Njeri
The full _expression_ for the estimation variance conains three terms:
1) twice the weighted average of the semi-variograms between each sample and the point to be estimated
2) the doubly weighted average of all the semi-variograms between every possible pair of samples used in the estimation
3) if estimating over an area or volume, the average semi-variogram between every pair of points inside that area or volume
(2) and (3) can also be described as the "variance amongst the sample values" and the "within-block variance" respectively and are subtracted from (1).
When ordinary kriging is derived the lagrangian multiplier is introduced to make sure the weights add up to 1. It turns out that the lagrangian multiplier is equal to half of term (1) minus term (2). Intuitively, it
is the balance between how well your samples relate to the unknown value and how well they relate to one another.
For example: if your samples are all close to the estimated location, term (1) will be small; if they are all close to one another term (2) will be small. Ideally we want term (1) to be as small as possible and term (2) to be as big as possible. This translates into: "lagrangian multiplier value big and positive" samples are either too far from point to be estimated or are highly clustered. "lagrangian multiplier big and negative" samples (too?) close to estimated point and widely spaced around it.
One might see a zero lagrangian multiplier as the perfect balance between the sampling layout and the prediction of unknown values. Or not, as you prefer.
Hope this helps
Isobel
Dear list
Just a newbabie question
What is the statistical interpretation of the Lagrange multiplier in
kriging.
At least I know if its positive we have a high kriging variance and vice
versa.
Grateful for a response and a reference
Njeri
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