小子样条件下正态先验信息的融合
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摘要
对于Bayes小子样检验方法,先验信息的有效性影响着统计推断的准确性。在对多源正态先验信息进行融合时,采用自助法将之转换为先验子分布,其中采用了改进的经验分布函数法进行再抽样。然后,基于专家水平确定其权重,再结合专家估计法确定各先验子分布的权重。最后,通过计算综合先验分布与假设的正态分布的差异部分的面积,对综合先验分布为正态分布的假设进行检验。案例分析表明此融合方法是有效的。
For the small sample Bayes verification method,the effectiveness of prior information affects the correct statistical inference.As for the fusion of multi-source normal prior information,the bootstrap method was used to convert a piece of prior information into a prior sub-distribution.Then experts' weight was determined based on their level,and the weight of the prior sub-distribution was determined by expert estimate method.At last,by calculating the discrepancy proportion between the integrated prior distribution and the hypothetical normal distribution,the hypothesis that the fused integrated prior distribution was normal distribution was tested,and the method to accurately calculating the distribution parameters was also put forward.The analysis by an example showed the fusion model was effective and accurate.
For the small sample Bayes verification method,the effectiveness of prior information affects the correct statistical inference.As for the fusion of multi-source normal prior information,the bootstrap method was used to convert a piece of prior information into a prior sub-distribution.Then experts' weight was determined based on their level,and the weight of the prior sub-distribution was determined by expert estimate method.At last,by calculating the discrepancy proportion between the integrated prior distribution and the hypothetical normal distribution,the hypothesis that the fused integrated prior distribution was normal distribution was tested,and the method to accurately calculating the distribution parameters was also put forward.The analysis by an example showed the fusion model was effective and accurate.
引文
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[17]张荣,刘思峰.一种基于判断矩阵信息的多属性群决策方法[J].系统工程与电子技术,2009,31(2):373-375.ZHANG RONG,LIU SIFENG.Multi-attribute group decision-making method based on the information of judgment matrixes[J].Systems Engineering and Electronics,2009,31(2):373-375.(in Chinese)
[18]董博超,宋保维,梁庆卫,等.武器装备小子样维修性试验与评定方法研究[J].兵工学报,2011,32(3):327-330.DONG BOCHAO,SONG BAOWEI,LIANG QINGWEI,et al.Research on small sample maintainability experimentation and evaluation of weapon system[J].Acta Armamentarii,2011,32(3):327-330.(in Chinese)
[19]刘勇,徐廷学,彭军.维修时间截尾序贯验后加权检验的实现[J].现代防御技术,2014,42(1):106-110.LIU YONG,XU TINGXUE,PENG JUN.Realization of truncated sequential posterior odd test of maintenance time[J].Modern Defence Technology,2014,42(1):106-110.(in Chinese)
[2]冯静,周经伦,孙权.Bayes分析中多源验前信息融合的ML-II方法[J].数学的实践与认识,2006,36(6):142-145.FENG JING,ZHOU JINGLUN,SUN QUAN.Fusion of information of multiple sources based on ML-II theory in bayesian analysis[J].Mathematics in Practice and Theory,2006,36(6):142-145.(in Chinese)
[3]孙锦,李国林,许诚,等.潜射反舰导弹靶场试验先验信息融合方法仿真[J].火力与指挥控制,2014,39(8):154-158.SUN JIN,LI GUOLIN,XU CHENG,et al.Simulation research on fusion submarine launched anti method for prior distribution of ship missile in range trial[J].Fire Control&Command Control,2014,39(8):154-158.(in Chinese)
[4]姜晨,徐廷学,刘勇,等.维修性小子样验证中先验信息的融合方法[J].科学技术与工程,2014,14(22):129-133.JIANG CHEN,XU TINGXUE,LIU YONG,et al.Prior information fusion method in maintainability small sample test[J].Science Technology and Engineering,2014,14(22):129-133.(in Chinese)
[5]徐廷学,刘勇,赵建忠,等.维修性先验信息的融合方法研究[J].系统工程与电子技术,2014,36(9):1887-1893.XU TINGXUE,LIU YONG,ZHAO JIANZHONG,et al.Maintainability prior information fusion method[J].Systems Engineering and Electronics,2014,36(9):1887-1893.(in Chinese)
[6]夏新涛,叶亮,李云飞,等.基于多层自助最大熵法的可靠性评估[J].兵工学报,2016,37(7):1317-1329.XIA XINTAO,YE LIANG,LI YUNFEI,et al.Reliability evaluation based on hierarchical bootstrap maximum entropy method[J].Acta Armamentarii,2016,37(7):1317-1329.(in Chinese)
[7]JI JIAN,LI YANG.An improved SAR image denoising method based on bootstrap statistical estimation with ICAbasis[J].Chinese Journal of Electronics,2016,25(4):786-792.(in Chinese)
[8]高攀东,沈雪瑾,陈晓阳,等.基于自助法的小样本Weibull分布可靠性分析[J].机械设计与研究,2015,31(2):164-167.GAO PANDONG,SHEN XUEJIN,CHEN XIAOYANG,et al.Reliability analysis under Weibull distribution in small samples based on bootstrap[J].Machine Design and Research,2015,31(2):164-167.(in Chinese)
[9]周慧,马擎宇.用自助法估计外弹道测量数据随机误差分布特性[J].飞行器测控学报,2012,31(1):75-79.ZHOU HUI,MA QINGYU.Estimation of the random error distribution characteristics of exterior ballistic measure data based on bootstrap method[J].Journal of Spacecraft TT&C Technology,2012,31(1):75-79.(in Chinese)
[10]GAO SHESHENG,GAO YI,ZHONG YONGMIN.Random weighting estimation method for dynamic navigation positioning[J].Chinese Journal of Aeronautics,2011,24(3):318-323.
[11]殷建,宋松柏.基于随机加权先验的P-Ⅲ分布参数贝叶斯估计[J].水文,2015,35(3):1-7.YIN JIAN,SONG SONGBAI.A Bayesian method for estimation parameters of P-Ⅲdistribution based on randomly weighted prior[J].Journal of China Hydrology,2015,35(3):1-7.(in Chinese)
[12]郑小兵,董景新,孟令晶,等.Bootstrap方法在导弹落点密集度评估中的误用[J].中国惯性技术学报,2012,20(2):239-243.ZHENG XIAOBING,DONG JINGXIN,MENGLINGJING,et al.Misapplication of Bootstrap method in dispersion assessment of missile fall points[J].Journal of Chinese Inertial Technology,2012,20(2):239-243.
[13]刘薇,常振海.自助法再生样本的获取方法研究[J].齐齐哈尔大学学报,2012,28(4):78-80.LIU WEI,CHANG ZHENHAI.Obtaining method research of bootstrap regenerated samples[J].Journal of Qiqihar University,2012,28(4):78-80.(in Chinese)
[14]冯静,刘琦,周经伦,等.相关函数融合法及其在可靠性分析中的应用[J].系统工程与电子技术,2003,25(6):682-684.FENG JING,LIU QI,ZHOU JINGLUN,et al.Correlation information fusion method and application in reliability analysis[J].Systems Engineering and Electronics,2003,25(6):682-684.(in Chinese)
[15]闫鹏飞,孙权.基于可信度加权融合方法在维修性评价的应用[J].计算机仿真,2010,27(6):31-35.YAN PENGFEI,SUN QUAN.Weight fusion based on credibility for maintain evaluation[J].Computer Simulation,2010,27(6):31-35.(in Chinese)
[16]王小林,郭驰名,程志君,等.一种多源先验分布权重确定的新方法[J].兵工自动化,2010,29(6):60-63.WANG XIAOLIN,GUO CHIMING,CHENG ZHIJUN,et al.A new method for determining weights of multisources of prior distribution[J].Ordnance Industry Automation,2010,29(6):60-63.(in Chinese)
[17]张荣,刘思峰.一种基于判断矩阵信息的多属性群决策方法[J].系统工程与电子技术,2009,31(2):373-375.ZHANG RONG,LIU SIFENG.Multi-attribute group decision-making method based on the information of judgment matrixes[J].Systems Engineering and Electronics,2009,31(2):373-375.(in Chinese)
[18]董博超,宋保维,梁庆卫,等.武器装备小子样维修性试验与评定方法研究[J].兵工学报,2011,32(3):327-330.DONG BOCHAO,SONG BAOWEI,LIANG QINGWEI,et al.Research on small sample maintainability experimentation and evaluation of weapon system[J].Acta Armamentarii,2011,32(3):327-330.(in Chinese)
[19]刘勇,徐廷学,彭军.维修时间截尾序贯验后加权检验的实现[J].现代防御技术,2014,42(1):106-110.LIU YONG,XU TINGXUE,PENG JUN.Realization of truncated sequential posterior odd test of maintenance time[J].Modern Defence Technology,2014,42(1):106-110.(in Chinese)