For calculating the predictive powers, we suggest an elegant expectation identity to directly calculate the expectations. We calculate the predictive powers of the hypotheses with a nonzero threshold for five different categories, which are non-sequential trials with classical power and Bayesian power, and sequential trials with hybrid predictions, Bayesian predictions, and classical predictions. Moreover, the calculations of the various predictive powers are illustrated through
three examples. Finally, when calculating the average success probability in \ncite{9}, it is tricky to find the predictive distribution for the predictive power, whereas, it is straightforward to utilize the expectation identity for the calculation.
The research was supported by the Fundamental Research Funds for the Central Universities (Grant Nos. 2019CDXYST0016; 2018CDXYST0024), the China Scholarship Council (Grant No. 201606055028), the National Natural Science Foundation of China (Grant No. 11671060), the MOE Project of Humanities and Social Sciences on the West and the Border Area (Grant Nos. 20XJC910001; 14XJC910001) and Chongqing Key Laboratory of Analytic Mathematics and Applications.
引用本文:
张应应;荣腾中;李曼曼. 一个新的期望恒等式及其在正态预测势计算中的应用[J]. 应用概率统计, 2020, 36(5): 523-535.
ZHANG Yingying; RONG Tengzhong; LI Manman. A New Expectation Identity and Its Application in the Calculations of Predictive Powers Assuming Normality. CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST, 2020, 36(5): 523-535.
