I understand from wikipedia that a variogram model must be
positive definite to be used for kriging:
Note that the experimental variogram is an empirical estimate of the covariance of a Gaussian process. As such, it may not be positive definite and hence not directly usable in kriging, without constraints or further processing. This explains why only a limited number of variogram models are used: most commonly, the linear, the spherical, the Gaussian and the exponential models.
...But, I don't understand why the variogram model must be positive definite?
I know that covariance matrices are always
positive semi-definite, so I might be able to understand why a
-definite matrix is necessary. But, why
I'm having trouble tying these concepts together: kriging, positive definite matrix, covariance, variogram.