A diagnostic procedure based on maximum likelihood estimation, to study the convergence of the Markov chain produced by Gibbs sampler, is presented. The unbiasedness, consistent and asymptotic normality are considered...A diagnostic procedure based on maximum likelihood estimation, to study the convergence of the Markov chain produced by Gibbs sampler, is presented. The unbiasedness, consistent and asymptotic normality are considered for the estimation of the parameters produced by the procedure. An example is provided to illustrate the procedure, and the numerical result is consistent with the theoretical one.展开更多
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
A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method...A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method by effectively making use of the information from the prior distribution and that from the discovery sequence according to posterior probabilities. All statistical inferences about the parameters of the model and total resources can be quantified by drawing samples directly from the joint posterior distribution. In addition, statistical errors of the samples can be easily assessed and the convergence properties can be monitored during the sampling. Because the information contained in a discovery sequence is not enough to estimate all parameters, especially the number of fields, geologically justified prior information is crucial to the estimation. The Bayesian approach allows the analyst to specify his subjective estimates of the required parameters and his degree of uncertainty about the estimates in a clearly identified fashion throughout the analysis. As an example, this approach is applied to the same data of the North Sea on which Smith demonstrated his maximum likelihood method. For this case, the Bayesian approach has really improved the overly pessimistic results and downward bias of the maximum likelihood procedure.展开更多
Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or h...Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or how to estimate the parameter. There are still some open problems,such as the error analysis of parameter estimation, the theoretical proof of the convergence of theiterative algorithm for maximum likelihood estimation of parameters. The Yule-Simon distributionis a heavy-tailed distribution and the parameter is usually less than 2, so the variance does notexist. This makes it difficult to give an interval estimation of the parameter. Using the compressiontransformation, this paper proposes a method of interval estimation based on the centrallimit theorem. This method can be applied to many heavy-tailed distributions. The other twoasymptotic confidence intervals of the parameter are obtained based on the maximum likelihoodand the mode method. These estimation methods are compared in simulations and applications toempirical data.展开更多
To estimate percentiles of a response distribution, the transformed response rule of Wetherill and Robbins-Monro sequential design were proposed under Log-Logistic model. Based on responses data, a necessary and suffi...To estimate percentiles of a response distribution, the transformed response rule of Wetherill and Robbins-Monro sequential design were proposed under Log-Logistic model. Based on responses data, a necessary and sufficient condition for the existence of maximum likelihood estimators and then the calculating formula were presented. After a simulation study, the proposed approach was applied to 65# detonator. Numerical results showed that estimators of percentiles from the proposed approach are robust to the parametric models lacking information on the original response distribution.展开更多
文摘A diagnostic procedure based on maximum likelihood estimation, to study the convergence of the Markov chain produced by Gibbs sampler, is presented. The unbiasedness, consistent and asymptotic normality are considered for the estimation of the parameters produced by the procedure. An example is provided to illustrate the procedure, and the numerical result is consistent with the theoretical one.
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A Bayesian approach using Markov chain Monte Carlo algorithms has been developed to analyze Smith’s discretized version of the discovery process model. It avoids the problems involved in the maximum likelihood method by effectively making use of the information from the prior distribution and that from the discovery sequence according to posterior probabilities. All statistical inferences about the parameters of the model and total resources can be quantified by drawing samples directly from the joint posterior distribution. In addition, statistical errors of the samples can be easily assessed and the convergence properties can be monitored during the sampling. Because the information contained in a discovery sequence is not enough to estimate all parameters, especially the number of fields, geologically justified prior information is crucial to the estimation. The Bayesian approach allows the analyst to specify his subjective estimates of the required parameters and his degree of uncertainty about the estimates in a clearly identified fashion throughout the analysis. As an example, this approach is applied to the same data of the North Sea on which Smith demonstrated his maximum likelihood method. For this case, the Bayesian approach has really improved the overly pessimistic results and downward bias of the maximum likelihood procedure.
基金supported by the National Natural Science Foundation of China(Grant No.11961035)Jiangxi Provincial Natural Science Foundation(Grant No.20224BCD41001).
文摘Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or how to estimate the parameter. There are still some open problems,such as the error analysis of parameter estimation, the theoretical proof of the convergence of theiterative algorithm for maximum likelihood estimation of parameters. The Yule-Simon distributionis a heavy-tailed distribution and the parameter is usually less than 2, so the variance does notexist. This makes it difficult to give an interval estimation of the parameter. Using the compressiontransformation, this paper proposes a method of interval estimation based on the centrallimit theorem. This method can be applied to many heavy-tailed distributions. The other twoasymptotic confidence intervals of the parameter are obtained based on the maximum likelihoodand the mode method. These estimation methods are compared in simulations and applications toempirical data.
文摘To estimate percentiles of a response distribution, the transformed response rule of Wetherill and Robbins-Monro sequential design were proposed under Log-Logistic model. Based on responses data, a necessary and sufficient condition for the existence of maximum likelihood estimators and then the calculating formula were presented. After a simulation study, the proposed approach was applied to 65# detonator. Numerical results showed that estimators of percentiles from the proposed approach are robust to the parametric models lacking information on the original response distribution.
