This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both ...This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.展开更多
Maximum likelihood estimation(MLE)is an effective method for localizing radioactive sources in a given area.However,it requires an exhaustive search for parameter estimation,which is time-consuming.In this study,heuri...Maximum likelihood estimation(MLE)is an effective method for localizing radioactive sources in a given area.However,it requires an exhaustive search for parameter estimation,which is time-consuming.In this study,heuristic techniques were employed to search for radiation source parameters that provide the maximum likelihood by using a network of sensors.Hence,the time consumption of MLE would be effectively reduced.First,the radiation source was detected using the k-sigma method.Subsequently,the MLE was applied for parameter estimation using the readings and positions of the detectors that have detected the radiation source.A comparative study was performed in which the estimation accuracy and time consump-tion of the MLE were evaluated for traditional methods and heuristic techniques.The traditional MLE was performed via a grid search method using fixed and multiple resolutions.Additionally,four commonly used heuristic algorithms were applied:the firefly algorithm(FFA),particle swarm optimization(PSO),ant colony optimization(ACO),and artificial bee colony(ABC).The experiment was conducted using real data collected by the Low Scatter Irradiator facility at the Savannah River National Laboratory as part of the Intelligent Radiation Sensing System program.The comparative study showed that the estimation time was 3.27 s using fixed resolution MLE and 0.59 s using multi-resolution MLE.The time consumption for the heuristic-based MLE was 0.75,0.03,0.02,and 0.059 s for FFA,PSO,ACO,and ABC,respectively.The location estimation error was approximately 0.4 m using either the grid search-based MLE or the heuristic-based MLE.Hence,heuristic-based MLE can provide comparable estimation accuracy through a less time-consuming process than traditional MLE.展开更多
As a widely used reconstruction algorithm in quantum state tomography, maximum likelihood estimation tends to assign a rank-deficient matrix, which decreases estimation accuracy for certain quantum states. Fortunately...As a widely used reconstruction algorithm in quantum state tomography, maximum likelihood estimation tends to assign a rank-deficient matrix, which decreases estimation accuracy for certain quantum states. Fortunately, hedged maximum likelihood estimation （HMLE） [Phys. Rev. Lett. 105 （2010）200504] was proposed to avoid this problem. Here we study more details about this proposal in the two-qubit case and further improve its performance. We ameliorate the HMLE method by updating the hedging function based on the purity of the estimated state. Both performances of HMLE and ameliorated HMLE are demonstrated by numerical simulation and experimental implementation on the Werner states of polarization-entangled photons.展开更多
为了解决故障先验概率估算不准的问题,提出了基于最大熵的故障先验概率的计算模型.该模型以相关的先验信息作为最大概率估计的约束条件,并通过拉格朗日函数,将故障先验概率估算问题转化成无约束优化问题.为了实现对无约束优化问题的快...为了解决故障先验概率估算不准的问题,提出了基于最大熵的故障先验概率的计算模型.该模型以相关的先验信息作为最大概率估计的约束条件,并通过拉格朗日函数,将故障先验概率估算问题转化成无约束优化问题.为了实现对无约束优化问题的快速求解,提出了一种基于最速下降法和牛顿法的混合梯度算法;并且,针对大规模系统中故障变量过多的情况,依据系统分解的原则,将高维故障空间分解为多个低维故障空间,给出了低维故障空间求解的快速计算方法.通过最大熵方法和故障平均间隔(MTTF,Mean Time To Failure)方法的结果比较,证明最大熵方法更具准确性.展开更多
基金supported by the National Science Foundations (DMS0504783 DMS0604207)National Science Fund for Distinguished Young Scholars of China (70825005)
文摘This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.
文摘Maximum likelihood estimation(MLE)is an effective method for localizing radioactive sources in a given area.However,it requires an exhaustive search for parameter estimation,which is time-consuming.In this study,heuristic techniques were employed to search for radiation source parameters that provide the maximum likelihood by using a network of sensors.Hence,the time consumption of MLE would be effectively reduced.First,the radiation source was detected using the k-sigma method.Subsequently,the MLE was applied for parameter estimation using the readings and positions of the detectors that have detected the radiation source.A comparative study was performed in which the estimation accuracy and time consump-tion of the MLE were evaluated for traditional methods and heuristic techniques.The traditional MLE was performed via a grid search method using fixed and multiple resolutions.Additionally,four commonly used heuristic algorithms were applied:the firefly algorithm(FFA),particle swarm optimization(PSO),ant colony optimization(ACO),and artificial bee colony(ABC).The experiment was conducted using real data collected by the Low Scatter Irradiator facility at the Savannah River National Laboratory as part of the Intelligent Radiation Sensing System program.The comparative study showed that the estimation time was 3.27 s using fixed resolution MLE and 0.59 s using multi-resolution MLE.The time consumption for the heuristic-based MLE was 0.75,0.03,0.02,and 0.059 s for FFA,PSO,ACO,and ABC,respectively.The location estimation error was approximately 0.4 m using either the grid search-based MLE or the heuristic-based MLE.Hence,heuristic-based MLE can provide comparable estimation accuracy through a less time-consuming process than traditional MLE.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11574291,61108009 and 61222504
文摘As a widely used reconstruction algorithm in quantum state tomography, maximum likelihood estimation tends to assign a rank-deficient matrix, which decreases estimation accuracy for certain quantum states. Fortunately, hedged maximum likelihood estimation （HMLE） [Phys. Rev. Lett. 105 （2010）200504] was proposed to avoid this problem. Here we study more details about this proposal in the two-qubit case and further improve its performance. We ameliorate the HMLE method by updating the hedging function based on the purity of the estimated state. Both performances of HMLE and ameliorated HMLE are demonstrated by numerical simulation and experimental implementation on the Werner states of polarization-entangled photons.
文摘为了解决故障先验概率估算不准的问题,提出了基于最大熵的故障先验概率的计算模型.该模型以相关的先验信息作为最大概率估计的约束条件,并通过拉格朗日函数,将故障先验概率估算问题转化成无约束优化问题.为了实现对无约束优化问题的快速求解,提出了一种基于最速下降法和牛顿法的混合梯度算法;并且,针对大规模系统中故障变量过多的情况,依据系统分解的原则,将高维故障空间分解为多个低维故障空间,给出了低维故障空间求解的快速计算方法.通过最大熵方法和故障平均间隔(MTTF,Mean Time To Failure)方法的结果比较,证明最大熵方法更具准确性.
