## [SOLVED] Integration of threshold value into dataset

Any question regarding the Interpolation method using Kriging

### [SOLVED] Integration of threshold value into dataset

Hello,

I would like to add a supplementary information into my dataset before kriging :
is it possible to add points where estimation value will be kept inferior to a threshold value ?

For example, instead of verifying that Z*=Zthreshold at a specific point, I would like to set this condition : Z*<Zthreshold.

Thanks for your help,

Mathias
Mat

Posts: 2
Joined: Wed Apr 12, 2017 4:22 pm

### Re: Integration of threshold value into dataset

Hello Mathias

The required procedure is to perform an estimation conditionned by inequality. This is possible using the Gibbs sampler (see function gibbs). But you need to know a bit more before using this function.
As a matter of fact, this function requires a single Db (a set of samples) where you can define data (say "hard"), some inequality constraints and some target points... all of them located within the same db.

Finally the principle is to provide a Db with the coordinates (with locators "x1", "x2",... with no limitation on the dimension of the space) and two other attributes:
- lower (with locator "lower") which contains the lowest value that the result mut fulfill
- upper (with locator "upper") which contains the upper value
Then it suffices to set:
- upper=lower=data value for hard data
- lower or upper or both defined at samples where the constraint is defined
- lower and upper left to NA at free target points.

Then it suffices to perform Gibbs by providing the relevant model.

Hope this will help.
Didier Renard

Posts: 281
Joined: Thu Sep 20, 2012 4:22 pm

### Re: Integration of threshold value into dataset

Hi Didier,

thanks for this answer,
I applied default gibbs function on my dataset, and I obtained resulting simulation map.
Is it OK to re-use simulation results at inequality target points into kriging dataset ?

Mathias
Mat

Posts: 2
Joined: Wed Apr 12, 2017 4:22 pm

### Re: Integration of threshold value into dataset

Hi Mathias,
You rmethodology is the usual one. However let us mention that, when you run Gibbs (iterative method), you essentially generate several simulations (different trajectories) which will give several sets of simulated outcomes at each site where some inequality is defined.
Then we usually average them out in order to produce a mean value that is called a conditional expectation.
Then, if your aim is to produce an estimation over the field, it is OK to use this average as a hard data for the kriging step (this is what is done in Isatis for example). However, note that this operation generates a strange result: the variance os estimation error will zero at those inequality point, although the data is not as hard.
Morever, I warn you that using this conditional expectation would not be correct if you wanted to run simulations conditioned by hard data and inequality data, as reducing the set of simulated values (at inequalities) to a conditional expectation dramatically reduces the variability. Instead, you should use each set of simulated values at inequalities to condition the simulation over the field.

Hope my explanations are clear enough.
Didier Renard

Posts: 281
Joined: Thu Sep 20, 2012 4:22 pm