[ai-geostats] Lagrange Multiplier

[Isobel Clark]

Colin

 

In most software the lagrangian multiplier is simply used to shortcut the calculation of the kriging variance. It is, basically, equal to the "average semi-variogram between samples and estimated point" minus the "average semi-variogram amongst the samples". In a sense, it is the balance between getting your samples as close to the estimated point as possible and getting them as far away from one another as possible.

 

The lagrangian multiplier (l.m.) is scaled as a variance, so the actual magnitude will depend on your total sill.

 

A positive l.m. (sorry, tired of typing!) means that your samples are not efficiently spread around the estimated point -- for example you might have clustering, be using points 'behind' other points, etc.

 

A negative l.m. means that your samples are well spread out relative to how close they are to the estimator. So, big and negative is good!

 

I have a suspicion that the reason software packages have taken to giving you the lagragian multiplier is because it is needed for back-transforms such as the lognormal. Datamine has always made this quantity available but not many other packages until now.

 

Hope this helps

Isobel

Colin Badenhorst <[EMAIL PROTECTED]> wrote:

Hi List,

 

I’ve noticed that the latest version of my estimation software now stores the Lagrange multiplier (parameter) for each estimated block in my model. I was wondering if anyone had any thoughts on how I could use this variable in some practical sense to further interpret or validate my estimates. Unfortunately, my understanding of the Lagrange multiplier has always been poor, so I’m not sure exactly what it means.

 

Regards,

Colin

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