针对经典MCMC(Markov chain Monte Carlo)算法求解河流水污染源信息(排放量、排放时间和排放位置)时初始点的选取和接受率不高导致的计算效率低下问题,通过COMSOL仿真软件构建污染物二维扩散模型,利用不同算法对比分析了上述两方面对水...针对经典MCMC(Markov chain Monte Carlo)算法求解河流水污染源信息(排放量、排放时间和排放位置)时初始点的选取和接受率不高导致的计算效率低下问题,通过COMSOL仿真软件构建污染物二维扩散模型,利用不同算法对比分析了上述两方面对水污染溯源结果的影响,并由此提出了基于等距随机抽样方法(equidistant random sampling)的两阶段多链Metropolis Hastings算法(ERS-TSMH).仿真结果表明,传统的MH算法和TSMH算法在求解时易陷入局部最优值或不收敛的情况,前者接受率在20%左右,后者却达到近50%;多链ERS-MH算法提高了反演的准确性,但经过10 000次左右迭代后收敛,效率低下;多链ERS-TSMH算法在保证溯源精度的同时,在5 000次左右迭代后收敛,效率显著提高且表现出高稳定性和可靠性.展开更多
Metropolis-Hastings algorithms are slowed down by the computation of complex target distributions. To solve this problem, one can use the delayed acceptance Metropolis-Hastings algorithm (MHDA) of Christen and Fox (20...Metropolis-Hastings algorithms are slowed down by the computation of complex target distributions. To solve this problem, one can use the delayed acceptance Metropolis-Hastings algorithm (MHDA) of Christen and Fox (2005). However, the acceptance rate of a proposed value will always be less than in the standard Metropolis-Hastings. We can fix this problem by using the Metropolis-Hastings algorithm with delayed rejection (MHDR) proposed by Tierney and Mira (1999). In this paper, we combine the ideas of MHDA and MHDR to propose a new MH algorithm, named the Metropolis-Hastings algorithm with delayed acceptance and rejection (MHDAR). The new algorithm reduces the computational cost by division of the prior or likelihood functions and increase the acceptance probability by delay rejection of the second stage. We illustrate those accelerating features by a realistic example.展开更多
A fast MUltiple SIgnal Classification (MUSIC) spectrum peak search algorithm is devised, which regards the power of the MUSIC spectrum function as target distribution up to a constant of proportionality, and uses Metr...A fast MUltiple SIgnal Classification (MUSIC) spectrum peak search algorithm is devised, which regards the power of the MUSIC spectrum function as target distribution up to a constant of proportionality, and uses Metropolis-Hastings (MH) sampler, one of the most popular Markov Chain Monte Carlo (MCMC) techniques, to sample from it. The proposed method reduces greatly the tremendous computation and storage costs in conventional MUSIC techniques i.e., about two and four orders of magnitude in computation and storage costs under the conditions of the experiment in the paper respectively.展开更多
FastSLAM is a popular framework which uses a Rao-Blackwellized particle filter to solve the simultaneous localization and mapping problem（SLAM）. However, in this framework there are two important potential limitatio...FastSLAM is a popular framework which uses a Rao-Blackwellized particle filter to solve the simultaneous localization and mapping problem（SLAM）. However, in this framework there are two important potential limitations, the particle depletion problem and the linear approximations of the nonlinear functions. To overcome these two drawbacks, this paper proposes a new FastSLAM algorithm based on revised genetic resampling and square root unscented particle filter（SR-UPF）. Double roulette wheels as the selection operator, and fast Metropolis-Hastings（MH） as the mutation operator and traditional crossover are combined to form a new resampling method. Amending the particle degeneracy and keeping the particle diversity are both taken into considerations in this method. As SR-UPF propagates the sigma points through the true nonlinearity, it decreases the linearization errors. By directly transferring the square root of the state covariance matrix, SR-UPF has better numerical stability. Both simulation and experimental results demonstrate that the proposed algorithm can improve the diversity of particles, and perform well on estimation accuracy and consistency.展开更多
The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the unc...The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.展开更多
为研究串联系统下多部件应力-强度模型的可靠性问题,基于Kumaraswamy分布,采用极大似然法给出参数及应力-强度模型可靠度的极大似然估计(maximum likelihood estimation,MLE);再利用Jeffreys准则构造无信息先验分布,运用马尔可夫链蒙特...为研究串联系统下多部件应力-强度模型的可靠性问题,基于Kumaraswamy分布,采用极大似然法给出参数及应力-强度模型可靠度的极大似然估计(maximum likelihood estimation,MLE);再利用Jeffreys准则构造无信息先验分布,运用马尔可夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)方法给出参数及应力-强度模型可靠度的贝叶斯估计;最后,利用逆矩估计方法给出参数及应力-强度模型可靠度的逆矩估计(inverse moment estimation,IME)。数值模拟结果表明,在不同系统可靠度及不同样本量条件下,通过对3种估计方法的数值进行比较发现贝叶斯估计效果最好,IME优于MLE。该研究为探讨串联系统多部件应力-强度模型可靠性提供了一定的理论基础。展开更多
文摘针对经典MCMC(Markov chain Monte Carlo)算法求解河流水污染源信息(排放量、排放时间和排放位置)时初始点的选取和接受率不高导致的计算效率低下问题,通过COMSOL仿真软件构建污染物二维扩散模型,利用不同算法对比分析了上述两方面对水污染溯源结果的影响,并由此提出了基于等距随机抽样方法(equidistant random sampling)的两阶段多链Metropolis Hastings算法(ERS-TSMH).仿真结果表明,传统的MH算法和TSMH算法在求解时易陷入局部最优值或不收敛的情况,前者接受率在20%左右,后者却达到近50%;多链ERS-MH算法提高了反演的准确性,但经过10 000次左右迭代后收敛,效率低下;多链ERS-TSMH算法在保证溯源精度的同时,在5 000次左右迭代后收敛,效率显著提高且表现出高稳定性和可靠性.
文摘Metropolis-Hastings algorithms are slowed down by the computation of complex target distributions. To solve this problem, one can use the delayed acceptance Metropolis-Hastings algorithm (MHDA) of Christen and Fox (2005). However, the acceptance rate of a proposed value will always be less than in the standard Metropolis-Hastings. We can fix this problem by using the Metropolis-Hastings algorithm with delayed rejection (MHDR) proposed by Tierney and Mira (1999). In this paper, we combine the ideas of MHDA and MHDR to propose a new MH algorithm, named the Metropolis-Hastings algorithm with delayed acceptance and rejection (MHDAR). The new algorithm reduces the computational cost by division of the prior or likelihood functions and increase the acceptance probability by delay rejection of the second stage. We illustrate those accelerating features by a realistic example.
基金Supported by the National Natural Science Foundation of China (No.60172028).
文摘A fast MUltiple SIgnal Classification (MUSIC) spectrum peak search algorithm is devised, which regards the power of the MUSIC spectrum function as target distribution up to a constant of proportionality, and uses Metropolis-Hastings (MH) sampler, one of the most popular Markov Chain Monte Carlo (MCMC) techniques, to sample from it. The proposed method reduces greatly the tremendous computation and storage costs in conventional MUSIC techniques i.e., about two and four orders of magnitude in computation and storage costs under the conditions of the experiment in the paper respectively.
基金supported by National Natural Science Foundation of China(No.61101197)Research Fund for the Doctoral Program of Higher Education of China(No.20093219120025)
文摘FastSLAM is a popular framework which uses a Rao-Blackwellized particle filter to solve the simultaneous localization and mapping problem（SLAM）. However, in this framework there are two important potential limitations, the particle depletion problem and the linear approximations of the nonlinear functions. To overcome these two drawbacks, this paper proposes a new FastSLAM algorithm based on revised genetic resampling and square root unscented particle filter（SR-UPF）. Double roulette wheels as the selection operator, and fast Metropolis-Hastings（MH） as the mutation operator and traditional crossover are combined to form a new resampling method. Amending the particle degeneracy and keeping the particle diversity are both taken into considerations in this method. As SR-UPF propagates the sigma points through the true nonlinearity, it decreases the linearization errors. By directly transferring the square root of the state covariance matrix, SR-UPF has better numerical stability. Both simulation and experimental results demonstrate that the proposed algorithm can improve the diversity of particles, and perform well on estimation accuracy and consistency.
文摘The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.
文摘为研究串联系统下多部件应力-强度模型的可靠性问题,基于Kumaraswamy分布,采用极大似然法给出参数及应力-强度模型可靠度的极大似然估计(maximum likelihood estimation,MLE);再利用Jeffreys准则构造无信息先验分布,运用马尔可夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)方法给出参数及应力-强度模型可靠度的贝叶斯估计;最后,利用逆矩估计方法给出参数及应力-强度模型可靠度的逆矩估计(inverse moment estimation,IME)。数值模拟结果表明,在不同系统可靠度及不同样本量条件下,通过对3种估计方法的数值进行比较发现贝叶斯估计效果最好,IME优于MLE。该研究为探讨串联系统多部件应力-强度模型可靠性提供了一定的理论基础。
