Estimation

ISATIS offers a large panel of estimation methods. They can be distinguished by:

 the model to which the field is associated (if any)
 the algorithm used to tackle the question (generality, efficiency, speed...)

In addition to the model, all the algorithms depend on a neighborhood (recipe for selecting a part of the information available for the estimation of a target point).

• Model-Free Methods

A variety of algorithms (with a limited number of parameters) are provided, such as:
 Inverse (power of the) distance
 Closest neighbour
 Least square fit (order 2)
 Moving average
 Moving median
 Moving projected slope
 Discrete spline
 Kriging with a linear variogram (no fitting)
 Kriging with a spline generalized covariance (no fitting)

• Kriging

This well-known method provides the Best Linear Unbiased Estimator of the target variable. For each target point, it provides:
 the estimated value
 the corresponding standard deviation which measures the quality of the estimation

For each target point, this method not only gives the estimated value of the variable, but any function derived linearly from the variable, such as:
 the punctual value
 its mean value over a cell
 its derivatives (gradients)
 its convoluted value
 its derivatives

Kriging has been enhanced in order to cope with:
 multivariate cases
 stationary hypothese
 intrinsic hypotheses
 non-stationary hypotheses

Kriging can deal with various types of data, such as:
 Data are provided with measurement errors
 Data correspond to the information convoluted and combined with an instrumental noise
 Data are provided through inequalities
 Data consist in the depth information and its gradient
 Data consist in a variable and its laplacian
 Sparse accurate data and a related indirect exhaustive variable: external drift, collocated cokriging

Kriging can also be considered as a relevant tool for double checking the quality of the model with regard to the data. This application is known as the cross-validation (blind test). Each sample is considered in turn as a target and estimated by kriging using the remaining information. The experimental error between the estimation and the true value is compared to the theoretical error predicted by the model through the standard deviation of the estimation.

Kriging has also been developed in order to tackle specific problems :

 Polygon Kriging for global estimations
 Disjunctive Kriging for non linear problems
 Lognormal Kriging for highly skeewed distributions
 Indicator Kriging for the estimation of discrete variables
 Factorial Kriging Analysis to extract components of a model

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