贝叶斯后验修正概率序列研究  

Research on Bayesian Posterior Modified Probability Sequence

作　　者：庞碧君[1] Pang Bijun(College of Mathematics Science,Luoyang Normal University,Luoyang Henan 471934,China)

机构地区：[1]洛阳师范学院数学科学学院,河南洛阳471934

出　　处：《统计与决策》2020年第21期43-46,共4页Statistics & Decision

摘　　要：后验修正概率序列是统计预测和决策的重要内容,研究贝叶斯后验修正概率序列及其应用有着重要的意义。文章利用贝叶斯公式,推导出了当试验结果 A连续发生n次和A、Aˉ发生m+n次时的后验修正概率序列;用极限的方法研究了影响后验修正概率序列的主要因素和序列的变化趋势,结果显示:后验修正概率序列的收敛性及收敛速度主要受每次主观概率估计值的影响,如果忽略主观概率重新估计的差异,后验修正概率对前面已经发生的m+n次试验中,Aˉ和A发生的顺序具有无记忆性。当后验概率小于η(0 <η<1)和后验概率大于ζ(0 <ζ<1)时,利用上述结论给出了A、Aˉ发生次数的计算方法。最后用实例说明了贝叶斯后验修正概率序列在研究后验概率动态数据中的重要价值。The posterior modified probability sequence is an important content of statistical prediction and decision making,and it is of great significance to study it and its applications. This paper uses Bayes formula to deduce the posterior modified probability sequence when test result A continuously occurs n times and A and to study the main factors affecting the posterior modified probability sequence and the variation trend of the sequence. The results show that the convergence and the convergence rate of the sequence of posterior modified probability are affected mainly by each subjective probability estimate, and that if the difference in subjective probability re-estimation is ignored, the posterior modified probability is memoryless for the order in which is less than η(0<η<1) and the posterior probability is greater than ζ(0<ζ<1), the conclusion above is used to give the calculation method of the A and terior modified probability sequence in the study of posterior probability dynamic data.

关 键 词：贝叶斯公式 后验概率 概率序列 收敛速度 

分 类 号：O211.9[理学—概率论与数理统计]