STK_EXAMPLE_DOE06  Sequential design for the estimation of an excursion set

 In this example, we consider the problem of estimating the set

    Gamma = { x in X | f(x) > z_crit },

 where z_crit is a given value, and/or its volume.

 In a typical "structural reliability analysis" problem, Gamma would
 represent the failure region of a certain system, and its volume would
 correspond to the probability of failure (assuming a uniform distribution
 for the input).

 A Matern 5/2 prior with known parameters is used for the function f, and
 the evaluations points are chosen sequentially using any of the sampling
 criterion described in [1] (see also [2], section 4.3).

 REFERENCE

   [1] B. Echard, N. Gayton and M. Lemaire (2011).   AK-MCS: an active
       learning reliability method combining Kriging and Monte Carlo
       simulation.  Structural Safety, 33(2), 145-154.

   [2] J. Bect, D. Ginsbourger, L. Li, V. Picheny and E. Vazquez (2012).
       Sequential design of computer experiments for the estimation of a
       probability of failure.  Statistics and Computing, 22(3), 773-793.