STK_DISTRIB_NORMAL_EI computes the normal (Gaussian) expected improvement CALL: EI = stk_distrib_normal_ei (Z) computes the expected improvement of a standard normal (Gaussian) random variable above the threshold Z. CALL: EI = stk_distrib_normal_ei (Z, MU, SIGMA) computes the expected improvement of a Gaussian random variable with mean MU and standard deviation SIGMA, above the threshold Z. CALL: EI = stk_distrib_normal_ei (Z, MU, SIGMA, MINIMIZE) computes the expected improvement of a Gaussian random variable with mean MU and standard deviation SIGMA, below the threshold Z if MINIMIZE is true, above the threshold Z otherwise. NOTE Starting with STK 2.4.1, it is recommended to use stk_sampcrit_ei_eval instead of this function. Be careful, however, with the "direction" of the improvement that you want to compute: EI = stk_sampcrit_ei_eval (MU, SIGMA, Z) computes the expected improvement *below* the threshold Z, and is thus equivalent to EI = stk_distrib_normal_ei (Z, MU, SIGMA, true) To compute the expected improvement *above* Z, change signs as follows: EI = stk_sampcrit_ei_eval (-MU, SIGMA, -Z) 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. See also stk_sampcrit_ei_eval, stk_distrib_student_ei
Package: stk