关于树指标隐Markov链及其等价定义

本文参照直线上隐Markov模型的概念,给出有限树指标隐Markov链的定义.在该定义中,树指标隐Markov链由两个树指标随机过程组成,其中第一个树指标随机过程是树指标Markov链,是不能被直接观测到的隐藏链;第二个树指标随机过程是可被观测的且关于第一个树指标随机过程条件独立,对于树上的任意一个顶点,第二个随机过程此处的取值只信赖于隐藏链中此处的取值.最后,我们给出了树指标隐Markov链的三个等价定义.     

新高阶多变量马尔可夫模型

本文提出了一种新高阶多变量马尔可夫模型,并对其收敛性进行了分析.给出了模型的参数估计方法.数值实验表明在预测精度方面新高阶多变量马尔可夫模型比高阶多变量马尔可夫模型更加有效.     

The Uncertainty of Storm Season Changes: Quantifying the Uncertainty of Autocovariance Changepoints

In oceanography, there is interest in determining storm season changes for logistical reasons such as equipment maintenance scheduling. In particular, there is interest in capturing the uncertainty associated with these changes in terms of the number and location of them. Such changes are associated with autocovariance changes. This article proposes a framework to quantify the uncertainty of autocovariance changepoints in time series motivated by this oceanographic application. More specifically, the framework considers time series under the locally stationary wavelet (LSW) framework, deriving a joint density for scale processes in the raw wavelet periodogram. By embedding this density within a hidden Markov model (HMM) framework, we consider changepoint characteristics under this multiscale setting. Such a methodology allows us to model changepoints and their uncertainty for a wide range of models, including piecewise second-order stationary processes, for example, piecewise moving average processes.     

马氏环境中马氏链的重对数律

本文讨论具有离散参数的马氏环境中马氏链的基本性质,研究了R_θ-链,得到了马氏环境中马氏链的重对数律成立的充分条件。     

非齐次马氏链样本相对熵率存在定理

样本相对熵率是信息论中一个重要的内容,在统计假设检验及编码理论中起着非常重要的作用.本文的目的是要研究在有限状态空间中取值的非齐次马氏链样本相对熵率的存在性.首先将数列绝对平均收敛的定义推广到平面上,并得到平面点列绝对平均收敛的定义及相关引理,然后利用非齐次马氏链二元函数的一类平均极限定理及强大数定律,给出非齐次马氏链样本相对熵率存在的条件.本文将信息论中关于独立同分布随机变量序列的假设检验问题做了更为广泛的推广.     

Markov chain Monte Carlo in Bayesian models for testing gamma and lognormal S-type process qualities

The process capability index C_pu is widely used to measure S-type process quality. Many researchers have presented adaptive techniques for assessing the true C_pu assuming normality. However, the quality characteristic is often abnormal, and the derived techniques based on the normality assumption could mislead the manager into making uninformed decisions. Therefore, this study provides an alternative method for assessing C_pu of non-normal processes. The Markov chain Monte Carlo, an emerging popular statistical tool, is integrated into Bayesian models to seek the empirical posterior distributions of specific gamma and lognormal parameters. Afterwards, the lower credible interval bound of C_pu can be derived for testing the non-normal process quality. Simulations show that the proposed method is adaptive and has good performance in terms of coverage probability.     

关于齐次树指标马氏链的广义熵遍历定理

本文主要研究有限状态齐次树指标Markov链的强大数定律和广义熵遍历定理．熵遍历定理研究的是信息论中信源的渐近均分割性,树指标Markov链是近年来概率论的研究方向之一．首先,参照非齐次Markov链广义熵密度概念,本文给出了树指标Markov链的广义熵密度的定义．然后,通过构造一组期望值为1的随机变量,利用Markov不等式和Borel-Cantelli引理,证明得到了定义在树指标Markov链上一类随机变量的延迟平均的强极限定理．最后,利用上述定理的推论,我们证明得到了Cayley树上有限状态Markov链状态出现次数的延迟平均的强大数定律和广义熵遍历定理．本文的结果是对一些已有结果的推广．     

Ruin Probability in a Generalised Risk Process under Rates of Interest with Homogenous Markov Chains

This article explores recursive and integral equations for ruin probabilities of generalised risk processes, under rates of interest with homogenous Markov chain claims and homogenous Markov chain premiums. We assume that claim and premium take a countable number of non-negative values. Generalised Lundberg inequalities for the ruin probabilities of these processes are derived via a recursive technique. Recursive equations for finite time ruin probabilities and an integral equation for the ultimate ruin probability are presented, from which corresponding probability inequalities and upper bounds are obtained. An illustrative numerical example is discussed.     

多重序列比对Alignment的信息度量准则

多重序列的比对（Alignment)的核心问题是对多重DNA（或RNA，蛋白质）序列，寻找它们的相似部分或稳定区域，但如何定义多重序列的相似度（或罚分函数）则是解决多重序列经对的前提。首先对多重序列相似度的合理性进行了讨论，给出了一组合理的相似度所必需具备的条件，再利用Shannon熵的特点，给出一个满足这些合理性条件的多重序列比对的优化准则。     

基于Markov链的重组细胞恒化培养的随机建模分析

本文研究了一类重组细胞恒化培养的连续时间Markov链模型.首先利用累积母函数表示出数字特征所满足的矩方程,然后通过对数正态分布近似的矩封闭技术得到了封闭后的矩方程,最后运用Euler-Maruyama方法构建了时间和状态都是连续的It随机微分方程.为了验证矩封闭的合理性,利用数值模拟给出了确定模型、随机模型和矩封闭后的方程的比较,并分析了重组细胞的变化趋势,结果表明其随机游走趋势与相应确定性模型是一致的.     

区域物流规模的改进灰色马尔可夫预测

在分析灰色GM(1,1)方法、灰色马尔可夫方法的基础上,建立区域物流规模预测的改进灰色马尔可夫模型,以国家统计局公布的陕西省1997-2006年货物周转量的统计数据为依据,对其2007-2008年的物流规模进行预测.与灰色GM(1,1)方法、灰色马尔可夫方法的预测结果相比,改进灰色马尔可夫链模型对区域物流规模的预测更加有效.     

一种基于马尔可夫随机场的运动目标检测算法

本文提出了一种基于马尔可夫随机场的运动目标检测算法.针对传统时间分割使用主观固定阁值的缺点,使用马尔可夫随机场模型对差分图像建模,并提出了一种新的模型阶次选择算法,以及一种可以加速收敛过程的随机场迭代算法.采用期望最大算法获取高斯分布参数并检测运动变化区域,利用形态学运算修正时间分割模板;空间分割部分提出了基于人眼视觉特征的改进分水岭算法,有效地解决了过分割问题;最后对时、空间分割结果进行信息融合处理,从而得到完整的运动目标.仿真实验结果证明了本文算法可以有效地分割视频运动目标.     

A new methodology for Bayesian history matching using parallel interacting Markov chain Monte Carlo

This paper presents an innovative application of a new class of parallel interacting Markov chains Monte Carlo to solve the Bayesian history matching (BHM) problem. BHM consists of sampling a posterior distribution given by the Bayesian theorem. Markov chain Monte Carlo (MCMC) is well suited for sampling, in principle, any type of distribution; however the number of iteration required by the traditional single-chain MCMC can be prohibitive in BHM applications. Furthermore, history matching is typically a highly nonlinear inverse problem, which leads in very complex posterior distributions, characterized by many separated modes. Therefore, single chain can be trapped into a local mode. Parallel interacting chains is an interesting way to overcome this problem, as shown in this paper. In addition, we presented new approaches to define starting points for the parallel chains. For validation purposes, the proposed methodology is firstly applied in a simple but challenging cross section reservoir model with many modes in the posterior distribution. Afterwards, the application to a realistic case integrated to geostatistical modelling is also presented. The results showed that the combination of parallel interacting chain with the capabilities of distributed computing commonly available nowadays is very promising to solve the BHM problem.     

Parameters Estimation for Condition Based Maintenance with Uncorrelated and Correlated Observations

Condition Based Maintenance (CBM) is based on the assessment of equipment state which is obtained by measuring some indicators. When there is uncertainty concerning the state of the equipment, the measurements gathered are called imperfect. In this case the equipment aging and degradation process is assumed to follow a Markov process and is modeled by a Hidden Markov Model (HMM). This article describes a general procedure that can be used to estimate the parameters of the HMM. It is based on the Expectation-Maximization (EM) algorithm. The procedure deals with independent as well as correlated maintenance observations. The latter are most common in CBM applications. Simulated examples are presented.     

Analysis of quality-caused re-entrance electrical test system in semiconductor manufacturing by Markov method

The electrical test system is one of the key components in semiconductor assembly and test factories. The products arrive at the system in lots and the processing times in the system are related to lot size. In the system, defective lots are identified by the tester machine and then analysed by engineers. The defective lots are subsequently reworked in the tester, forming a re-entrance system. This paper analyses system performance with respect to quality rate and system design parameters to provide suggestions for system improvement. A queue network model based on a semiconductor electrical test procedure is constructed, and system performance is obtained by the Markov method. The performance forecast, quality sensitivity analysis, and system improvement for a case study carried out in a factory are described in detail. The results show that the proposed method is valuable for system performance evaluation and improvement.     

火灾事故的灰色-马尔可夫模型预测研究

鉴于火灾事故的发生受多种复杂因素的影响,并且具有较大的随机性和波动性的特点,笔者等将灰色模型和马尔可夫模型相结合,建立火灾事故的灰色?马尔可夫模型,利用灰色模型的灰色性和马尔可夫模型的随机性来体现各自的优点,并运用该模型对全国农村火灾事故进行预测。实际应用表明,灰色?马尔可夫模型的预测精度明显高于灰色模型的预测精度,完全能满足预测精度的要求,可以较好地用于火灾事故的预测。     

中国手语手势词识别的一种快速方法

选取Cyberglove型号数据手套作为手语输入设备,采用DGMM（Dynamic Gaussian Mixture Model)作为手势词识别技术,提出了基于相对熵的搜索策略,并将其应用于基于半连续DGMM的手势词识别中以提高手势词识别速度。实验结果表明,采用搜索策略后手势识别效果与原来相当,而识别速度提高了近15倍。     

Modeling of Particle Concentration Distribution in a Fluidized Bed by Means of the Theory of Markov Chains

A one-dimensional mathematical model of particulate solids fluidization based on the theory of Markov chains is proposed. Transition probabilities that form the matrix and control the migration of particles over the bed are subdivided into two types, convection and diffusion. The convection transition probabilities depend on the local particle concentration in cells of the chain and mainly define the bed expansion at certain hydrodynamic conditions. The diffusion transition probabilities form particle concentration distribution over the bed height. On the basis of the model, the heat exchange between gas and particulate solids is described. The batch fluidization model is generalized to the case of continuous fluidization that allows predicting a connection between throughput and hold-up, as well as particle residence time distribution in a bed. Some aspects of the approach are verified experimentally.     

A multi-state Markov model for a short-term reliability analysis of a power generating unit

This paper presents a multi-state Markov model for a coal power generating unit. The paper proposes a technique for the estimation of transition intensities (rates) between the various generating capacity levels of the unit based on field observation. The technique can be applied to such units where output generating capacity is uniformly distributed. In order to estimate the transition intensities a special Markov chain embedded in the observed capacity process was defined. By using this technique, all transition intensities can be estimated from the observed realization of the unit generating capacity stochastic process. The proposed multi-state Markov model was used to calculate important reliability indices such as the Forced Outage Rate (FOR), the Expected Energy Not Supplied (EENS) to consumers, etc. These indices were found for short-time periods (about 100 h). It was shown that these indices are sensibly different from those calculated for a long-term range. Such Markov models could be very useful for power system security analysis and short-term operating decisions.     

采用马氏模型的点状动目标快速检测方法

提出了一种视频序列图像中点状运动目标三维快速检测方法。该方法利用目标运动的时域连续性假设,将目标在相邻多帧上的位置状态模型化为二阶马尔可夫数据链;依照该模型采用沿轨迹集成的检测算法,克服了传统三维检测造成搜索次数巨大的弱点,同时也避免了二维投影检测带来的信噪比下降。理论分析和仿真试验表明,该检测方法能稳定地检测出信号杂波噪声比（SCNR）超过3的缓动点状运动目标,而且在采用5帧集成时计算量比传统的穷尽轨迹匹配检测减少100倍。