Hyperparameter estimation for satellite image restoration using a MCMC maximum-likelihood method

The satellite image deconvolution problem is ill-posed and must be regularized. Herein, we use an edge-preserving regularization model using a ? function, involving two hyperparameters. Our goal is to estimate the optimal parameters in order to automatically reconstruct images. We propose to use the maximum-likelihood estimator (MLE), applied to the observed image. We need sampling from prior and posterior distributions. Since the convolution prevents use of standard samplers, we have developed a modified Geman-Yang algorithm, using an auxiliary variable and a cosine transform. We present a Markov chain Monte Carlo maximum-likelihood (MCMCML) technique which is able to simultaneously achieve the estimation and the reconstruction.     

基于Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪

在计算机视觉领域,由镜头切换、目标动力学突变、低帧率视频等引起的突变运动存在极大的不确定性,使得突变运动跟踪成为该领域的挑战性课题.以贝叶斯滤波框架为基础,提出一种基于有序超松弛Hamiltonian马氏链蒙特卡罗方法的突变运动跟踪算法.该算法将Hamiltonian动力学融入MCMC（Markov chain Monte Carlo）算法,目标状态被扩张为原始目标状态变量与一个动量项的组合.在提议阶段,为抑制由Gibbs采样带来的随机游动行为,提出采用有序超松弛迭代方法来抽取目标动量项.同时,提出自适应步长的Hamiltonian动力学实现方法,在跟踪过程中自适应地调整步长,以减少模拟误差.提出的跟踪算法可以避免传统的基于随机游动的MCMC跟踪算法所存在的局部最优问题,提高了跟踪的准确性而不需要额外的计算时间.实验结果表明,该算法在处理多种类型的突变运动时表现出出色的处理能力.     

运动目标跟踪系统的遮挡问题处理

遮挡是运动目标跟踪研究中的一个重要问题,介绍了基于Markov Chain Monte Carlo(MCMC)的运动物体遮挡问题解决方法.该方法通过建立贝叶斯模型,确定先验概率和条件概率,将车辆分割问题看成求后验概率最大时的车辆状态;然后运用MCMC方法对后验概率进行估计,设计MCMC标准对后验概率进行采样,用长方形模型来近似车辆外形.实验证明MCMC方法在不需对车辆单独初始化的前提下能有效的将相互遮挡的车辆分割出来,检测出车辆之间的相互遮挡.     

DECODE: a new method for discovering clusters of different densities in spatial data

When clusters with different densities and noise lie in a spatial point set, the major obstacle to classifying these data is the determination of the thresholds for classification, which may form a series of bins for allocating each point to different clusters. Much of the previous work has adopted a model-based approach, but is either incapable of estimating the thresholds in an automatic way, or limited to only two point processes, i.e. noise and clusters with the same density. In this paper, we present a new density-based cluster method (DECODE), in which a spatial data set is presumed to consist of different point processes and clusters with different densities belong to different point processes. DECODE is based upon a reversible jump Markov Chain Monte Carlo (MCMC) strategy and divided into three steps. The first step is to map each point in the data to its mth nearest distance, which is referred to as the distance between a point and its mth nearest neighbor. In the second step, classification thresholds are determined via a reversible jump MCMC strategy. In the third step, clusters are formed by spatially connecting the points whose mth nearest distances fall into a particular bin defined by the thresholds. Four experiments, including two simulated data sets and two seismic data sets, are used to evaluate the algorithm. Results on simulated data show that our approach is capable of discovering the clusters automatically. Results on seismic data suggest that the clustered earthquakes, identified by DECODE, either imply the epicenters of forthcoming strong earthquakes or indicate the areas with the most intensive seismicity, this is consistent with the tectonic states and estimated stress distribution in the associated areas. The comparison between DECODE and other state-of-the-art methods, such as DBSCAN, OPTICS and Wavelet Cluster, illustrates the contribution of our approach: although DECODE can be computationally expensive, it is capable of identifying the number of point processes and simultaneously estimating the classification thresholds with little prior knowledge.     

基于贝叶斯推理的包装件动力学模型优化选择研究

目的 在多种类型的模型中挑选出最优包装件模型,并实现参数识别的方法。方法 文中将包装件模型构建为参数不确定模型,在贝叶斯推理的框架下,采用马尔可夫链蒙特卡洛法识别模型参数,采用偏差信息准则(DIC)计算各备选模型的DIC参数,选择出最优包装件模型。结果 在振动实验台用质量块–缓冲材料模拟包装件并进行随机振动测试,分析结果表明,Bouc–Wen(n=2)模型为文中包装系统的最佳模型。结论 文中提出的基于贝叶斯推理的包装件模型优化选择和参数识别方法考虑了模型不确定性,构建的模型可准确预测包装件在随机振动下加速度响应的时域信号。     

MIMO系统中低复杂度的MCMC迭代检测算法

针对多输入多输出(MIMO)系统中现行的马尔科夫链蒙特卡洛(MCMC)检测算法复杂度较高的问题,提出了一种SIC-MMSE算法辅助的MCMC检测算法,信号的预估计值和软信息均作为软输入软输出(SISO)检测器的输入,提高了吉布斯采样值的可信度,进而减少采样点数。仿真结果表明,同样的信噪比情况下,达到相同误码率时,与传统MCMC算法相比,改进MCMC算法的复杂度明显降低。     

基于分层转移的粒子滤波MCMC重采样算法

针对粒子滤波中如何设计重采样策略以解决“权值蜕化”,同时又可避免“样本贫化”的问题,提出一种基于分层转移的Monte Carlo Markov链（MCMC）重采样算法．当样本容量检测出现“蜕化”时,将样本集按权值蜕化程度进行分层,利用提出的变异繁殖算法,将其与PSO融合产生MCMC转移核,并施以分层子集;然后通过Metroplis—Hastings算法进行接收-拒绝采样,由此构建的Markov链可收敛到与目标真实后验等价的平稳分布．数值仿真结果表明,所提出的算法能以更快的收敛速度和更小的估计误差贴近目标真实后验,从而提高了估计精度．     

A Bayesian analysis of spherical pattern based on finite Langevin mixture

Parameter estimation is a cornerstone of most fundamental problems of statistical research and practice. In particular, finite mixture models have long been heavily relied on deterministic approaches such as expectation maximization (EM). Despite their successful utilization in wide spectrum of areas, they have inclined to converge to local solutions. An alternative approach is the adoption of Bayesian inference that naturally addresses data uncertainty while ensuring good generalization. To this end, in this paper we propose a fully Bayesian approach for Langevin mixture model estimation and selection via MCMC algorithm based on Gibbs sampler, Metropolis–Hastings and Bayes factors. We demonstrate the effectiveness and the merits of the proposed learning framework through synthetic data and challenging applications involving topic detection and tracking and image categorization.     

GPU accelerated MCMC for modeling terrorist activity

The use of graphical processing unit (GPU) parallel processing is becoming a part of mainstream statistical practice. The reliance of Bayesian statistics on Markov Chain Monte Carlo (MCMC) methods makes the applicability of parallel processing not immediately obvious. It is illustrated that there are substantial gains in improved computational time for MCMC and other methods of evaluation by computing the likelihood using GPU parallel processing. Examples use data from the Global Terrorism Database to model terrorist activity in Colombia from 2000 through 2010 and a likelihood based on the explicit convolution of two negative-binomial processes. Results show decreases in computational time by a factor of over 200. Factors influencing these improvements and guidelines for programming parallel implementations of the likelihood are discussed.     

MCMC algorithms for Subset Simulation

Subset Simulation is an adaptive simulation method that efficiently solves structural reliability problems with many random variables. The method requires sampling from conditional distributions, which is achieved through Markov Chain Monte Carlo (MCMC) algorithms. This paper discusses different MCMC algorithms proposed for Subset Simulation and introduces a novel approach for MCMC sampling in the standard normal space. Two variants of the algorithm are proposed: a basic variant, which is simpler than existing algorithms with equal accuracy and efficiency, and a more efficient variant with adaptive scaling. It is demonstrated that the proposed algorithm improves the accuracy of Subset Simulation, without the need for additional model evaluations.