1343 partial_sill = 0.3125 range = 19.8642

I tried to create a variogram for a spatial grid of size 5x5, meaning for each of the location in the 5x5 grid, I calculated the value of the variogram with distance equal to its distance to the other locations in the grid.

So I had a matrix of size 25x25. However, this matrix is not positive definite and is singular. How can I remedy this issue with gaussian variogram?

$\endgroup$

closed as off-topic by whuber Aug 12 '14 at 19:16

  • This question does not appear to be about statistics within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ What values of $h$ do your 25 distance values take? $\endgroup$ – AdamO Aug 7 '13 at 19:33
  • $\begingroup$ It's just euclidean distance. I have the grid of size 5x5 a total of 25 locations. So the locations are like (1,1)(1,2)...(1,5)(2,1)... and so on the coordinates, I should say $\endgroup$ – user34790 Aug 7 '13 at 19:50
  • $\begingroup$ I cannot reproduce this. An SVD of the matrix has singular values ranging from $3.68$ down to $0.1343$ and so obviously is positive definite. Are you sure you have implemented the nugget correctly? By definition it is zero when $h=0$ and otherwise equals $0.1343$ for $h\gt 0$. $\endgroup$ – whuber Aug 7 '13 at 20:35
  • $\begingroup$ @whuber I am not sure but in that case the diagonal element is zero isn't it. $\endgroup$ – user34790 Aug 7 '13 at 23:30
  • 1
    $\begingroup$ That is correct: instead of "nugget" in your formula you should write nugget$(h)$ to indicate that the value is $0$ when $h=0$ and otherwise equals $0.1343$. Because the Gaussian model is $0$ when $h=0$, that makes all diagonal elements $0$. $\endgroup$ – whuber Aug 8 '13 at 16:34
0
$\begingroup$

Instead of using power 2, try using 1.99.

Check out the similar solution to a question I posed along those same lines

Prior selection for Gaussian Processes (GP)

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.