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.
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