Đang chuẩn bị liên kết để tải về tài liệu:
SIMULATION AND THE MONTE CARLO METHOD Episode 7

Tham khảo tài liệu 'simulation and the monte carlo method episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 160 CONTROLLING THE VARIANCE Table 5.9 represents the point estimators u and f u v their associated sample variances and the estimated efficiency E of the importance sampling estimator Ị. u v relative to the CMC one f u as functions of the sample size N. Note that in our experiments the CMC estimator used all N replications while the importance sampling estimator used only N N1 replications since N1 1000 samples were used to estimate the reference parameter V. Table 5.9 The efficiency e of the importance sampling estimator u v relative to the CMC one u as functions of the sample size N. N Z u u v Varu u Varv u v 2000 15.0260 14.4928 4.55 0.100 45.5 4000 14.6215 14.4651 1.09 0.052 21.0 6000 14.0757 14.4861 0.66 0.036 18.3 8000 14.4857 14.4893 0.53 0.027 19.6 10000 14.8674 14.4749 0.43 0.021 20.5 12000 14.7839 14.4762 035 0.017 20.6 14000 14.8053 14.4695 0.30 0.015 20.0 16000 15.0781 14.4657 0.28 0.013 21.5 18000 14.8278 14.4607 0.24 0.011 21.8 20000 14.8048 14.4613 0.22 0.010 22.0 From the data in Table 5.9 if follows that the importance sampling estimator u v is more efficient than the CMC one by at least a factor of 18. Table 5.8 indicates that only a few of the reference parameters Vị namely those numbered 12 13 22 23 and 32 out of a total of 70 called the bottleneck parameters differ significantly from their corresponding original values Ui i 1 . 70. This implies that instead of solving the original 70-dimensional CE program 5.65 one could solve in fact only a 5dimensional one. These bottleneck components could be efficiently identified by using the screening algorithm developed in 22 . Motivated by this screening algorithm we solved the 5-dimensional CE program instead of the 70-dimensional one while keeping Vi Ui for the remaining 65 parameters. In this case we obtained better results than those in Table 5.9 the resulting importance sampling estimator Í u v was more efficient than the CMC one by at least a factor of 20. The reason for that is obvious the 65 .