Stochastic Signal Processing > Kriging

Once the probability model is defined in terms of stationarity, spatial average and variogram, it enables to mathematically compute the averages and variances of any linear combination or derivative of variables Z of x. In particular, the probability model allows to compute the average and variance of the variable Z of x minus Z star of x, that is of the estimation error made when replacing unknown true Z of x value by a linear estimator Z star of x .

The average of estimation error is called bias and the variance of estimation error is called estimation variance. Computing bias and estimation variance is the "objective" basis of uncertainty quantification.

Among all types of linear operators, the kriging operator Z k star of x is the one that:

  • Is unbiased meaning that the average of estimation error Z of x minus Z star of x is 0
  • Is the most accurate, meaning that it minimizes the variance of estimation

There are many types of kriging operators, depending on the type of probability models and the estimation problem to be solved,