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
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
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
The ocean bottom seismograph(OBS)is a powerful device deployed on the seafloor for acquiring marine seismic data,capable of detecting the multi-scale Earth’s interiors from submarine sediments to the mantle.Due to th...The ocean bottom seismograph(OBS)is a powerful device deployed on the seafloor for acquiring marine seismic data,capable of detecting the multi-scale Earth’s interiors from submarine sediments to the mantle.Due to the frequent use of free-fall deployment,it is challenging to accurately track its precise position.Additionally,the internal crystal oscillator clock of the OBS has limited accuracy,resulting in clock drift for long-term work on the seabed.To improve the reliability of OBS detections,it is crucial to calculate the precise OBS location and time correction.Focusing on accurately determining OBS position and timing,this study developed a positioning method that integrates time correction based on the Markov Chain Monte Carlo(MCMC)algorithm,utilizing travel times of direct water waves triggered by two-dimensional(2-D)shot lines or three-dimensional(3-D)airgun arrays.This newly developed method can simultaneously estimate accurate OBS location and time correction,incorporating bathymetric data into the inversion procedures to improve sampling efficiency and enhance the reliability of the final results.Synthetic tests with appropriate noise levels are performed independently to evaluate the feasibility and reliability of our method,indicating that it is robust enough to determine OBS location and time correction precisely.Finally,we use travel-time data recorded at three OBSs deployed in the Southwest Indian Ridge to relocate locations and calculate time corrections.The results exhibit high consistency when using 2-D and 3-D shot data,indicating that high-resolution bathymetric data plays a fingerprint role in inversion to evaluate precise OBS location and time correction.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
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.
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.
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The National Key Research and Development Program of China under contract No.2021YFC3101404the National Natural Science Foundation of China under contract Nos 42106068,42376052,42276064 and 42276075+1 种基金the Foundation of State Key Laboratory of Submarine Geoscience under contract No.sglkfkt2025-2the Zhejiang Provincial Natural Science Foundation of China under contract No.LZ23D060004.
文摘The ocean bottom seismograph(OBS)is a powerful device deployed on the seafloor for acquiring marine seismic data,capable of detecting the multi-scale Earth’s interiors from submarine sediments to the mantle.Due to the frequent use of free-fall deployment,it is challenging to accurately track its precise position.Additionally,the internal crystal oscillator clock of the OBS has limited accuracy,resulting in clock drift for long-term work on the seabed.To improve the reliability of OBS detections,it is crucial to calculate the precise OBS location and time correction.Focusing on accurately determining OBS position and timing,this study developed a positioning method that integrates time correction based on the Markov Chain Monte Carlo(MCMC)algorithm,utilizing travel times of direct water waves triggered by two-dimensional(2-D)shot lines or three-dimensional(3-D)airgun arrays.This newly developed method can simultaneously estimate accurate OBS location and time correction,incorporating bathymetric data into the inversion procedures to improve sampling efficiency and enhance the reliability of the final results.Synthetic tests with appropriate noise levels are performed independently to evaluate the feasibility and reliability of our method,indicating that it is robust enough to determine OBS location and time correction precisely.Finally,we use travel-time data recorded at three OBSs deployed in the Southwest Indian Ridge to relocate locations and calculate time corrections.The results exhibit high consistency when using 2-D and 3-D shot data,indicating that high-resolution bathymetric data plays a fingerprint role in inversion to evaluate precise OBS location and time correction.
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.
