STK_SAMPCRIT_EI_EVAL computes the EI criterion
CALL: EI = stk_sampcrit_ei_eval (ZP_MEAN, ZP_STD, ZI)
computes the value EI of the Expected Improvement (EI) criterion for a
minimization problem, with respect to the observed values ZI, assuming
Gaussian predictive distributions with means ZP_MEAN and standard
deviations ZP_STD. The input argument must have the following sizes:
* ZP_MEAN M x 1,
* ZP_STD M x 1,
* ZI N x 1,
where M is the number of points where the EI must be computed, and N the
number of observations. The output has size M x 1.
REMARK
Since the EI is computed for a minimization problem, the result depends
on the minimum of the obervations only, not on the entire set of observed
values. The above call is thus equivalent to
EI = stk_sampcrit_ei_eval (ZP_MEAN, ZP_STD, min (ZI))
NOTE
This function was added in STK 2.4.1, and will in the future completely
replace stk_distrib_normal_ei. Note that, unlike the present function,
stk_distrib_normal_ei returns as a default the EI for a *maximization*
problem.
REFERENCES
[1] D. R. Jones, M. Schonlau and William J. Welch. Efficient global
optimization of expensive black-box functions. Journal of Global
Optimization, 13(4):455-492, 1998.
[2] J. Mockus, V. Tiesis and A. Zilinskas. The application of Bayesian
methods for seeking the extremum. In L.C.W. Dixon and G.P. Szego,
editors, Towards Global Optimization, volume 2, pages 117-129, North
Holland, New York, 1978.