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.
Package: stk