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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?

Glen_b
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user34790
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  • What values of $h$ do your 25 distance values take? – AdamO Aug 07 '13 at 19:33
  • 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 – user34790 Aug 07 '13 at 19:50
  • 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 $h\gt 0$. – whuber Aug 07 '13 at 20:35
  • @whuber I am not sure but in that case the diagonal element is zero isn't it. – user34790 Aug 07 '13 at 23:30
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    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 $0$. – whuber Aug 08 '13 at 16:34
  • @whuber. I think you can answer my second question as well. http://stats.stackexchange.com/questions/66823/issues-with-ordinary-kriging. I am running into similar issues. It may be some misunderstanding like in this case – user34790 Aug 08 '13 at 16:49
  • This question appears to be off-topic because it is about a circumstance that could not be reproduced. – whuber Aug 12 '14 at 19:16

1 Answers1

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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)

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