Estimation in autoregressive models with Markov regime
Ríos, Ricardo; Rodríguez, Luis
2005-01-01
In this paper we derive the consistency of the penalized likelihood method for the number state of the hidden Markov chain in autoregressive models with Markov regimen. Using a SAEM type algorithm to estimate the models parameters. We test the null hypothesis of hidden Markov Model against an autoregressive process with Markov regime.
A new approach to simulating stream isotope dynamics using Markov switching autoregressive models
Birkel, Christian; Paroli, Roberta; Spezia, Luigi; Dunn, Sarah M.; Tetzlaff, Doerthe; Soulsby, Chris
2012-09-01
In this study we applied Markov switching autoregressive models (MSARMs) as a proof-of-concept to analyze the temporal dynamics and statistical characteristics of the time series of two conservative water isotopes, deuterium (δ2H) and oxygen-18 (δ18O), in daily stream water samples over two years in a small catchment in eastern Scotland. MSARMs enabled us to explicitly account for the identified non-linear, non-Normal and non-stationary isotope dynamics of both time series. The hidden states of the Markov chain could also be associated with meteorological and hydrological drivers identifying the short (event) and longer-term (inter-event) transport mechanisms for both isotopes. Inference was based on the Bayesian approach performed through Markov Chain Monte Carlo algorithms, which also allowed us to deal with a high rate of missing values (17%). Although it is usually assumed that both isotopes are conservative and exhibit similar dynamics, δ18O showed somewhat different time series characteristics. Both isotopes were best modelled with two hidden states, but δ18O demanded autoregressions of the first order, whereas δ2H of the second. Moreover, both the dynamics of observations and the hidden states of the two isotopes were explained by two different sets of covariates. Consequently use of the two tracers for transit time modelling and hydrograph separation may result in different interpretations on the functioning of a catchment system.
Birkel, C.; Paroli, R.; Spezia, L.; Tetzlaff, D.; Soulsby, C.
2012-12-01
In this paper we present a novel model framework using the class of Markov Switching Autoregressive Models (MSARMs) to examine catchments as complex stochastic systems that exhibit non-stationary, non-linear and non-Normal rainfall-runoff and solute dynamics. Hereby, MSARMs are pairs of stochastic processes, one observed and one unobserved, or hidden. We model the unobserved process as a finite state Markov chain and assume that the observed process, given the hidden Markov chain, is conditionally autoregressive, which means that the current observation depends on its recent past (system memory). The model is fully embedded in a Bayesian analysis based on Markov Chain Monte Carlo (MCMC) algorithms for model selection and uncertainty assessment. Hereby, the autoregressive order and the dimension of the hidden Markov chain state-space are essentially self-selected. The hidden states of the Markov chain represent unobserved levels of variability in the observed process that may result from complex interactions of hydroclimatic variability on the one hand and catchment characteristics affecting water and solute storage on the other. To deal with non-stationarity, additional meteorological and hydrological time series along with a periodic component can be included in the MSARMs as covariates. This extension allows identification of potential underlying drivers of temporal rainfall-runoff and solute dynamics. We applied the MSAR model framework to streamflow and conservative tracer (deuterium and oxygen-18) time series from an intensively monitored 2.3 km2 experimental catchment in eastern Scotland. Statistical time series analysis, in the form of MSARMs, suggested that the streamflow and isotope tracer time series are not controlled by simple linear rules. MSARMs showed that the dependence of current observations on past inputs observed by transport models often in form of the long-tailing of travel time and residence time distributions can be efficiently explained by
Directory of Open Access Journals (Sweden)
Githure John I
2009-09-01
Full Text Available Abstract Background Autoregressive regression coefficients for Anopheles arabiensis aquatic habitat models are usually assessed using global error techniques and are reported as error covariance matrices. A global statistic, however, will summarize error estimates from multiple habitat locations. This makes it difficult to identify where there are clusters of An. arabiensis aquatic habitats of acceptable prediction. It is therefore useful to conduct some form of spatial error analysis to detect clusters of An. arabiensis aquatic habitats based on uncertainty residuals from individual sampled habitats. In this research, a method of error estimation for spatial simulation models was demonstrated using autocorrelation indices and eigenfunction spatial filters to distinguish among the effects of parameter uncertainty on a stochastic simulation of ecological sampled Anopheles aquatic habitat covariates. A test for diagnostic checking error residuals in an An. arabiensis aquatic habitat model may enable intervention efforts targeting productive habitats clusters, based on larval/pupal productivity, by using the asymptotic distribution of parameter estimates from a residual autocovariance matrix. The models considered in this research extends a normal regression analysis previously considered in the literature. Methods Field and remote-sampled data were collected during July 2006 to December 2007 in Karima rice-village complex in Mwea, Kenya. SAS 9.1.4® was used to explore univariate statistics, correlations, distributions, and to generate global autocorrelation statistics from the ecological sampled datasets. A local autocorrelation index was also generated using spatial covariance parameters (i.e., Moran's Indices in a SAS/GIS® database. The Moran's statistic was decomposed into orthogonal and uncorrelated synthetic map pattern components using a Poisson model with a gamma-distributed mean (i.e. negative binomial regression. The eigenfunction
A flexible prior distribution for Markov switching autoregressions with Student-t errors
Philippe J. DESCHAMPS
2012-01-01
This paper proposes an empirical Bayes approach for Markov switching autoregressions that can constrain some of the state-dependent parameters (regression coefficients and error variances) to be approximately equal across regimes. By flexibly reducing the dimension of the parameter space, this can help to ensure regime separation and to detect the Markov switching nature of the data. The permutation sampler with a hierarchical prior is used for choosing the prior moments, the identification c...
Directory of Open Access Journals (Sweden)
Michael Seifert
Full Text Available Changes in gene expression programs play a central role in cancer. Chromosomal aberrations such as deletions, duplications and translocations of DNA segments can lead to highly significant positive correlations of gene expression levels of neighboring genes. This should be utilized to improve the analysis of tumor expression profiles. Here, we develop a novel model class of autoregressive higher-order Hidden Markov Models (HMMs that carefully exploit local data-dependent chromosomal dependencies to improve the identification of differentially expressed genes in tumor. Autoregressive higher-order HMMs overcome generally existing limitations of standard first-order HMMs in the modeling of dependencies between genes in close chromosomal proximity by the simultaneous usage of higher-order state-transitions and autoregressive emissions as novel model features. We apply autoregressive higher-order HMMs to the analysis of breast cancer and glioma gene expression data and perform in-depth model evaluation studies. We find that autoregressive higher-order HMMs clearly improve the identification of overexpressed genes with underlying gene copy number duplications in breast cancer in comparison to mixture models, standard first- and higher-order HMMs, and other related methods. The performance benefit is attributed to the simultaneous usage of higher-order state-transitions in combination with autoregressive emissions. This benefit could not be reached by using each of these two features independently. We also find that autoregressive higher-order HMMs are better able to identify differentially expressed genes in tumors independent of the underlying gene copy number status in comparison to the majority of related methods. This is further supported by the identification of well-known and of previously unreported hotspots of differential expression in glioblastomas demonstrating the efficacy of autoregressive higher-order HMMs for the analysis of individual
Bias-correction in vector autoregressive models: A simulation study
DEFF Research Database (Denmark)
Engsted, Tom; Pedersen, Thomas Quistgaard
We analyze and compare the properties of various methods for bias-correcting parameter estimates in vector autoregressions. First, we show that two analytical bias formulas from the existing literature are in fact identical. Next, based on a detailed simulation study, we show that this simple and...... pushing an otherwise stationary model into the non-stationary region of the parameter space during the process of correcting for bias....
DEFF Research Database (Denmark)
Pinson, Pierre; Madsen, Henrik
2008-01-01
Better modelling and forecasting of very short-term power fluctuations at large offshore wind farms may significantly enhance control and management strategies of their power output. The paper introduces a new methodology for modelling and forecasting such very short-term fluctuations. The proposed...... methodology is based on a Markov-switching autoregressive model with time-varying coefficients. An advantage of the method is that one can easily derive full predictive densities. The quality of this methodology is demonstrated from the test case of 2 large offshore wind farms in Denmark. The exercise...... consists in 1-step ahead forecasting exercise on time-series of wind generation with a time resolution of 10 minute. The quality of the introduced forecasting methodology and its interest for better understanding power fluctuations are finally discussed....
Institute of Scientific and Technical Information of China (English)
DONG Ming
2008-01-01
As a new maintenance method, CBM (condition based maintenance) is becoming more and more important for the health management of complicated and costly equipment. A prerequisite to widespread deployment of CBM technology and prac-tice in industry is effective diagnostics and prognostics. Recently, a pattern recog-nition technique called HMM (hidden Markov model) was widely used in many fields. However, due to some unrealistic assumptions, diagnositic results from HMM were not so good, and it was difficult to use HMM directly for prognosis. By relaxing the unrealistic assumptions in HMM, this paper presents a novel approach to equip-ment health management based on auto-regressive hidden semi-Markov model (AR-HSMM). Compared with HMM, AR-HSMM has three advantages: 1)It allows explicitly modeling the time duration of the hidden states and therefore is capable of prognosis. 2) It can relax observations' independence assumption by accom-modating a link between consecutive observations. 3) It does not follow the unre-alistic Markov chain's memoryless assumption and therefore provides more pow-erful modeling and analysis capability for real problems. To facilitate the computation in the proposed AR-HSMM-based diagnostics and prognostics, new forwardbackward variables are defined and a modified forward-backward algorithm is developed. The evaluation of the proposed methodology was carried out through a real world application case study: health diagnosis and prognosis of hydraulic pumps in Caterpillar Inc. The testing results show that the proposed new approach based on AR-HSMM is effective and can provide useful support for the decision-making in equipment health management.
DEFF Research Database (Denmark)
Pinson, Pierre; Madsen, Henrik
Wind power production data at temporal resolutions of a few minutes exhibits successive periods with fluctuations of various dynamic nature and magnitude, which cannot be explained (so far) by the evolution of some explanatory variable. Our proposal is to capture this regime-switching behaviour...... recursively optimized is based on penalized maximum-likelihood, with exponential forgetting of past observations. MSAR models are then employed for 1-step-ahead point forecasting of 10-minute resolution time-series of wind power at two large offshore wind farms. They are favourably compared against...... persistence and AutoRegressive (AR) models. It is finally shown that the main interest of MSAR models lies in their ability to generate interval/density forecasts of significantly higher skill....
DEFF Research Database (Denmark)
Pinson, Pierre; Madsen, Henrik
2012-01-01
Wind power production data at temporal resolutions of a few minutes exhibit successive periods with fluctuations of various dynamic nature and magnitude, which cannot be explained (so far) by the evolution of some explanatory variable. Our proposal is to capture this regime-switching behaviour with...... recursively optimized is based on penalized maximum likelihood, with exponential forgetting of past observations. MSAR models are then employed for one-step-ahead point forecasting of 10 min resolution time series of wind power at two large offshore wind farms. They are favourably compared against persistence...... and autoregressive models. It is finally shown that the main interest of MSAR models lies in their ability to generate interval/density forecasts of significantly higher skill....
Revisiting Weak Simulation for Substochastic Markov Chains
DEFF Research Database (Denmark)
Jansen, David N.; Song, Lei; Zhang, Lijun
2013-01-01
The spectrum of branching-time relations for probabilistic systems has been investigated thoroughly by Baier, Hermanns, Katoen and Wolf (2003, 2005), including weak simulation for systems involving substochastic distributions. Weak simulation was proven to be sound w.r.t. the liveness fragment...... of the logic PCTL\\x, and its completeness was conjectured. We revisit this result and show that soundness does not hold in general, but only for Markov chains without divergence. It is refuted for some systems with substochastic distributions. Moreover, we provide a counterexample to completeness....... In this paper, we present a novel definition that is sound for live PCTL\\x, and a variant that is both sound and complete. A long version of this article containing full proofs is available from [11]....
Markov chain analysis of single spin flip Ising simulations
International Nuclear Information System (INIS)
The Markov processes defined by random and loop-based schemes for single spin flip attempts in Monte Carlo simulations of the 2D Ising model are investigated, by explicitly constructing their transition matrices. Their analysis reveals that loops over all lattice sites using a Metropolis-type single spin flip probability often do not define ergodic Markov chains, and have distorted dynamical properties even if they are ergodic. The transition matrices also enable a comparison of the dynamics of random versus loop spin selection and Glauber versus Metropolis probabilities
Directory of Open Access Journals (Sweden)
Vasios C.E.
2003-01-01
Full Text Available In the present work, a new method for the classification of Event Related Potentials (ERPs is proposed. The proposed method consists of two modules: the feature extraction module and the classification module. The feature extraction module comprises the implementation of the Multivariate Autoregressive model in conjunction with the Simulated Annealing technique, for the selection of optimum features from ERPs. The classification module is implemented with a single three-layer neural network, trained with the back-propagation algorithm and classifies the data into two classes: patients and control subjects. The method, in the form of a Decision Support System (DSS, has been thoroughly tested to a number of patient data (OCD, FES, depressives and drug users, resulting successful classification up to 100%.
Directory of Open Access Journals (Sweden)
Carlos Alejandro De Luna Ortega
2006-01-01
Full Text Available En este artículo se aborda el diseño de un reconocedor de voz, con el idioma español mexicano, del estado de Aguascalientes, de palabras aisladas, con dependencia del hablante y vocabulario pequeño, empleando Redes Neuronales Artificiales (ANN por sus siglas en inglés, Alineamiento Dinámico del Tiempo (DTW por sus siglas en inglés y Modelos Ocultos de Markov (HMM por sus siglas en inglés para la realización del algoritmo de reconocimiento.
Parallel algorithms for simulating continuous time Markov chains
Nicol, David M.; Heidelberger, Philip
1992-01-01
We have previously shown that the mathematical technique of uniformization can serve as the basis of synchronization for the parallel simulation of continuous-time Markov chains. This paper reviews the basic method and compares five different methods based on uniformization, evaluating their strengths and weaknesses as a function of problem characteristics. The methods vary in their use of optimism, logical aggregation, communication management, and adaptivity. Performance evaluation is conducted on the Intel Touchstone Delta multiprocessor, using up to 256 processors.
Cost Effective Community Based Dementia Screening: A Markov Model Simulation
Directory of Open Access Journals (Sweden)
Erin Saito
2014-01-01
Full Text Available Background. Given the dementia epidemic and the increasing cost of healthcare, there is a need to assess the economic benefit of community based dementia screening programs. Materials and Methods. Markov model simulations were generated using data obtained from a community based dementia screening program over a one-year period. The models simulated yearly costs of caring for patients based on clinical transitions beginning in pre dementia and extending for 10 years. Results. A total of 93 individuals (74 female, 19 male were screened for dementia and 12 meeting clinical criteria for either mild cognitive impairment (n=7 or dementia (n=5 were identified. Assuming early therapeutic intervention beginning during the year of dementia detection, Markov model simulations demonstrated 9.8% reduction in cost of dementia care over a ten-year simulation period, primarily through increased duration in mild stages and reduced time in more costly moderate and severe stages. Discussion. Community based dementia screening can reduce healthcare costs associated with caring for demented individuals through earlier detection and treatment, resulting in proportionately reduced time in more costly advanced stages.
Variance reduction techniques in the simulation of Markov processes
International Nuclear Information System (INIS)
We study a functional r of the stationary distribution of a homogeneous Markov chain. It is often difficult or impossible to perform the analytical calculation of r and so it is reasonable to estimate r by a simulation process. A consistent estimator r(n) of r is obtained with respect to a chain with a countable state space. Suitably modifying the estimator r(n) of r one obtains a new consistent estimator which has a smaller variance than r(n). The same is obtained in the case of finite state space
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbek, Anders Christian; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time...
DEFF Research Database (Denmark)
Fokianos, Konstantinos; Rahbæk, Anders; Tjøstheim, Dag
This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, making an interpretation as an integer valued GARCH process possible. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for...
Institute of Scientific and Technical Information of China (English)
刘震; 王厚军; 龙兵; 张治国
2009-01-01
针对电子系统状态趋势预测问题,提出了一种加权隐马尔可夫模型的自回归趋势预测方法.该方法以自回归模型作为隐马尔可夫的状态输出,利用加权预测思想对马尔可夫链中的隐状态进行混合高斯模型的加权序列预测,并利用最大概率隐状态下的自回归系数计算模型输出.通过对实际的复杂混沌序列和电子系统BIT状态数据进行趋势预测,并针对不同模型参数下的预测结果进行实验分析,结果表明该方法对系统状态变化的趋势具有较好的预测性能.%A novel trend prediction approach based on weighed hidden Markov model (HMM) and autoregressive model (AR) is presented in order to solve this problem of bend prediction for complex electronic system. This approach regards the autoregressive model as the output of HMM, uses weighted prediction method and mixed Gaussianin model to predict the hidden state of Markov chain,and calculates the output of model by using the regression coefficient of the maximum probability hidden state. This approach is applied to the trend prediction of complex chaotic time series and typical electronic equipment's BIT data, and the effects of various model parameters on trend prediction precision are discussed.The experiments based on condition trend prediction for electronic equipments demonstrate the effectiveness of the method.
Simulation of daily rainfall through markov chain modeling
International Nuclear Information System (INIS)
Being an agricultural country, the inhabitants of dry land in cultivated areas mainly rely on the daily rainfall for watering their fields. A stochastic model based on first order Markov Chain was developed to simulate daily rainfall data for Multan, D. I. Khan, Nawabshah, Chilas and Barkhan for the period 1981-2010. Transitional probability matrices of first order Markov Chain was utilized to generate the daily rainfall occurrence while gamma distribution was used to generate the daily rainfall amount. In order to achieve the parametric values of mentioned cities, method of moments is used to estimate the shape and scale parameters which lead to synthetic sequence generation as per gamma distribution. In this study, unconditional and conditional probabilities of wet and dry days in sum with means and standard deviations are considered as the essential parameters for the simulated stochastic generation of daily rainfalls. It has been found that the computerized synthetic rainfall series concurred pretty well with the actual observed rainfall series. (author)
Noncausal Bayesian Vector Autoregression
DEFF Research Database (Denmark)
Lanne, Markku; Luoto, Jani
We propose a Bayesian inferential procedure for the noncausal vector autoregressive (VAR) model that is capable of capturing nonlinearities and incorporating effects of missing variables. In particular, we devise a fast and reliable posterior simulator that yields the predictive distribution as a...
Simulation-based algorithms for Markov decision processes
Chang, Hyeong Soo; Fu, Michael C; Marcus, Steven I
2013-01-01
Markov decision process (MDP) models are widely used for modeling sequential decision-making problems that arise in engineering, economics, computer science, and the social sciences. Many real-world problems modeled by MDPs have huge state and/or action spaces, giving an opening to the curse of dimensionality and so making practical solution of the resulting models intractable. In other cases, the system of interest is too complex to allow explicit specification of some of the MDP model parameters, but simulation samples are readily available (e.g., for random transitions and costs). For these settings, various sampling and population-based algorithms have been developed to overcome the difficulties of computing an optimal solution in terms of a policy and/or value function. Specific approaches include adaptive sampling, evolutionary policy iteration, evolutionary random policy search, and model reference adaptive search. This substantially enlarged new edition reflects the latest developments in novel ...
English, Thomas
2005-01-01
A standard tool of reliability analysis used at NASA-JSC is the event tree. An event tree is simply a probability tree, with the probabilities determining the next step through the tree specified at each node. The nodal probabilities are determined by a reliability study of the physical system at work for a particular node. The reliability study performed at a node is typically referred to as a fault tree analysis, with the potential of a fault tree existing.for each node on the event tree. When examining an event tree it is obvious why the event tree/fault tree approach has been adopted. Typical event trees are quite complex in nature, and the event tree/fault tree approach provides a systematic and organized approach to reliability analysis. The purpose of this study was two fold. Firstly, we wanted to explore the possibility that a semi-Markov process can create dependencies between sojourn times (the times it takes to transition from one state to the next) that can decrease the uncertainty when estimating time to failures. Using a generalized semi-Markov model, we studied a four element reliability model and were able to demonstrate such sojourn time dependencies. Secondly, we wanted to study the use of semi-Markov processes to introduce a time variable into the event tree diagrams that are commonly developed in PRA (Probabilistic Risk Assessment) analyses. Event tree end states which change with time are more representative of failure scenarios than are the usual static probability-derived end states.
Srinath, Sriakr; Rudy, Alexander R; Ammons, S Mark
2015-01-01
We present a sample-based, autoregressive (AR) method for the generation and time evolution of atmospheric phase screens that is computationally efficient and uses a single parameter per Fourier mode to vary the power contained in the frozen flow and stochastic components. We address limitations of Fourier-based methods such as screen periodicity and low spatial frequency power content. Comparisons of adaptive optics (AO) simulator performance when fed AR phase screens and translating phase screens reveal significantly elevated residual closed-loop temporal power for small increases in added stochastic content at each time step, thus displaying the importance of properly modeling atmospheric "boiling". We present preliminary evidence that our model fits to AO telemetry are better reflections of real conditions than the pure frozen flow assumption.
Using Markov models to simulate electron spin resonance spectra from molecular dynamics trajectories
Sezer, Deniz; Freed, Jack H.; Roux, Benoît
2008-01-01
Simulating electron spin resonance (ESR) spectra directly from molecular dynamics simulations of a spin labeled protein necessitates a large number (hundreds or thousands) of relatively long (hundreds of ns) trajectories. To meet this challenge, we explore the possibility of constructing accurate stochastic models of the spin label dynamics from atomistic trajectories. A systematic, two-step procedure, based on the probabilistic framework of hidden Markov models, is developed to build a discr...
Simulation of ion movement in soil using a continuous-time Markov process
International Nuclear Information System (INIS)
Simulation of solute transport using a continuous-time Markov process is a new approach for modeling chemical movement in soils. The authors describe the model and apply it to the results of tracer experiments on the transport of iodine, bromine, strontium and lithium in Bandalier tuff. The model successfully describes most of the data but was not able to simulate strontium displacement in the current study. The reasons for this are not clear
A fast exact simulation method for a class of Markov jump processes
International Nuclear Information System (INIS)
A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems
RESTART Simulation of Non-Markov Consecutive-K-Out-of-N: F Repairable Systems
Villén Altamirano, José
2010-01-01
The reliability of consecutive-k-out-of-n: F repairable systems and (k−1)-step Markov dependence is studied. The model analyzed in this paper is more general than those of previous studies given that repair time and component lifetimes are random variables that follow a general distribution. The system has one repair service which adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly dependable systems, the RESTART method wa...
Bayesian Variable Selection in Spatial Autoregressive Models
Jesus Crespo Cuaresma; Philipp Piribauer
2015-01-01
This paper compares the performance of Bayesian variable selection approaches for spatial autoregressive models. We present two alternative approaches which can be implemented using Gibbs sampling methods in a straightforward way and allow us to deal with the problem of model uncertainty in spatial autoregressive models in a flexible and computationally efficient way. In a simulation study we show that the variable selection approaches tend to outperform existing Bayesian model averaging tech...
Rudzinski, Joseph F; Bereau, Tristan
2016-01-01
Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between simulated and reference (e.g., from experiments or higher-level simulations) observables. To bound the microscopic information generated by computer simulations within reference measurements, we propose a method that reweights the microscopic transitions of the system to improve consistency with a set of coarse kinetic observables. The method employs the well-developed Markov state modeling framework to efficiently link microscopic dynamics with long-time scale constraints, thereby consistently addressing a wide range of time scales. To emphasize the robustness of the method, we consider two distinct coarse-grained models with significant kinetic inconsistencies. When applied to the simulated conformational dynamics of small peptides, the reweighting procedure systematically ...
Stochastic Differential Equations and Markov Processes in the Modeling of Electrical Circuits
Directory of Open Access Journals (Sweden)
R. Rezaeyan
2010-06-01
Full Text Available Stochastic differential equations(SDEs, arise from physical systems that possess inherent noise and certainty. We derive a SDE for electrical circuits. In this paper, we will explore the close relationship between the SDE and autoregressive(AR model. We will solve SDE related to RC circuit with using of AR(1 model (Markov process and however with Euler-Maruyama(EM method. Then, we will compare this solutions. Numerical simulations in MATLAB are obtained.
Institute of Scientific and Technical Information of China (English)
刘芳; 毛志忠
2011-01-01
针对过程工业中强噪声环境下实时采集的控制过程海量数据难以在线精确检测的问题,提出了基于阶数自学习自回归隐马尔可夫模型(ARHMM)的工业控制过程异常数据在线检测方法.该算法采用自同归(AR)模型对时间序列进行拟合,利用隐马尔科夫模型(HMM)作为数据检测的工具,避免了传统检测方法中需要预先设定检测阈值的问题,并将传统的BDT(Brockwell-Dahlhaus-Trindade)算法改进成为对于时间和阶数均实施迭代的双重迭代结构,以实现ARHMM参数在线更新.为了减小异常数据对ARHMM参数更新的影响,本文采用先检测后更新的方式,根据检测结果采取不同的更新方法,提高了该算法的鲁棒性.模型数据仿真与应用试验结果证明,该算法具有较高的检测精度和抗干扰能力,同时具备在线检测的能力.通过与传统基于AR模型的异常数据检测方法比较,证明了该方法更适合作为过程工业控制过程数据的异常检测工具.%For the accurate online detection and collection of massive real-time data of a control process in strong noise environment, we propose an autoregressive hidden Markov model (AJRHMM) algorithm with order self-learning. This algorithm employs an AR model to fit the time series and makes use of the hidden Markov model as the basic detection tool for avoiding the deficiency in presetting the threshold in traditional detection methods. In order to update the parameters of ARHMM online, we adopt the improved traditional BDT(Brockwell-Dahlhaus-Trindade) algorithm with double iterative structures, in which the iterative calculations are performed respectively for both time and order. To reduce the influence of outlier on parameter updating in ARHMM, we adopt the strategy of detection-before-update, and select the method for updating based on the detection results. This strategy improves the robustness of the algorithm. Simulation with emulation data and
Institute of Scientific and Technical Information of China (English)
Zhao Zhi-Jin; Zheng Shi-Lian; Xu Chun-Yun; Kong Xian-Zheng
2007-01-01
Hidden Markov models (HMMs) have been used to model burst error sources of wireless channels. This paper proposes a hybrid method of using genetic algorithm (GA) and simulated annealing (SA) to train HMM for discrete channel modelling. The proposed method is compared with pure GA, and experimental results show that the HMMs trained by the hybrid method can better describe the error sequences due to SA's ability of facilitating hill-climbing at the later stage of the search. The burst error statistics of the HMMs trained by the proposed method and the corresponding error sequences are also presented to validate the proposed method.
International Nuclear Information System (INIS)
Reliability assessments based on probabilistic fracture mechanics can give insight into the effects of changes in design parameters, operational conditions and maintenance schemes. Although they are often not capable of providing absolute reliability values, these methods at least allow the ranking of different solutions among alternatives. Due to the variety of possible solutions for design, operation and maintenance problems numerous probabilistic reliability assessments have to be carried out. This is a laborous task especially for crack containing welds of nuclear pipes subjected to fatigue. The objective of this paper is to compare the Monte Carlo simulation method and a newly developed approximative approach using the Markov process ansatz for this task
Energy Technology Data Exchange (ETDEWEB)
Vrugt, Jasper A [Los Alamos National Laboratory; Hyman, James M [Los Alamos National Laboratory; Robinson, Bruce A [Los Alamos National Laboratory; Higdon, Dave [Los Alamos National Laboratory; Ter Braak, Cajo J F [NETHERLANDS; Diks, Cees G H [UNIV OF AMSTERDAM
2008-01-01
Markov chain Monte Carlo (MCMC) methods have found widespread use in many fields of study to estimate the average properties of complex systems, and for posterior inference in a Bayesian framework. Existing theory and experiments prove convergence of well constructed MCMC schemes to the appropriate limiting distribution under a variety of different conditions. In practice, however this convergence is often observed to be disturbingly slow. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves in the Markov Chain. Here we show that significant improvements to the efficiency of MCMC simulation can be made by using a self-adaptive Differential Evolution learning strategy within a population-based evolutionary framework. This scheme, entitled DiffeRential Evolution Adaptive Metropolis or DREAM, runs multiple different chains simultaneously for global exploration, and automatically tunes the scale and orientation of the proposal distribution in randomized subspaces during the search. Ergodicity of the algorithm is proved, and various examples involving nonlinearity, high-dimensionality, and multimodality show that DREAM is generally superior to other adaptive MCMC sampling approaches. The DREAM scheme significantly enhances the applicability of MCMC simulation to complex, multi-modal search problems.
Rudzinski, Joseph F.; Kremer, Kurt; Bereau, Tristan
2016-02-01
Molecular simulations can provide microscopic insight into the physical and chemical driving forces of complex molecular processes. Despite continued advancement of simulation methodology, model errors may lead to inconsistencies between simulated and reference (e.g., from experiments or higher-level simulations) observables. To bound the microscopic information generated by computer simulations within reference measurements, we propose a method that reweights the microscopic transitions of the system to improve consistency with a set of coarse kinetic observables. The method employs the well-developed Markov state modeling framework to efficiently link microscopic dynamics with long-time scale constraints, thereby consistently addressing a wide range of time scales. To emphasize the robustness of the method, we consider two distinct coarse-grained models with significant kinetic inconsistencies. When applied to the simulated conformational dynamics of small peptides, the reweighting procedure systematically improves the time scale separation of the slowest processes. Additionally, constraining the forward and backward rates between metastable states leads to slight improvement of their relative stabilities and, thus, refined equilibrium properties of the resulting model. Finally, we find that difficulties in simultaneously describing both the simulated data and the provided constraints can help identify specific limitations of the underlying simulation approach.
A hidden Markov model combined with climate indices for multidecadal streamflow simulation
Bracken, C.; Rajagopalan, B.; Zagona, E.
2014-10-01
Hydroclimate time series often exhibit very low year-to-year autocorrelation while showing prolonged wet and dry epochs reminiscent of regime-shifting behavior. Traditional stochastic time series models cannot capture the regime-shifting features thereby misrepresenting the risk of prolonged wet and dry periods, consequently impacting management and planning efforts. Upper Colorado River Basin (UCRB) annual flow series highlights this clearly. To address this, a simulation framework is developed using a hidden Markov (HM) model in combination with large-scale climate indices that drive multidecadal variability. We demonstrate this on the UCRB flows and show that the simulations are able to capture the regime features by reproducing the multidecadal spectral features present in the data where a basic HM model without climate information cannot.
Simulating Replica Exchange: Markov State Models, Proposal Schemes, and the Infinite Swapping Limit.
Zhang, Bin W; Dai, Wei; Gallicchio, Emilio; He, Peng; Xia, Junchao; Tan, Zhiqiang; Levy, Ronald M
2016-08-25
Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host-guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE "simulations of simulations" as well as from relatively short runs of the actual replica exchange simulations. PMID:27079355
Adu, Nurlia; Indriati Retno, P.; Suharsono
2016-02-01
Monitoring of micro seismic activity in the geothermal field is useful to know the fracture controllers in the geothermal reservoir area. However, in determining the point of micro earthquake, hypocenters still contain inherent uncertainties due to several factors such as mismatches velocity model used by the actual subsurface conditions. For that reason, hypocenter relocation by Markov Chain method is used, to simulate the hypocenter point spatially based opportunities transition containing the principle of conditional probability. The purpose of this relocation is to improve the models of the hypocenter so that the interpretation of the subsurface structure is better. From the result of the relocation of using Markov Chain identified fault structures trending below the surface of the northeast-southwest (NE-SW) with approximately N38°E. This structure is suspected as the continuity of the structure in the surface. The depth of the hypocenter is located 758 m above mean sea level more than 800 m below mean sea level.
Generalizing smooth transition autoregressions
DEFF Research Database (Denmark)
Chini, Emilio Zanetti
We introduce a variant of the smooth transition autoregression - the GSTAR model - capable to parametrize the asymmetry in the tails of the transition equation by using a particular generalization of the logistic function. A General-to-Specific modelling strategy is discussed in detail, with part......We introduce a variant of the smooth transition autoregression - the GSTAR model - capable to parametrize the asymmetry in the tails of the transition equation by using a particular generalization of the logistic function. A General-to-Specific modelling strategy is discussed in detail...... forecasting experiment to evaluate its point and density forecasting performances. In all the cases, the dynamic asymmetry in the cycle is efficiently captured by the new model. The GSTAR beats AR and STAR competitors in point forecasting, while this superiority becomes less evident in density forecasting...
DIM SUM: demography and individual migration simulated using a Markov chain.
Brown, Jeremy M; Savidge, Kevin; McTavish, Emily Jane B
2011-03-01
An increasing number of studies seek to infer demographic history, often jointly with genetic relationships. Despite numerous analytical methods for such data, few simulations have investigated the methods' power and robustness, especially when underlying assumptions have been violated. DIM SUM (Demography and Individual Migration Simulated Using a Markov chain) is a stand-alone Java program for the simulation of population demography and individual migration while recording ancestor-descendant relationships. It does not employ coalescent assumptions or discrete population boundaries. It is extremely flexible, allowing the user to specify border positions, reactions of organisms to borders, local and global carrying capacities, individual dispersal kernels, rates of reproduction and strategies for sampling individuals. Spatial variables may be specified using image files (e.g., as exported from gis software) and may vary through time. In combination with software for genetic marker simulation, DIM SUM will be useful for testing phylogeographic (e.g., nested clade phylogeographic analysis, coalescent-based tests and continuous-landscape frameworks) and landscape-genetic methods, specifically regarding violations of coalescent assumptions. It can also be used to explore the qualitative features of proposed demographic scenarios (e.g. regarding biological invasions) and as a pedagogical tool. DIM SUM (with user's manual) can be downloaded from http://code.google.com/p/bio-dimsum. PMID:21429144
Autoregressive conditional beta
Yunmi Kim
2012-01-01
The capital asset pricing model provides various predictions about equilibrium expected returns on risky assets. One key prediction is that the risk premium on a risky asset is proportional to the nondiversifiable market risk measured by the asset's beta coefficient. This paper proposes a new method for estimating and drawing inferences from a time-varying capital asset pricing model. The proposed method, which can be considered a vector autoregressive model for multiple beta coefficients, is...
RESTART simulation of non-Markov consecutive-k-out-of-n: F repairable systems
Energy Technology Data Exchange (ETDEWEB)
Villen-Altamirano, Jose, E-mail: jvillen@eui.upm.e [Departamento de Matematica Aplicada (E.U. Informatica), Universidad Politecnica de Madrid, Calle Arboleda s/n, 28031 Madrid (Spain)
2010-03-15
The reliability of consecutive-k-out-of-n: F repairable systems and (k-1)-step Markov dependence is studied. The model analyzed in this paper is more general than those of previous studies given that repair time and component lifetimes are random variables that follow a general distribution. The system has one repair service which adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly dependable systems, the RESTART method was used for the estimation of steady-state unavailability, MTBF and unreliability. Probabilities up to the order of 10{sup -16} have been accurately estimated with little computational effort. In this method, a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of a rare event (e.g., a system failure) is higher. The main difficulty for the application of this method is to find a suitable function, called the importance function, to define the regions. Given the simplicity involved in changing some model assumptions with RESTART, the importance function used in this paper could be useful for dependability estimation of many systems.
RESTART simulation of non-Markov consecutive-k-out-of-n: F repairable systems
International Nuclear Information System (INIS)
The reliability of consecutive-k-out-of-n: F repairable systems and (k-1)-step Markov dependence is studied. The model analyzed in this paper is more general than those of previous studies given that repair time and component lifetimes are random variables that follow a general distribution. The system has one repair service which adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly dependable systems, the RESTART method was used for the estimation of steady-state unavailability, MTBF and unreliability. Probabilities up to the order of 10-16 have been accurately estimated with little computational effort. In this method, a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of a rare event (e.g., a system failure) is higher. The main difficulty for the application of this method is to find a suitable function, called the importance function, to define the regions. Given the simplicity involved in changing some model assumptions with RESTART, the importance function used in this paper could be useful for dependability estimation of many systems.
Witowski, Vitali; Foraita, Ronja; Pitsiladis, Yannis; Pigeot, Iris; Wirsik, Norman
2014-01-01
Introduction The use of accelerometers to objectively measure physical activity (PA) has become the most preferred method of choice in recent years. Traditionally, cutpoints are used to assign impulse counts recorded by the devices to sedentary and activity ranges. Here, hidden Markov models (HMM) are used to improve the cutpoint method to achieve a more accurate identification of the sequence of modes of PA. Methods 1,000 days of labeled accelerometer data have been simulated. For the simulated data the actual sedentary behavior and activity range of each count is known. The cutpoint method is compared with HMMs based on the Poisson distribution (HMM[Pois]), the generalized Poisson distribution (HMM[GenPois]) and the Gaussian distribution (HMM[Gauss]) with regard to misclassification rate (MCR), bout detection, detection of the number of activities performed during the day and runtime. Results The cutpoint method had a misclassification rate (MCR) of 11% followed by HMM[Pois] with 8%, HMM[GenPois] with 3% and HMM[Gauss] having the best MCR with less than 2%. HMM[Gauss] detected the correct number of bouts in 12.8% of the days, HMM[GenPois] in 16.1%, HMM[Pois] and the cutpoint method in none. HMM[GenPois] identified the correct number of activities in 61.3% of the days, whereas HMM[Gauss] only in 26.8%. HMM[Pois] did not identify the correct number at all and seemed to overestimate the number of activities. Runtime varied between 0.01 seconds (cutpoint), 2.0 minutes (HMM[Gauss]) and 14.2 minutes (HMM[GenPois]). Conclusions Using simulated data, HMM-based methods were superior in activity classification when compared to the traditional cutpoint method and seem to be appropriate to model accelerometer data. Of the HMM-based methods, HMM[Gauss] seemed to be the most appropriate choice to assess real-life accelerometer data. PMID:25464514
Zeng, Xiaojun; Zhang, Liyun; Xiao, Xiuchan; Jiang, Yuanyuan; Guo, Yanzhi; Yu, Xinyan; Pu, Xuemei; Li, Menglong
2016-04-01
Thrombin-binding aptamer (TBA) with the sequence 5‧GGTTGGTGTGGTTGG3‧ could fold into G-quadruplex, which correlates with functionally important genomic regionsis. However, unfolding mechanism involved in the structural stability of G-quadruplex has not been satisfactorily elucidated on experiments so far. Herein, we studied the unfolding pathway of TBA by a combination of molecular dynamics simulation (MD) and Markov State Model (MSM). Our results revealed that the unfolding of TBA is not a simple two-state process but proceeds along multiple pathways with multistate intermediates. One high flux confirms some observations from NMR experiment. Another high flux exhibits a different and simpler unfolding pathway with less intermediates. Two important intermediate states were identified. One is similar to the G-triplex reported in the folding of G-quadruplex, but lack of H-bonding between guanines in the upper plane. More importantly, another intermediate state acting as a connector to link the folding region and the unfolding one, was the first time identified, which exhibits higher population and stability than the G-triplex-like intermediate. These results will provide valuable information for extending our understanding the folding landscape of G-quadruplex formation.
Dynamic temperature selection for parallel-tempering in Markov chain Monte Carlo simulations
Vousden, Will; Farr, Will M.; Mandel, Ilya
2015-01-01
Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multi-modal probability distributions. Most popular methods, such as Markov chain Monte Carlo sampling, perform poorly on strongly multi-modal probability distributions, rarely jumping between modes or settling on just one mode without finding others. Parallel tempering addresses this problem by sampling simultaneously with separate Markov chains from tempered versio...
Directory of Open Access Journals (Sweden)
Vitali Witowski
Full Text Available INTRODUCTION: The use of accelerometers to objectively measure physical activity (PA has become the most preferred method of choice in recent years. Traditionally, cutpoints are used to assign impulse counts recorded by the devices to sedentary and activity ranges. Here, hidden Markov models (HMM are used to improve the cutpoint method to achieve a more accurate identification of the sequence of modes of PA. METHODS: 1,000 days of labeled accelerometer data have been simulated. For the simulated data the actual sedentary behavior and activity range of each count is known. The cutpoint method is compared with HMMs based on the Poisson distribution (HMM[Pois], the generalized Poisson distribution (HMM[GenPois] and the Gaussian distribution (HMM[Gauss] with regard to misclassification rate (MCR, bout detection, detection of the number of activities performed during the day and runtime. RESULTS: The cutpoint method had a misclassification rate (MCR of 11% followed by HMM[Pois] with 8%, HMM[GenPois] with 3% and HMM[Gauss] having the best MCR with less than 2%. HMM[Gauss] detected the correct number of bouts in 12.8% of the days, HMM[GenPois] in 16.1%, HMM[Pois] and the cutpoint method in none. HMM[GenPois] identified the correct number of activities in 61.3% of the days, whereas HMM[Gauss] only in 26.8%. HMM[Pois] did not identify the correct number at all and seemed to overestimate the number of activities. Runtime varied between 0.01 seconds (cutpoint, 2.0 minutes (HMM[Gauss] and 14.2 minutes (HMM[GenPois]. CONCLUSIONS: Using simulated data, HMM-based methods were superior in activity classification when compared to the traditional cutpoint method and seem to be appropriate to model accelerometer data. Of the HMM-based methods, HMM[Gauss] seemed to be the most appropriate choice to assess real-life accelerometer data.
Daniels, Noah M.; Hosur, Raghavendra; Berger, Bonnie; Lenore J Cowen
2012-01-01
Motivation: One of the most successful methods to date for recognizing protein sequences that are evolutionarily related has been profile hidden Markov models (HMMs). However, these models do not capture pairwise statistical preferences of residues that are hydrogen bonded in beta sheets. These dependencies have been partially captured in the HMM setting by simulated evolution in the training phase and can be fully captured by Markov random fields (MRFs). However, the MRFs can be computationa...
Jokar Arsanjani, J.; Helbich, M.; Kainz, W.; Boloorani, A.
2013-01-01
This research analyses the suburban expansion in the metropolitan area of Tehran, Iran. A hybrid model consisting of logistic regression model, Markov chain (MC), and cellular automata (CA) was designed to improve the performance of the standard logistic regression model. Environmental and socio-eco
DEFF Research Database (Denmark)
Hobolth, Asger; Stone, Eric
2009-01-01
Analyses of serially-sampled data often begin with the assumption that the observations represent discrete samples from a latent continuous-time stochastic process. The continuous-time Markov chain (CTMC) is one such generative model whose popularity extends to a variety of disciplines ranging from...... computational finance to human genetics and genomics. A common theme among these diverse applications is the need to simulate sample paths of a CTMC conditional on realized data that is discretely observed. Here we present a general solution to this sampling problem when the CTMC is defined on a discrete and...
Dynamic temperature selection for parallel-tempering in Markov chain Monte Carlo simulations
Vousden, Will; Mandel, Ilya
2015-01-01
Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multi-modal probability distributions. Most popular methods, such as Markov chain Monte Carlo sampling, perform poorly on strongly multi-modal probability distributions, rarely jumping between modes or settling on just one mode without finding others. Parallel tempering addresses this problem by sampling simultaneously with separate Markov chains from tempered versions of the target distribution with reduced contrast levels. Gaps between modes can be traversed at higher temperatures, while individual modes can be efficiently explored at lower temperatures. In this paper, we investigate how one might choose the ladder of temperatures to achieve lower autocorrelation time for the sampler (and therefore more efficient sampling). In particular, we present a simple, easily-implemented algorithm for dynamically adapting the temperature configuration of a sampler while sampling in order to ...
Approximate regenerative-block bootstrap for Markov chains: some simulation studies
Bertail, Patrice; Clémençon, Stéphan
2007-01-01
Abstract : In Bertail & Clémençon (2005a) a novel methodology for bootstrappinggeneral Harris Markov chains has been proposed, which crucially exploits their renewalproperties (when eventually extended via the Nummelin splitting technique) and has theoreticalproperties that surpass other existing methods within the Markovian framework(bmoving block bootstrap, sieve bootstrap etc...). This paper is devoted to discuss practicalissues related to the implementation of this specific resampling met...
Bias-correction in vector autoregressive models
DEFF Research Database (Denmark)
Engsted, Tom; Pedersen, Thomas Quistgaard
2014-01-01
We analyze the properties of various methods for bias-correcting parameter estimates in both stationary and non-stationary vector autoregressive models. First, we show that two analytical bias formulas from the existing literature are in fact identical. Next, based on a detailed simulation study...... improvement over ordinary least squares. We pay special attention to the risk of pushing an otherwise stationary model into the non-stationary region of the parameter space when correcting for bias. Finally, we consider a recently proposed reduced-bias weighted least squares estimator, and we find that it...
Blind identification of threshold auto-regressive model for machine fault diagnosis
Institute of Scientific and Technical Information of China (English)
LI Zhinong; HE Yongyong; CHU Fulei; WU Zhaotong
2007-01-01
A blind identification method was developed for the threshold auto-regressive (TAR) model. The method had good identification accuracy and rapid convergence, especially for higher order systems. The proposed method was then combined with the hidden Markov model (HMM) to determine the auto-regressive (AR) coefficients for each interval used for feature extraction, with the HMM as a classifier. The fault diagnoses during the speed-up and speed- down processes for rotating machinery have been success- fully completed. The result of the experiment shows that the proposed method is practical and effective.
Markov-switching model for nonstationary runoff conditioned on El Nino information
DEFF Research Database (Denmark)
Gelati, Emiliano; Madsen, H.; Rosbjerg, Dan
2010-01-01
We define a Markov-modulated autoregressive model with exogenous input (MARX) to generate runoff scenarios using climatic information. Runoff parameterization is assumed to be conditioned on a hidden climate state following a Markov chain, where state transition probabilities are functions...
Directory of Open Access Journals (Sweden)
Avdhesh Kr. Sharma
2012-10-01
Full Text Available In recent years, the availability of power plants has become increasingly important issue in most developed and developing countries. This paper aims to propose a methodology based on Markov approach to evaluate the availability simulation model for power generation system (Turbine in a thermal power plant under realistic working environment. The effects of occurrence of failure/course of actions and availability of repair facilities on system performance have been investigated. Higher availability of the components/equipments is inherently associated with their higher reliability and maintainability. The power generation system consists of five subsystems with four possible states: full working, reduced capacity, reduced efficiency and failed state. So, its availability should be carefully evaluated in order to foresee the performance of the power plant. The availability simulation model (Av. has been developed with the help of mathematical formulation based on Markov Birth-Death process using probabilistic approach. For this purpose, first differential equations have been generated. These equations are then solved using normalizing condition so as to determine the steady state availability of power generation system. In fact, availability analysis is very much effective in finding critical subsystems and deciding their preventive maintenance program for improving availability of the power plant as well as the power supply. From the graphs illustrated, the optimum values of failure/repair rates for maximum availability, of each subsystem is analyzed and then maintenance priorities are decided for all subsystems.The present paper highlights that in this system, Turbine governing subsystem is most sensitive demands more improvement in maintainability as compared to the other subsystems. While Turbine lubrication subsystem is least sensitive.
An autoregressive growth model for longitudinal item analysis.
Jeon, Minjeong; Rabe-Hesketh, Sophia
2016-09-01
A first-order autoregressive growth model is proposed for longitudinal binary item analysis where responses to the same items are conditionally dependent across time given the latent traits. Specifically, the item response probability for a given item at a given time depends on the latent trait as well as the response to the same item at the previous time, or the lagged response. An initial conditions problem arises because there is no lagged response at the initial time period. We handle this problem by adapting solutions proposed for dynamic models in panel data econometrics. Asymptotic and finite sample power for the autoregressive parameters are investigated. The consequences of ignoring local dependence and the initial conditions problem are also examined for data simulated from a first-order autoregressive growth model. The proposed methods are applied to longitudinal data on Korean students' self-esteem. PMID:26645083
Saloranta, Tuomo M; Armitage, James M; Haario, Heikki; Naes, Kristoffer; Cousins, Ian T; Barton, David N
2008-01-01
Multimedia environmental fate models are useful tools to investigate the long-term impacts of remediation measures designed to alleviate potential ecological and human health concerns in contaminated areas. Estimating and communicating the uncertainties associated with the model simulations is a critical task for demonstrating the transparency and reliability of the results. The Extended Fourier Amplitude Sensitivity Test(Extended FAST) method for sensitivity analysis and Bayesian Markov chain Monte Carlo (MCMC) method for uncertainty analysis and model calibration have several advantages over methods typically applied for multimedia environmental fate models. Most importantly, the simulation results and their uncertainties can be anchored to the available observations and their uncertainties. We apply these techniques for simulating the historical fate of polychlorinated dibenzo-p-dioxins and dibenzofurans (PCDD/Fs) in the Grenland fjords, Norway, and for predicting the effects of different contaminated sediment remediation (capping) scenarios on the future levels of PCDD/Fs in cod and crab therein. The remediation scenario simulations show that a significant remediation effect can first be seen when significant portions of the contaminated sediment areas are cleaned up, and that increase in capping area leads to both earlier achievement of good fjord status and narrower uncertainty in the predicted timing for this. PMID:18350897
Multivariate elliptically contoured autoregressive process
Taras Bodnar; Arjun K. Gupta
2014-01-01
In this paper, we introduce a new class of elliptically contoured processes. The suggested process possesses both the generality of the conditional heteroscedastic autoregressive process and the elliptical symmetry of the elliptically contoured distributions. In the empirical study we find the link between the conditional time varying behavior of the covariance matrix of the returns and the time variability of the investor’s coefficient of risk aversion. Moreover, it is shown that the non-dia...
Gregor, Karol; Danihelka, Ivo; Mnih, Andriy; Blundell, Charles; Wierstra, Daan
2013-01-01
We introduce a deep, generative autoencoder capable of learning hierarchies of distributed representations from data. Successive deep stochastic hidden layers are equipped with autoregressive connections, which enable the model to be sampled from quickly and exactly via ancestral sampling. We derive an efficient approximate parameter estimation method based on the minimum description length (MDL) principle, which can be seen as maximising a variational lower bound on the log-likelihood, with ...
Gaussian Processes for Functional Autoregression
Kowal, Daniel R.; David S. Matteson; Ruppert, David
2016-01-01
We develop a hierarchical Gaussian process model for forecasting and inference of functional time series data. Unlike existing methods, our approach is especially suited for sparsely or irregularly sampled curves and for curves sampled with non-negligible measurement error. The latent process is dynamically modeled as a functional autoregression (FAR) with Gaussian process innovations. We propose a fully nonparametric dynamic functional factor model for the dynamic innovation process, with br...
Dynamic temperature selection for parallel tempering in Markov chain Monte Carlo simulations
Vousden, W. D.; Farr, W. M.; Mandel, I.
2016-01-01
Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multimodal probability distributions. Most popular methods, such as MCMC sampling, perform poorly on strongly multimodal probability distributions, rarely jumping between modes or settling on just one mode without finding others. Parallel tempering addresses this problem by sampling simultaneously with separate Markov chains from tempered versions of the target distribution with reduced contrast levels. Gaps between modes can be traversed at higher temperatures, while individual modes can be efficiently explored at lower temperatures. In this paper, we investigate how one might choose the ladder of temperatures to achieve more efficient sampling, as measured by the autocorrelation time of the sampler. In particular, we present a simple, easily implemented algorithm for dynamically adapting the temperature configuration of a sampler while sampling. This algorithm dynamically adjusts the temperature spacing to achieve a uniform rate of exchanges between chains at neighbouring temperatures. We compare the algorithm to conventional geometric temperature configurations on a number of test distributions and on an astrophysical inference problem, reporting efficiency gains by a factor of 1.2-2.5 over a well-chosen geometric temperature configuration and by a factor of 1.5-5 over a poorly chosen configuration. On all of these problems, a sampler using the dynamical adaptations to achieve uniform acceptance ratios between neighbouring chains outperforms one that does not.
Bracken, C. W.; Rajagopalan, B.; Zagona, E. A.
2011-12-01
Upper Colorado River Basin annual flow exhibits very low autocorrelation but regime shifting behavior causing long departures from the historical average flow producing sustained wet and dry periods. Traditional stochastic time series models do not capture this feature thereby misleading the water resources system risk and consequently impacting the management and planning efforts. To address this, we developed a nonstationary Hidden Markov (HM) model with Gamma component distributions, as opposed to Normal distributions which is widely used in literature, for stochastic simulation and short term forecasting. Global decoding from this model reveals and captures strong underlying persistent structure in the Lees Ferry flow time series. In addition to capturing the shifting mean, simulations from this model have a 20% greater chance than a first order Auto Regressive model (AR1), the best time series model for this data, of simulating wet and dry runs of 6 or more years. Relative to AR1 the HM model also captures the spectral features quite well. When applied to short term forecasting (i.e. of 1-2 years) they show higher skill relative to climatology but also to an AR1 model.
Lesage, James P.; Vance, Colin; Chih, Yao-Yu
2016-01-01
We apply a heterogenous coefficient spatial autoregressive panel model from Aquaro, Bailey and Pesaran (2015) to explore competition/cooperation by Berlin fueling stations in setting prices for diesel and E5 fuel. Unlike the maximum likelihood estimation method set forth by Aquaro, Bailey and Pesaran (2015), we rely on a Markov Chain Monte Carlo (MCMC) estimation methodology. MCMC estimates as applied here with non-informative priors will produce estimates equal to those from maximum likeliho...
A Note on Parameter Estimations of Panel Vector Autoregressive Models with Intercorrelation
Institute of Scientific and Technical Information of China (English)
Jian-hong Wu; Li-xing Zhu; Zai-xing Li
2009-01-01
This note considers parameter estimation for panel vector autoregressive models with intercorrela-tion. Conditional least squares estimators are derived and the asymptotic normality is established. A simulation is carried out for illustration.
Multivariate elliptically contoured autoregressive process
Directory of Open Access Journals (Sweden)
Taras Bodnar
2014-05-01
Full Text Available In this paper, we introduce a new class of elliptically contoured processes. The suggested process possesses both the generality of the conditional heteroscedastic autoregressive process and the elliptical symmetry of the elliptically contoured distributions. In the empirical study we find the link between the conditional time varying behavior of the covariance matrix of the returns and the time variability of the investor’s coefficient of risk aversion. Moreover, it is shown that the non-diagonal elements of the dispersion matrix are slowly varying in time.
Schoups, G.; Vrugt, J. A.; Fenicia, F.; van de Giesen, N. C.
2010-10-01
Conceptual rainfall-runoff models have traditionally been applied without paying much attention to numerical errors induced by temporal integration of water balance dynamics. Reliance on first-order, explicit, fixed-step integration methods leads to computationally cheap simulation models that are easy to implement. Computational speed is especially desirable for estimating parameter and predictive uncertainty using Markov chain Monte Carlo (MCMC) methods. Confirming earlier work of Kavetski et al. (2003), we show here that the computational speed of first-order, explicit, fixed-step integration methods comes at a cost: for a case study with a spatially lumped conceptual rainfall-runoff model, it introduces artificial bimodality in the marginal posterior parameter distributions, which is not present in numerically accurate implementations of the same model. The resulting effects on MCMC simulation include (1) inconsistent estimates of posterior parameter and predictive distributions, (2) poor performance and slow convergence of the MCMC algorithm, and (3) unreliable convergence diagnosis using the Gelman-Rubin statistic. We studied several alternative numerical implementations to remedy these problems, including various adaptive-step finite difference schemes and an operator splitting method. Our results show that adaptive-step, second-order methods, based on either explicit finite differencing or operator splitting with analytical integration, provide the best alternative for accurate and efficient MCMC simulation. Fixed-step or adaptive-step implicit methods may also be used for increased accuracy, but they cannot match the efficiency of adaptive-step explicit finite differencing or operator splitting. Of the latter two, explicit finite differencing is more generally applicable and is preferred if the individual hydrologic flux laws cannot be integrated analytically, as the splitting method then loses its advantage.
Rainfall data simulation by hidden Markov model and discrete wavelet transformation
Jayawardena, AW; Xu, PC; Li, WK
2009-01-01
In many regions, monthly (or bimonthly) rainfall data can be considered as deterministic while daily rainfall data may be treated as random. As a result, deterministic models may not sufficiently fit the daily data because of the strong stochastic nature, while stochastic models may also not reliably fit into daily rainfall time series because of the deterministic nature at the large scale (i.e. coarse scale). Although there are different approaches for simulating daily rainfall, mixing of de...
A stochastic Markov chain approach for tennis: Monte Carlo simulation and modeling
Aslam, Kamran
This dissertation describes the computational formulation of probability density functions (pdfs) that facilitate head-to-head match simulations in tennis along with ranking systems developed from their use. A background on the statistical method used to develop the pdfs , the Monte Carlo method, and the resulting rankings are included along with a discussion on ranking methods currently being used both in professional sports and in other applications. Using an analytical theory developed by Newton and Keller in [34] that defines a tennis player's probability of winning a game, set, match and single elimination tournament, a computational simulation has been developed in Matlab that allows further modeling not previously possible with the analytical theory alone. Such experimentation consists of the exploration of non-iid effects, considers the concept the varying importance of points in a match and allows an unlimited number of matches to be simulated between unlikely opponents. The results of these studies have provided pdfs that accurately model an individual tennis player's ability along with a realistic, fair and mathematically sound platform for ranking them.
Kepler AutoRegressive Planet Search: Motivation & Methodology
Caceres, Gabriel; Feigelson, Eric; Jogesh Babu, G.; Bahamonde, Natalia; Bertin, Karine; Christen, Alejandra; Curé, Michel; Meza, Cristian
2015-08-01
The Kepler AutoRegressive Planet Search (KARPS) project uses statistical methodology associated with autoregressive (AR) processes to model Kepler lightcurves in order to improve exoplanet transit detection in systems with high stellar variability. We also introduce a planet-search algorithm to detect transits in time-series residuals after application of the AR models. One of the main obstacles in detecting faint planetary transits is the intrinsic stellar variability of the host star. The variability displayed by many stars may have autoregressive properties, wherein later flux values are correlated with previous ones in some manner. Auto-Regressive Moving-Average (ARMA) models, Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH), and related models are flexible, phenomenological methods used with great success to model stochastic temporal behaviors in many fields of study, particularly econometrics. Powerful statistical methods are implemented in the public statistical software environment R and its many packages. Modeling involves maximum likelihood fitting, model selection, and residual analysis. These techniques provide a useful framework to model stellar variability and are used in KARPS with the objective of reducing stellar noise to enhance opportunities to find as-yet-undiscovered planets. Our analysis procedure consisting of three steps: pre-processing of the data to remove discontinuities, gaps and outliers; ARMA-type model selection and fitting; and transit signal search of the residuals using a new Transit Comb Filter (TCF) that replaces traditional box-finding algorithms. We apply the procedures to simulated Kepler-like time series with known stellar and planetary signals to evaluate the effectiveness of the KARPS procedures. The ARMA-type modeling is effective at reducing stellar noise, but also reduces and transforms the transit signal into ingress/egress spikes. A periodogram based on the TCF is constructed to concentrate the signal
Autoregressive description of biological phenomena
Morariu, Vasile V; Pop, Alexadru; Soltuz, Stefan M; Buimaga-Iarinca, Luiza; Zainea, Oana
2008-01-01
Many natural phenomena can be described by power-laws. A closer look at various experimental data reveals more or less significant deviations from a 1/f spectrum. We exemplify such cases with phenomena offered by molecular biology, cell biophysics, and cognitive psychology. Some of these cases can be described by first order autoregressive (AR) models or by higher order AR models which are short range correlation models. The calculations are checked against astrophysical data which were fitted to a an AR model by a different method. We found that our fitting method of the data give similar results for the astrhophysical data and therefore applied the method for examples mentioned above. Our results show that such phenomena can be described by first or higher order of AR models. Therefore such examples are described by short range correlation properties while they can be easily confounded with long range correlation phenomena.
Weinberg, Martin D
2009-01-01
Computation of the marginal likelihood or "Bayesian Evidence" from a simulated posterior distribution is central to Bayesian model selection but is fraught with difficulty. The often-used harmonic mean approximation uses the posterior directly but is unstably sensitive to samples with anomalously small values of the likelihood and converges very slowly. The Laplace approximation is stable but makes strong, and often inappropriate, assumptions about the shape of the posterior distribution. It is useful, but not general. We need an algorithm that is general and easy to apply, like the harmonic mean approximation, but robust to sample size and multimodality. Here, I argue that the evidence can be stably computed from a posterior sample by careful attention to the numerics of the probability integral. Posing the expression for the Bayesian evidence as a Lebesgue integral, we may convert the evaluation of the sample statistic to a quadrature rule and show that the harmonic mean approximation suffers from enormous ...
Graphs: Associated Markov Chains
Murthy, Garimella Rama
2012-01-01
In this research paper, weighted / unweighted, directed / undirected graphs are associated with interesting Discrete Time Markov Chains (DTMCs) as well as Continuous Time Markov Chains (CTMCs). The equilibrium / transient behaviour of such Markov chains is studied. Also entropy dynamics (Shannon entropy) of certain structured Markov chains is investigated. Finally certain structured graphs and the associated Markov chains are studied.
International Nuclear Information System (INIS)
We present a single-particle Lennard–Jones (L-J) model for CO2 and N2. Simplified L-J models for other small polyatomic molecules can be obtained following the methodology described herein. The phase-coexistence diagrams of single-component systems computed using the proposed single-particle models for CO2 and N2 agree well with experimental data over a wide range of temperatures. These diagrams are computed using the Markov Chain Monte Carlo method based on the Gibbs-NVT ensemble. This good agreement validates the proposed simplified models. That is, with properly selected parameters, the single-particle models have similar accuracy in predicting gas-phase properties as more complex, state-of-the-art molecular models. To further test these single-particle models, three binary mixtures of CH4, CO2 and N2 are studied using a Gibbs-NPT ensemble. These results are compared against experimental data over a wide range of pressures. The single-particle model has similar accuracy in the gas phase as traditional models although its deviation in the liquid phase is greater. Since the single-particle model reduces the particle number and avoids the time-consuming Ewald summation used to evaluate Coulomb interactions, the proposed model improves the computational efficiency significantly, particularly in the case of high liquid density where the acceptance rate of the particle-swap trial move increases. We compare, at constant temperature and pressure, the Gibbs-NPT and Gibbs-NVT ensembles to analyze their performance differences and results consistency. As theoretically predicted, the agreement between the simulations implies that Gibbs-NVT can be used to validate Gibbs-NPT predictions when experimental data is not available
Jadoon, K. Z.; Altaf, M. U.; McCabe, M. F.; Hoteit, I.; Moghadas, D.
2014-12-01
In arid and semi-arid regions, soil salinity has a major impact on agro-ecosystems, agricultural productivity, environment and sustainability. High levels of soil salinity adversely affect plant growth and productivity, soil and water quality, and may eventually result in soil erosion and land degradation. Being essentially a hazard, it's important to monitor and map soil salinity at an early stage to effectively use soil resources and maintain soil salinity level below the salt tolerance of crops. In this respect, low frequency electromagnetic induction (EMI) systems can be used as a noninvasive method to map the distribution of soil salinity at the field scale and at a high spatial resolution. In this contribution, an EMI system (the CMD Mini-Explorer) is used to estimate soil salinity using a Bayesian approach implemented via a Markov chain Monte Carlo (MCMC) sampling for inversion of multi-configuration EMI measurements. In-situ and EMI measurements were conducted across a farm where Acacia trees are irrigated with brackish water using a drip irrigation system. The electromagnetic forward model is based on the full solution of Maxwell's equation, and the subsurface is considered as a three-layer problem. In total, five parameters (electrical conductivity of three layers and thickness of top two layers) were inverted and modeled electrical conductivities were converted into the universal standard of soil salinity measurement (i.e. using the method of electrical conductivity of a saturated soil paste extract). Simulation results demonstrate that the proposed scheme successfully recovers soil salinity and reduces the uncertainties in the prior estimate. Analysis of the resulting posterior distribution of parameters indicates that electrical conductivity of the top two layers and the thickness of the first layer are well constrained by the EMI measurements. The proposed approach allows for quantitative mapping and monitoring of the spatial electrical conductivity
Li, Jun
2013-09-01
We present a single-particle Lennard-Jones (L-J) model for CO2 and N2. Simplified L-J models for other small polyatomic molecules can be obtained following the methodology described herein. The phase-coexistence diagrams of single-component systems computed using the proposed single-particle models for CO2 and N2 agree well with experimental data over a wide range of temperatures. These diagrams are computed using the Markov Chain Monte Carlo method based on the Gibbs-NVT ensemble. This good agreement validates the proposed simplified models. That is, with properly selected parameters, the single-particle models have similar accuracy in predicting gas-phase properties as more complex, state-of-the-art molecular models. To further test these single-particle models, three binary mixtures of CH4, CO2 and N2 are studied using a Gibbs-NPT ensemble. These results are compared against experimental data over a wide range of pressures. The single-particle model has similar accuracy in the gas phase as traditional models although its deviation in the liquid phase is greater. Since the single-particle model reduces the particle number and avoids the time-consuming Ewald summation used to evaluate Coulomb interactions, the proposed model improves the computational efficiency significantly, particularly in the case of high liquid density where the acceptance rate of the particle-swap trial move increases. We compare, at constant temperature and pressure, the Gibbs-NPT and Gibbs-NVT ensembles to analyze their performance differences and results consistency. As theoretically predicted, the agreement between the simulations implies that Gibbs-NVT can be used to validate Gibbs-NPT predictions when experimental data is not available. © 2013 Elsevier Inc.
Directory of Open Access Journals (Sweden)
Chow John L
2006-03-01
Full Text Available Abstract Background Management of acute respiratory distress syndrome (ARDS in the intensive care unit (ICU is clinically challenging and costly. Neuromuscular blocking agents may facilitate mechanical ventilation and improve oxygenation, but may result in prolonged recovery of neuromuscular function and acute quadriplegic myopathy syndrome (AQMS. The goal of this study was to address a hypothetical question via computer modeling: Would a reduction in intubation time of 6 hours and/or a reduction in the incidence of AQMS from 25% to 21%, provide enough benefit to justify a drug with an additional expenditure of $267 (the difference in acquisition cost between a generic and brand name neuromuscular blocker? Methods The base case was a 55 year-old man in the ICU with ARDS who receives neuromuscular blockade for 3.5 days. A Markov model was designed with hypothetical patients in 1 of 6 mutually exclusive health states: ICU-intubated, ICU-extubated, hospital ward, long-term care, home, or death, over a period of 6 months. The net monetary benefit was computed. Results Our computer simulation modeling predicted the mean cost for ARDS patients receiving standard care for 6 months to be $62,238 (5% – 95% percentiles $42,259 – $83,766, with an overall 6-month mortality of 39%. Assuming a ceiling ratio of $35,000, even if a drug (that cost $267 more hypothetically reduced AQMS from 25% to 21% and decreased intubation time by 6 hours, the net monetary benefit would only equal $137. Conclusion ARDS patients receiving a neuromuscular blocker have a high mortality, and unpredictable outcome, which results in large variability in costs per case. If a patient dies, there is no benefit to any drug that reduces ventilation time or AQMS incidence. A prospective, randomized pharmacoeconomic study of neuromuscular blockers in the ICU to asses AQMS or intubation times is impractical because of the highly variable clinical course of patients with ARDS.
Energy Technology Data Exchange (ETDEWEB)
Frank, T.D. [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States)], E-mail: till.frank@uconn.edu
2008-06-16
Some elementary properties and examples of Markov processes are reviewed. It is shown that the definition of the Markov property naturally leads to a classification of Markov processes into linear and nonlinear ones.
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Some elementary properties and examples of Markov processes are reviewed. It is shown that the definition of the Markov property naturally leads to a classification of Markov processes into linear and nonlinear ones
Single-Index Additive Vector Autoregressive Time Series Models
LI, YEHUA
2009-09-01
We study a new class of nonlinear autoregressive models for vector time series, where the current vector depends on single-indexes defined on the past lags and the effects of different lags have an additive form. A sufficient condition is provided for stationarity of such models. We also study estimation of the proposed model using P-splines, hypothesis testing, asymptotics, selection of the order of the autoregression and of the smoothing parameters and nonlinear forecasting. We perform simulation experiments to evaluate our model in various settings. We illustrate our methodology on a climate data set and show that our model provides more accurate yearly forecasts of the El Niño phenomenon, the unusual warming of water in the Pacific Ocean. © 2009 Board of the Foundation of the Scandinavian Journal of Statistics.
Nonlinear autoregressive models and long memory
Kapetanios, George
2004-01-01
This note shows that regime switching nonlinear autoregressive models widely used in the time series literature can exhibit arbitrary degrees of long memory via appropriate definition of the model regimes.
Confidence Intervals for Autoregressive Coefficients Near One
Elliott, Graham; Stock, James H.
2000-01-01
Often we are interested in the largest root of an autoregressive process. Available methods rely on inverting t-tests to obtain confidence intervals. However, for large autoregressive roots, t-tests do not approximate asymptotically uniformly most powerful tests and do not have optimality properties when inverted for confidence intervals. We exploit the relationship between the power of tests and accuracy of confidence intervals, and suggest methods which are asymptotically more accurate than...
International Nuclear Information System (INIS)
This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are
Energy Technology Data Exchange (ETDEWEB)
Xu, Zuwei; Zhao, Haibo, E-mail: klinsmannzhb@163.com; Zheng, Chuguang
2015-01-15
This paper proposes a comprehensive framework for accelerating population balance-Monte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulation-rule matrix of differentially-weighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the two-particle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by single-looping over all particles, and meanwhile the mean time-step of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentially-weighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zero-dimensional system (single cell). Finally, for a spatially inhomogeneous multi-dimensional (multi-cell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multi-cores on a GPU that can implement the massively threaded data-parallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are
Katsuhiro Sugita
2015-01-01
In this paper we analyze the predictive power of the yield curve on output growth using a vector autoregressive model with multiple structural breaks in the intercept term and the volatility. To estimate the model and to detect the number of breaks, we apply a Bayesian approach with Markov chain Monte Carlo algorithm. We find strong evidence of three structural breaks using the US data.
Hidaka, Shohei
2015-01-01
A Markov process, which is constructed recursively, arises in stochastic games with Markov strategies. In this study, we defined a special class of random processes called the recursive Markov process, which has infinitely many states but can be expressed in a closed form. We derive the characteristic equation which the marginal stationary distribution of an arbitrary recursive Markov process needs to satisfy.
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A model of consecutive-k-out-of-n: F repairable system with non-exponential repair time distribution and (k-1)-step Markov dependence is introduced in this paper along with algorithms of three Monte Carlo methods, i.e. importance sampling, conditional expectation estimation and combination of the two methods, to estimate dependability of the non-Markov model including reliability, transient unavailability, MTTF, and MTBF. A numerical example is presented to demonstrate the efficiencies of above methods. The results show that combinational method has the highest efficiency for estimation of unreliability and unavailability, while conditional expectation estimation is the most efficient method for estimation of MTTF and MTBF. Conditional expectation estimation seems to have overall higher speedups in estimating dependability of such systems
Markov processes and controlled Markov chains
Filar, Jerzy; Chen, Anyue
2002-01-01
The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South Ameri...
Discrete Quantum Markov Chains
Faigle, Ulrich
2010-01-01
A framework for finite-dimensional quantum Markov chains on Hilbert spaces is introduced. Quantum Markov chains generalize both classical Markov chains with possibly hidden states and existing models of quantum walks on finite graphs. Quantum Markov chains are based on Markov operations that may be applied to quantum systems and include quantum measurements, for example. It is proved that quantum Markov chains are asymptotically stationary and hence possess ergodic and entropic properties. With a quantum Markov chain one may associate a quantum Markov process, which is a stochastic process in the classical sense. Generalized Markov chains allow a representation with respect to a generalized Markov source model with definite (but possibly hidden) states relative to which observables give rise to classical stochastic processes. It is demonstrated that this model allows for observables to violate Bell's inequality.
Jalayer, Fatemeh; Ebrahimian, Hossein
2014-05-01
Introduction The first few days elapsed after the occurrence of a strong earthquake and in the presence of an ongoing aftershock sequence are quite critical for emergency decision-making purposes. Epidemic Type Aftershock Sequence (ETAS) models are used frequently for forecasting the spatio-temporal evolution of seismicity in the short-term (Ogata, 1988). The ETAS models are epidemic stochastic point process models in which every earthquake is a potential triggering event for subsequent earthquakes. The ETAS model parameters are usually calibrated a priori and based on a set of events that do not belong to the on-going seismic sequence (Marzocchi and Lombardi 2009). However, adaptive model parameter estimation, based on the events in the on-going sequence, may have several advantages such as, tuning the model to the specific sequence characteristics, and capturing possible variations in time of the model parameters. Simulation-based methods can be employed in order to provide a robust estimate for the spatio-temporal seismicity forecasts in a prescribed forecasting time interval (i.e., a day) within a post-main shock environment. This robust estimate takes into account the uncertainty in the model parameters expressed as the posterior joint probability distribution for the model parameters conditioned on the events that have already occurred (i.e., before the beginning of the forecasting interval) in the on-going seismic sequence. The Markov Chain Monte Carlo simulation scheme is used herein in order to sample directly from the posterior probability distribution for ETAS model parameters. Moreover, the sequence of events that is going to occur during the forecasting interval (and hence affecting the seismicity in an epidemic type model like ETAS) is also generated through a stochastic procedure. The procedure leads to two spatio-temporal outcomes: (1) the probability distribution for the forecasted number of events, and (2) the uncertainty in estimating the
International Nuclear Information System (INIS)
Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system's potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide
Kadoura, Ahmad; Sun, Shuyu; Salama, Amgad
2014-08-01
Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system's potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide.
Kadoura, Ahmad Salim
2014-08-01
Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system\\'s potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide. © 2014 Elsevier Inc.
Testing the Markov condition in ion channel recordings
Timmer, J
1997-01-01
A statistical test is presented to decide whether data are adequately described by probabilistic functions of finite state Markov chains (''hidden Markov models'') as applied in the analysis of ion channel data. Particularly, the test can be used to decide whether a system obeys the Markov condition. Simulation studies are performed in order to investigate the sensitivity of the proposed test against violations of the model assumptions. The test can be applied analogously to Markov models.
Oracle Inequalities for High Dimensional Vector Autoregressions
DEFF Research Database (Denmark)
Callot, Laurent; Kock, Anders Bredahl
This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of...... hence the correct sparsity pattern). Finally conditions under which the Adaptive LASSO reveals the correct sign pattern with probability tending to one are given. Again, the number of parameters may be much larger than the sample size. Some maximal inequalities for vector autoregressions which might be...
International Nuclear Information System (INIS)
Non-linear autoregressive Markov regime-switching models are intuitive. Time-series approaches for the modelling of electricity spot prices are frequently proposed. In this paper, such models are compared with an ordinary linear autoregressive model with regard to their forecast performances. The study is carried out using German daily spot-prices from the European Energy Exchange in Leipzig. Four non-linear models are used for the forecast study. The results of the study suggest that Markov regime-switching models provide better forecasts than linear models. (author)
Nonuniform Markov Geometric Measures
Neunhäuserer, J.
2015-01-01
We generalize results of Fan and Zhang [6] on absolute continuity and singularity of the golden Markov geometric series to nonuniform stochastic series given by arbitrary Markov process. In addition we describe an application of these results in fractal geometry.
Cardiac arrhythmia classification using autoregressive modeling
Srinivasan Narayanan; Ge Dingfei; Krishnan Shankar M
2002-01-01
Abstract Background Computer-assisted arrhythmia recognition is critical for the management of cardiac disorders. Various techniques have been utilized to classify arrhythmias. Generally, these techniques classify two or three arrhythmias or have significantly large processing times. A simpler autoregressive modeling (AR) technique is proposed to classify normal sinus rhythm (NSR) and various cardiac arrhythmias including atrial premature contraction (APC), premature ventricular contraction (...
The Integration Order of Vector Autoregressive Processes
DEFF Research Database (Denmark)
Franchi, Massimo
We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2...
Quantum Markov fields on graphs
Accardi, Luigi; Ohno, Hiromichi; Mukhamedov, Farrukh
2009-01-01
We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on $C^*$-algebras defined by general graphs. As examples of generalized d-Markov chains, we construct the entangled Markov fields on tree graphs. The concrete examples of generalized d-Markov chains on Cayley trees are also investigated.
Directory of Open Access Journals (Sweden)
Kianoush Fathi Vajargah
2015-01-01
Full Text Available An available method of modeling and predicting the economic time series is the use of stochastic differential equations, which are often determined as jump-diffusion stochastic differential equations in financial markets and underlier economic dynamics. Besides the diffusion term that is a geometric Brownian model with Wiener random process, these equations contain a jump term that follows Poisson process and depends on the type of market. This study presented two different models based on a certain class of jump-diffusion stochastic differential equations with random fluctuations: Black- Scholes model and Merton model (1976, including jump-diffusion (JD model, which were compared, and their parameters and hidden variables were evaluated using Markov chain Monte Carlo (MCMC method.
Monaco, James Peter; Madabhushi, Anant
2011-07-01
The ability of classification systems to adjust their performance (sensitivity/specificity) is essential for tasks in which certain errors are more significant than others. For example, mislabeling cancerous lesions as benign is typically more detrimental than mislabeling benign lesions as cancerous. Unfortunately, methods for modifying the performance of Markov random field (MRF) based classifiers are noticeably absent from the literature, and thus most such systems restrict their performance to a single, static operating point (a paired sensitivity/specificity). To address this deficiency we present weighted maximum posterior marginals (WMPM) estimation, an extension of maximum posterior marginals (MPM) estimation. Whereas the MPM cost function penalizes each error equally, the WMPM cost function allows misclassifications associated with certain classes to be weighted more heavily than others. This creates a preference for specific classes, and consequently a means for adjusting classifier performance. Realizing WMPM estimation (like MPM estimation) requires estimates of the posterior marginal distributions. The most prevalent means for estimating these--proposed by Marroquin--utilizes a Markov chain Monte Carlo (MCMC) method. Though Marroquin's method (M-MCMC) yields estimates that are sufficiently accurate for MPM estimation, they are inadequate for WMPM. To more accurately estimate the posterior marginals we present an equally simple, but more effective extension of the MCMC method (E-MCMC). Assuming an identical number of iterations, E-MCMC as compared to M-MCMC yields estimates with higher fidelity, thereby 1) allowing a far greater number and diversity of operating points and 2) improving overall classifier performance. To illustrate the utility of WMPM and compare the efficacies of M-MCMC and E-MCMC, we integrate them into our MRF-based classification system for detecting cancerous glands in (whole-mount or quarter) histological sections of the prostate
Directory of Open Access Journals (Sweden)
Kevin McNally
2012-01-01
Full Text Available There are numerous biomonitoring programs, both recent and ongoing, to evaluate environmental exposure of humans to chemicals. Due to the lack of exposure and kinetic data, the correlation of biomarker levels with exposure concentrations leads to difficulty in utilizing biomonitoring data for biological guidance values. Exposure reconstruction or reverse dosimetry is the retrospective interpretation of external exposure consistent with biomonitoring data. We investigated the integration of physiologically based pharmacokinetic modelling, global sensitivity analysis, Bayesian inference, and Markov chain Monte Carlo simulation to obtain a population estimate of inhalation exposure to m-xylene. We used exhaled breath and venous blood m-xylene and urinary 3-methylhippuric acid measurements from a controlled human volunteer study in order to evaluate the ability of our computational framework to predict known inhalation exposures. We also investigated the importance of model structure and dimensionality with respect to its ability to reconstruct exposure.
Dynkin, E B
1960-01-01
Theory of Markov Processes provides information pertinent to the logical foundations of the theory of Markov random processes. This book discusses the properties of the trajectories of Markov processes and their infinitesimal operators.Organized into six chapters, this book begins with an overview of the necessary concepts and theorems from measure theory. This text then provides a general definition of Markov process and investigates the operations that make possible an inspection of the class of Markov processes corresponding to a given transition function. Other chapters consider the more c
Context Tree Estimation in Variable Length Hidden Markov Models
Dumont, Thierry
2011-01-01
We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove that the estimator is strongly consistent. This uses information-theoretic mixture inequalities in the spirit of Finesso and Lorenzo(Consistent estimation of the order for Markov and hidden Markov chains(1990)) and E.Gassiat and S.Boucheron (Optimal error exponents in hidden Markov model order estimation(2003)). We propose an algorithm to efficiently compute the estimator and provide simulation studies to support our result.
Directory of Open Access Journals (Sweden)
J. A. Vrugt
2011-04-01
Full Text Available Formal and informal Bayesian approaches are increasingly being used to treat forcing, model structural, parameter and calibration data uncertainty, and summarize hydrologic prediction uncertainty. This requires posterior sampling methods that approximate the (evolving posterior distribution. We recently introduced the DiffeRential Evolution Adaptive Metropolis (DREAM algorithm, an adaptive Markov Chain Monte Carlo (MCMC method that is especially designed to solve complex, high-dimensional and multimodal posterior probability density functions. The method runs multiple chains in parallel, and maintains detailed balance and ergodicity. Here, I present the latest algorithmic developments, and introduce a discrete sampling variant of DREAM that samples the parameter space at fixed points. The development of this new code, DREAM(D, has been inspired by the existing class of integer optimization problems, and emerging class of experimental design problems. Such non-continuous parameter estimation problems are of considerable theoretical and practical interest. The theory developed herein is applicable to DREAM(ZS (Vrugt et al., 2011 and MT-DREAM(ZS (Laloy and Vrugt, 2011 as well. Two case studies involving a sudoku puzzle and rainfall – runoff model calibration problem are used to illustrate DREAM(D.
Order 1 autoregressive process of finite length
Vamos, Calin; Craciun, Maria
2007-01-01
The stochastic processes of finite length defined by recurrence relations request additional relations specifying the first terms of the process analogously to the initial conditions for the differential equations. As a general rule, in time series theory one analyzes only stochastic processes of infinite length which need no such initial conditions and their properties are less difficult to be determined. In this paper we compare the properties of the order 1 autoregressive processes of finite and infinite length and we prove that the time series length has an important influence mainly if the serial correlation is significant. These different properties can manifest themselves as transient effects produced when a time series is numerically generated. We show that for an order 1 autoregressive process the transient behavior can be avoided if the first term is a Gaussian random variable with standard deviation equal to that of the theoretical infinite process and not to that of the white noise innovation.
Generalization of Brownian Motion with Autoregressive Increments
Fendick, Kerry
2011-01-01
This paper introduces a generalization of Brownian motion with continuous sample paths and stationary, autoregressive increments. This process, which we call a Brownian ray with drift, is characterized by three parameters quantifying distinct effects of drift, volatility, and autoregressiveness. A Brownian ray with drift, conditioned on its state at the beginning of an interval, is another Brownian ray with drift over the interval, and its expected path over the interval is a ray with a slope that depends on the conditioned state. This paper shows how Brownian rays can be applied in finance for the analysis of queues or inventories and the valuation of options. We model a queue's net input process as a superposition of Brownian rays with drift and derive the transient distribution of the queue length conditional on past queue lengths and on past states of the individual Brownian rays comprising the superposition. The transient distributions of Regulated Brownian Motion and of the Regulated Brownian Bridge are...
Markov chains analytic and Monte Carlo computations
Graham, Carl
2014-01-01
Markov Chains: Analytic and Monte Carlo Computations introduces the main notions related to Markov chains and provides explanations on how to characterize, simulate, and recognize them. Starting with basic notions, this book leads progressively to advanced and recent topics in the field, allowing the reader to master the main aspects of the classical theory. This book also features: Numerous exercises with solutions as well as extended case studies.A detailed and rigorous presentation of Markov chains with discrete time and state space.An appendix presenting probabilistic notions that are nec
Some correlation properties of spatial autoregressions
Martellosio, Federico
2009-01-01
This paper investigates how the correlations implied by a first-order simultaneous autoregressive (SAR(1)) process are affected by the weights matrix and the autocorrelation parameter. An interpretation of the covariance structure of the process is provided, based on the walks connecting the spatial units. The interpretation serves to explain a number of correlation properties of SAR(1) processes, and clarifies why in practical applications it is difficult, or even impossible, to use SAR(1) p...
Directory of Open Access Journals (Sweden)
Knuiman Matthew
2008-06-01
Full Text Available Abstract Background Treatments for coronary heart disease (CHD have evolved rapidly over the last 15 years with considerable change in the number and effectiveness of both medical and surgical treatments. This period has seen the rapid development and uptake of statin drugs and coronary artery revascularization procedures (CARPs that include Coronary Artery Bypass Graft procedures (CABGs and Percutaneous Coronary Interventions (PCIs. It is difficult in an era of such rapid change to accurately forecast requirements for treatment services such as CARPs. In a previous paper we have described and outlined the use of a Markov Monte Carlo simulation model for analyzing and predicting the requirements for CARPs for the population of Western Australia (Mannan et al, 2007. In this paper, we expand on the use of this model for forecasting CARPs in Western Australia with a focus on the lack of adequate performance of the (standard model for forecasting CARPs in a period during the mid 1990s when there were considerable changes to CARP technology and implementation policy and an exploration and demonstration of how the standard model may be adapted to achieve better performance. Methods Selected key CARP event model probabilities are modified based on information relating to changes in the effectiveness of CARPs from clinical trial evidence and an awareness of trends in policy and practice of CARPs. These modified model probabilities and the ones obtained by standard methods are used as inputs in our Markov simulation model. Results The projected numbers of CARPs in the population of Western Australia over 1995–99 only improve marginally when modifications to model probabilities are made to incorporate an increase in effectiveness of PCI procedures. However, the projected numbers improve substantially when, in addition, further modifications are incorporated that relate to the increased probability of a PCI procedure and the reduced probability of a CABG
Energy Technology Data Exchange (ETDEWEB)
Saldanha Filho, Paulo Carlos
1998-02-01
Stochastic simulation has been employed in petroleum reservoir characterization as a modeling tool able to reconcile information from several different sources. It has the ability to preserve the variability of the modeled phenomena and permits transference of geological knowledge to numerical models of flux, whose predictions on reservoir constitute the main basis for reservoir management decisions. Several stochastic models have been used and/or suggested, depending on the nature of the phenomena to be described. Markov Random Fields (MRFs) appear as an alternative for the modeling of discrete variables, mainly reservoirs with mosaic architecture of facies. In this dissertation, the reader is introduced to the stochastic modeling by MRFs in a generic sense. The main aspects of the technique are reviewed. MRF Conceptual Background is described: its characterization through the Markovian property and the equivalence to Gibbs distributions. The framework for generic modeling of MRFs is described. The classical models of Ising and Potts-Strauss are specific in this context and are related to models of Ising and Potts-Strauss are specific in this context and are related to models used in petroleum reservoir characterization. The problem of parameter estimation is discussed. The maximum pseudolikelihood estimators for some models are presented. Estimators for two models useful for reservoir characterization are developed, and represent a new contribution to the subject. Five algorithms for the Conditional Simulation of MRFs are described: the Metropolis algorithm, the algorithm of German and German (Gibbs sampler), the algorithm of Swendsen-Wang, the algorithm of Wolff, and the algorithm of Flinn. Finally, examples of simulation for some of the models discussed are presented, along with their implications on the modelling of petroleum reservoirs. (author)
Modeling of non-stationary autoregressive alpha-stable processe
National Aeronautics and Space Administration — In the literature, impulsive signals are mostly modeled by symmetric alpha-stable processes. To represent their temporal dependencies, usually autoregressive models...
Multiple phase derivative estimation using autoregressive modeling in holographic interferometry
International Nuclear Information System (INIS)
A novel technique is proposed for the direct and simultaneous estimation of multiple phase derivatives from a deformation modulated carrier fringe pattern in a multi-wave holographic interferometry set-up. The fringe intensity is represented as a spatially-varying autoregressive (SVAR) model. The spatially-varying coefficients of the SVAR model are derived using a forward–backward approach of linear estimation of the fringe intensity. Using these coefficients, the poles of the SVAR model transfer function are computed and the angles of these poles provide the estimation of phase derivatives. The estimation of carrier frequency is performed by the proposed method using a reference interferogram. Simulation results are provided in the presence of noise and fringe amplitude modulation. (paper)
DEFF Research Database (Denmark)
Justesen, Jørn
2005-01-01
A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly.......A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly....
DEFF Research Database (Denmark)
Li, Chunjian; Andersen, Søren Vang
2007-01-01
We propose two blind system identification methods that exploit the underlying dynamics of non-Gaussian signals. The two signal models to be identified are: an Auto-Regressive (AR) model driven by a discrete-state Hidden Markov process, and the same model whose output is perturbed by white Gaussian...... iterative schemes. The proposed methods also enjoy good data efficiency since only second order statistics is involved in the computation. When measurement noise is present, a novel Switching Kalman Smoother is incorporated into the EM algorithm, obtaining optimum nonlinear MMSE estimates of the system...
Directory of Open Access Journals (Sweden)
Badawi A
2012-04-01
Full Text Available Soroush Mortaz*, Christine Wessman*, Ross Duncan, Rachel Gray, Alaa Badawi Office of Biotechnology Genomics and Population Health, Public Health Agency of Canada, Toronto, Ontario, Canada*Both authors contributed equally to this workBackground: Type 2 diabetes mellitus (T2DM is a major global health problem. An estimated 20%–50% of diabetic subjects in Canada are currently undiagnosed, and around 20%–30% have already developed complications. Screening for high blood glucose levels can identify people with prediabetic conditions and permit introduction of timely and effective prevention. This study examines the benefit of screening for impaired fasting glucose (IFG and T2DM. If intervention is introduced at this prediabetic stage, it can be most effective in delaying the onset and complications of T2DM.Methods: Using a Markov model simulation, we compare the cost-effectiveness of screening for prediabetes (IFG and T2DM with the strategy of no screening. An initial cohort of normoglycemic, prediabetic, or undiagnosed diabetic adults with one or more T2DM risk factors was used to model the strategies mentioned over a 10-year period. Subjects without known prediabetes or diabetes are screened every 3 years and persons with prediabetes were tested for diabetes on an annual basis. The model weighs the increase in quality-adjusted life-years (QALYs associated with early detection of prediabetes and earlier diagnosis of T2DM due to lifestyle intervention and early treatment in asymptomatic subjects.Results: Costs for each QALY gained were $2281 for conventional screening compared with $2890 for no screening. Thus, in this base-case analysis, conventional screening with a frequency of once every 3 years was favored over no screening. Furthermore, conventional screening was more favorable compared with no screening over a wide range of willingness-to-pay thresholds. Changing the frequency of screening did not affect the overall results. Screening
A General Representation Theorem for Integrated Vector Autoregressive Processes
DEFF Research Database (Denmark)
Franchi, Massimo
We study the algebraic structure of an I(d) vector autoregressive process, where d is restricted to be an integer. This is useful to characterize its polynomial cointegrating relations and its moving average representation, that is to prove a version of the Granger representation theorem valid...... for I(d) vector autoregressive processes...
Markov chain Monte Carlo test of toric homogeneous Markov chains
Takemura, Akimichi; Hara, Hisayuki
2010-01-01
Markov chain models are used in various fields, such behavioral sciences or econometrics. Although the goodness of fit of the model is usually assessed by large sample approximation, it is desirable to use conditional tests if the sample size is not large. We study Markov bases for performing conditional tests of the toric homogeneous Markov chain model, which is the envelope exponential family for the usual homogeneous Markov chain model. We give a complete description of a Markov basis for ...
Semi-Markov Arnason-Schwarz models.
King, Ruth; Langrock, Roland
2016-06-01
We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis. PMID:26584064
Rates of convergence of some multivariate Markov chains with polynomial eigenfunctions
Khare, Kshitij; 10.1214/08-AAP562
2009-01-01
We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our examples include the Moran model in population genetics and its variants in community ecology, the Dirichlet-multinomial Gibbs sampler, a class of generalized Bernoulli--Laplace processes, a generalized Ehrenfest urn model and the multivariate normal autoregressive process.
Windisch, Tobias
2015-01-01
The mixing behaviour of Markov chains on lattice points of polytopes using Markov bases is examined. It is shown that, in fixed dimension, these Markov chains do not mix rapidly. As a way out, a method of how to adapt Markov bases in order to achieve the fastest mixing behaviour is introduced.
Fuzzy Markov chains: uncertain probabilities
James J. Buckley; Eslami, Esfandiar
2002-01-01
We consider finite Markov chains where there are uncertainties in some of the transition probabilities. These uncertainties are modeled by fuzzy numbers. Using a restricted fuzzy matrix multiplication we investigate the properties of regular, and absorbing, fuzzy Markov chains and show that the basic properties of these classical Markov chains generalize to fuzzy Markov chains.
Directory of Open Access Journals (Sweden)
Yu Zhao
2013-01-01
Full Text Available In the study, we discussed the generalized autoregressive conditional heteroskedasticity model and enhanced it with wavelet transform to evaluate the daily returns for 1/4/2002-30/12/2011 period in Brent oil market. We proposed discrete wavelet transform generalized autoregressive conditional heteroskedasticity model to increase the forecasting performance of the generalized autoregressive conditional heteroskedasticity model. Our new approach can overcome the defect of generalized autoregressive conditional heteroskedasticity family models which can’t describe the detail and partial features of times series and retain the advantages of them at the same time. Comparing with the generalized autoregressive conditional heteroskedasticity model, the new approach significantly improved forecast results and greatly reduces conditional variances.
Kepler AutoRegressive Planet Search
Caceres, Gabriel Antonio; Feigelson, Eric
2016-01-01
The Kepler AutoRegressive Planet Search (KARPS) project uses statistical methodology associated with autoregressive (AR) processes to model Kepler lightcurves in order to improve exoplanet transit detection in systems with high stellar variability. We also introduce a planet-search algorithm to detect transits in time-series residuals after application of the AR models. One of the main obstacles in detecting faint planetary transits is the intrinsic stellar variability of the host star. The variability displayed by many stars may have autoregressive properties, wherein later flux values are correlated with previous ones in some manner. Our analysis procedure consisting of three steps: pre-processing of the data to remove discontinuities, gaps and outliers; AR-type model selection and fitting; and transit signal search of the residuals using a new Transit Comb Filter (TCF) that replaces traditional box-finding algorithms. The analysis procedures of the project are applied to a portion of the publicly available Kepler light curve data for the full 4-year mission duration. Tests of the methods have been made on a subset of Kepler Objects of Interest (KOI) systems, classified both as planetary `candidates' and `false positives' by the Kepler Team, as well as a random sample of unclassified systems. We find that the ARMA-type modeling successfully reduces the stellar variability, by a factor of 10 or more in active stars and by smaller factors in more quiescent stars. A typical quiescent Kepler star has an interquartile range (IQR) of ~10 e-/sec, which may improve slightly after modeling, while those with IQR ranging from 20 to 50 e-/sec, have improvements from 20% up to 70%. High activity stars (IQR exceeding 100) markedly improve. A periodogram based on the TCF is constructed to concentrate the signal of these periodic spikes. When a periodic transit is found, the model is displayed on a standard period-folded averaged light curve. Our findings to date on real
Dodani, Sheel C.; Kiss, Gert; Cahn, Jackson K. B.; Su, Ye; Pande, Vijay S.; Arnold, Frances H.
2016-05-01
The dynamic motions of protein structural elements, particularly flexible loops, are intimately linked with diverse aspects of enzyme catalysis. Engineering of these loop regions can alter protein stability, substrate binding and even dramatically impact enzyme function. When these flexible regions are unresolvable structurally, computational reconstruction in combination with large-scale molecular dynamics simulations can be used to guide the engineering strategy. Here we present a collaborative approach that consists of both experiment and computation and led to the discovery of a single mutation in the F/G loop of the nitrating cytochrome P450 TxtE that simultaneously controls loop dynamics and completely shifts the enzyme's regioselectivity from the C4 to the C5 position of L-tryptophan. Furthermore, we find that this loop mutation is naturally present in a subset of homologous nitrating P450s and confirm that these uncharacterized enzymes exclusively produce 5-nitro-L-tryptophan, a previously unknown biosynthetic intermediate.
Dodani, Sheel C; Kiss, Gert; Cahn, Jackson K B; Su, Ye; Pande, Vijay S; Arnold, Frances H
2016-05-01
The dynamic motions of protein structural elements, particularly flexible loops, are intimately linked with diverse aspects of enzyme catalysis. Engineering of these loop regions can alter protein stability, substrate binding and even dramatically impact enzyme function. When these flexible regions are unresolvable structurally, computational reconstruction in combination with large-scale molecular dynamics simulations can be used to guide the engineering strategy. Here we present a collaborative approach that consists of both experiment and computation and led to the discovery of a single mutation in the F/G loop of the nitrating cytochrome P450 TxtE that simultaneously controls loop dynamics and completely shifts the enzyme's regioselectivity from the C4 to the C5 position of L-tryptophan. Furthermore, we find that this loop mutation is naturally present in a subset of homologous nitrating P450s and confirm that these uncharacterized enzymes exclusively produce 5-nitro-L-tryptophan, a previously unknown biosynthetic intermediate. PMID:27102675
Massey, J. L.
1975-01-01
A regular Markov source is defined as the output of a deterministic, but noisy, channel driven by the state sequence of a regular finite-state Markov chain. The rate of such a source is the per letter uncertainty of its digits. The well-known result that the rate of a unifilar regular Markov source is easily calculable is demonstrated, where unifilarity means that the present state of the Markov chain and the next output of the deterministic channel uniquely determine the next state. At present, there is no known method to calculate the rate of a nonunifilar source. Two tentative approaches to this unsolved problem are given, namely source identical twins and the master-slave source, which appear to shed some light on the question of rate calculation for a nonunifilar source.
Bidirectional Texture Function Simultaneous Autoregressive Model
Czech Academy of Sciences Publication Activity Database
Haindl, Michal; Havlíček, Michal
Berlin: Springer, 2012, s. 149-159. (Lecture Notes in Computer Science. 7252). ISBN 978-3-642-32435-2. ISSN 0302-9743. [MUSCLE. Pisa (IT), 13.12.2011-15.12.2011] R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/0593; GA ČR GAP103/11/0335 Grant ostatní: CESNET(CZ) 387/2010 Institutional support: RVO:67985556 Keywords : bidirectional texture function * texture analysis * texture synthesis * data compression * virtual reality Subject RIV: BD - Theory of Information http://library.utia.cas.cz/separaty/2012/RO/haindl-bidirectional texture function simultaneous autoregressive model.pdf
Model reduction methods for vector autoregressive processes
Brüggemann, Ralf
2004-01-01
1. 1 Objective of the Study Vector autoregressive (VAR) models have become one of the dominant research tools in the analysis of macroeconomic time series during the last two decades. The great success of this modeling class started with Sims' (1980) critique of the traditional simultaneous equation models (SEM). Sims criticized the use of 'too many incredible restrictions' based on 'supposed a priori knowledge' in large scale macroeconometric models which were popular at that time. Therefore, he advo cated largely unrestricted reduced form multivariate time series models, unrestricted VAR models in particular. Ever since his influential paper these models have been employed extensively to characterize the underlying dynamics in systems of time series. In particular, tools to summarize the dynamic interaction between the system variables, such as impulse response analysis or forecast error variance decompo sitions, have been developed over the years. The econometrics of VAR models and related quantities i...
Autoregressive Time Series Forecasting of Computational Demand
Sandholm, Thomas
2007-01-01
We study the predictive power of autoregressive moving average models when forecasting demand in two shared computational networks, PlanetLab and Tycoon. Demand in these networks is very volatile, and predictive techniques to plan usage in advance can improve the performance obtained drastically. Our key finding is that a random walk predictor performs best for one-step-ahead forecasts, whereas ARIMA(1,1,0) and adaptive exponential smoothing models perform better for two and three-step-ahead forecasts. A Monte Carlo bootstrap test is proposed to evaluate the continuous prediction performance of different models with arbitrary confidence and statistical significance levels. Although the prediction results differ between the Tycoon and PlanetLab networks, we observe very similar overall statistical properties, such as volatility dynamics.
Bielecki, Tomasz R.; Jakubowski, Jacek; Niewęgłowski, Mariusz
2011-01-01
This article continues our study of Markovian consistency and Markov copulae. In particular, we characterize the weak Markovian consistency for finite Markov chains. We discuss some aspects of dependence between the components of a multivariate Markov chain in the context of weak Markovian consistency and strong Markovian consistency. In this connection, we also introduce and discuss the concept of weak Markov copulae.
Directory of Open Access Journals (Sweden)
R.J. Boys
2002-01-01
Full Text Available This paper describes a Bayesian approach to determining the order of a finite state Markov chain whose transition probabilities are themselves governed by a homogeneous finite state Markov chain. It extends previous work on homogeneous Markov chains to more general and applicable hidden Markov models. The method we describe uses a Markov chain Monte Carlo algorithm to obtain samples from the (posterior distribution for both the order of Markov dependence in the observed sequence and the other governing model parameters. These samples allow coherent inferences to be made straightforwardly in contrast to those which use information criteria. The methods are illustrated by their application to both simulated and real data sets.
Microstructure Image Simulation of Minced Pork Based on Markov Random Field%基于Markov随机场的猪肉糜微结构图像模拟
Institute of Scientific and Technical Information of China (English)
李华北; 赵杰文
2001-01-01
A stochastic simulation model of minced pork microstructure image was derived with the help of Markov random field theory and Gibbs distribution. The minced pork images of various microstructure were simulated iteratively, and the obtained images were compared with their original ones. The analysis and simulation for the microstructure images of minced food material are key processes in quantitatively studying the influence of microstructure pattern on rheological behavior. By getting the geometry features of minced food material microstructure from the known rheological behavior, the dynamic mechanism and process of the microstructure can be investigated and studied further, therefore the relationship between the rheological behavior and the microstructure was founded. So the conditions quantitatively describing rheological behavior of the minced food material were provided.%利用Markov随机场和Gibbs分布理论，建立了猪肉糜微结构图像的随机场模型，然后通过迭代方法，对不同微结构的猪肉糜图像进行了随机模拟，同时对随机模拟图像和原始图像作了对比分析。 糜状食品物料微观结构图像的分析和模拟是定量研究其微结构模式形态对流变特性影响的关键问题。通过从已知流变特性反演糜状食品物料微结构的几何形态，可以更深入地探讨、研究微结构形成的动力学机制和过程，进而沟通流变特性和微结构形态之间的联系，从而为定量描述糜状食品物料的流变特性提供了条件。
Continuous Time Markov Networks
El-Hay, Tal; Friedman, Nir; Koller, Daphne; Kupferman, Raz
2012-01-01
A central task in many applications is reasoning about processes that change in a continuous time. The mathematical framework of Continuous Time Markov Processes provides the basic foundations for modeling such systems. Recently, Nodelman et al introduced continuous time Bayesian networks (CTBNs), which allow a compact representation of continuous-time processes over a factored state space. In this paper, we introduce continuous time Markov networks (CTMNs), an alternative representation lang...
Stable continuous-time autoregressive process driven by stable subordinator
Wyłomańska, Agnieszka; Gajda, Janusz
2016-02-01
In this paper we examine the continuous-time autoregressive moving average process driven by α-stable Lévy motion delayed by inverse stable subordinator. This process can be applied to high-frequency data with visible jumps and so-called "trapping-events". Those properties are often visible in financial time series but also in amorphous semiconductors, technical data describing the rotational speed of a machine working under various load regimes or data related to indoor air quality. We concentrate on the main characteristics of the examined subordinated process expressed in the language of the measures of dependence which are main tools used in statistical investigation of real data. However, because the analyzed system is based on the α-stable distribution therefore we cannot consider here the correlation (or covariance) as a main measure which indicates at the dependence inside the process. In the paper we examine the codifference, the more general measure of dependence defined for wide class of processes. Moreover we present the simulation procedure of the considered system and indicate how to estimate its parameters. The theoretical results we illustrate by the simulated data analysis.
Dealing with Multiple Solutions in Structural Vector Autoregressive Models.
Beltz, Adriene M; Molenaar, Peter C M
2016-01-01
Structural vector autoregressive models (VARs) hold great potential for psychological science, particularly for time series data analysis. They capture the magnitude, direction of influence, and temporal (lagged and contemporaneous) nature of relations among variables. Unified structural equation modeling (uSEM) is an optimal structural VAR instantiation, according to large-scale simulation studies, and it is implemented within an SEM framework. However, little is known about the uniqueness of uSEM results. Thus, the goal of this study was to investigate whether multiple solutions result from uSEM analysis and, if so, to demonstrate ways to select an optimal solution. This was accomplished with two simulated data sets, an empirical data set concerning children's dyadic play, and modifications to the group iterative multiple model estimation (GIMME) program, which implements uSEMs with group- and individual-level relations in a data-driven manner. Results revealed multiple solutions when there were large contemporaneous relations among variables. Results also verified several ways to select the correct solution when the complete solution set was generated, such as the use of cross-validation, maximum standardized residuals, and information criteria. This work has immediate and direct implications for the analysis of time series data and for the inferences drawn from those data concerning human behavior. PMID:27093380
Autoregressive logistic regression applied to atmospheric circulation patterns
Guanche, Y.; Mínguez, R.; Méndez, F. J.
2014-01-01
Autoregressive logistic regression models have been successfully applied in medical and pharmacology research fields, and in simple models to analyze weather types. The main purpose of this paper is to introduce a general framework to study atmospheric circulation patterns capable of dealing simultaneously with: seasonality, interannual variability, long-term trends, and autocorrelation of different orders. To show its effectiveness on modeling performance, daily atmospheric circulation patterns identified from observed sea level pressure fields over the Northeastern Atlantic, have been analyzed using this framework. Model predictions are compared with probabilities from the historical database, showing very good fitting diagnostics. In addition, the fitted model is used to simulate the evolution over time of atmospheric circulation patterns using Monte Carlo method. Simulation results are statistically consistent with respect to the historical sequence in terms of (1) probability of occurrence of the different weather types, (2) transition probabilities and (3) persistence. The proposed model constitutes an easy-to-use and powerful tool for a better understanding of the climate system.
El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar
2014-11-01
Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data. PMID:26353069
Institute of Scientific and Technical Information of China (English)
Zhao Haijun; Ma Yan; Huang Xiaohong; Su Yujie
2008-01-01
Predicting heartbeat message arrival time is crucial for the quality of failure detection service over internet. However, internet dynamic characteristics make it very difficult to understand message behavior and accurately predict heartbeat arrival time. To solve this problem, a novel black-box model is proposed to predict the next heartbeat arrival time. Heartbeat arrival time is modeled as auto-regressive process, heartbeat sending time is modeled as exogenous variable, the model's coefficients are estimated based on the sliding window of observations and this result is used to predict the next heartbeat arrival time. Simulation shows that this adaptive auto-regressive exogenous (ARX) model can accurately capture heartbeat arrival dynamics and minimize prediction error in different network environments.
International Nuclear Information System (INIS)
In the past few decades many types of structural damage indices based on structural health monitoring signals have been proposed, requiring performance evaluation and comparison studies on these indices in a quantitative manner. One tool to help accomplish this objective is analytical sensitivity analysis, which has been successfully used to evaluate the influences of system operational parameters on observable characteristics in many fields of study. In this paper, the sensitivity expressions of two damage features, namely the Mahalanobis distance of autoregressive coefficients and the Cosh distance of autoregressive spectra, will be derived with respect to both structural damage and measurement noise level. The effectiveness of the proposed methods is illustrated in a numerical case study on a 10-DOF system, where their results are compared with those from direct simulation and theoretical calculation. (paper)
Putting Markov Chains Back into Markov Chain Monte Carlo
Barker, Richard J.; Schofield, Matthew R.
2007-01-01
Markov chain theory plays an important role in statistical inference both in the formulation of models for data and in the construction of efficient algorithms for inference. The use of Markov chains in modeling data has a long history, however the use of Markov chain theory in developing algorithms for statistical inference has only become popular recently. Using mark-recapture models as an illustration, we show how Markov chains can be used for developing demographic models and also ...
Hidden hybrid Markov/semi-Markov chains.
GUÉDON, YANN
2005-01-01
http://www.sciencedirect.com/science?ₒb=IssueURL&_tockey=%23TOC%235880%232005%23999509996%23596026%23FLA%23&ₐuth=y&view=c&ₐcct=C000056834&_version=1&_urlVersion=0&_userid=2292769&md5=87e7f8be94f92a8574da566c600ce631 International audience Models that combine Markovian states with implicit geometric state occupancy distributions and semi-Markovian states with explicit state occupancy distributions, are investigated. This type of model retains the flexibility of hidden semi-Markov chains ...
Markov chains for testing redundant software
White, Allan L.; Sjogren, Jon A.
1988-01-01
A preliminary design for a validation experiment has been developed that addresses several problems unique to assuring the extremely high quality of multiple-version programs in process-control software. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process-control testing, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level using confidence intervals obtained for the transition probabilities during the experiment. An example demonstrating the method is provided.
Estimation of Time Varying Autoregressive Symmetric Alpha Stable
National Aeronautics and Space Administration — In this work, we present a novel method for modeling time-varying autoregressive impulsive signals driven by symmetric alpha stable distributions. The proposed...
Modeling non-Gaussian time-varying vector autoregressive process
National Aeronautics and Space Administration — We present a novel and general methodology for modeling time-varying vector autoregressive processes which are widely used in many areas such as modeling of...
Cardiac arrhythmia classification using autoregressive modeling
Directory of Open Access Journals (Sweden)
Srinivasan Narayanan
2002-11-01
Full Text Available Abstract Background Computer-assisted arrhythmia recognition is critical for the management of cardiac disorders. Various techniques have been utilized to classify arrhythmias. Generally, these techniques classify two or three arrhythmias or have significantly large processing times. A simpler autoregressive modeling (AR technique is proposed to classify normal sinus rhythm (NSR and various cardiac arrhythmias including atrial premature contraction (APC, premature ventricular contraction (PVC, superventricular tachycardia (SVT, ventricular tachycardia (VT and ventricular fibrillation (VF. Methods AR Modeling was performed on ECG data from normal sinus rhythm as well as various arrhythmias. The AR coefficients were computed using Burg's algorithm. The AR coefficients were classified using a generalized linear model (GLM based algorithm in various stages. Results AR modeling results showed that an order of four was sufficient for modeling the ECG signals. The accuracy of detecting NSR, APC, PVC, SVT, VT and VF were 93.2% to 100% using the GLM based classification algorithm. Conclusion The results show that AR modeling is useful for the classification of cardiac arrhythmias, with reasonably high accuracies. Further validation of the proposed technique will yield acceptable results for clinical implementation.
Turner, Sean; Galelli, Stefano; Wilcox, Karen
2015-04-01
Water reservoir systems are often affected by recurring large-scale ocean-atmospheric anomalies, known as teleconnections, that cause prolonged periods of climatological drought. Accurate forecasts of these events -- at lead times in the order of weeks and months -- may enable reservoir operators to take more effective release decisions to improve the performance of their systems. In practice this might mean a more reliable water supply system, a more profitable hydropower plant or a more sustainable environmental release policy. To this end, climate indices, which represent the oscillation of the ocean-atmospheric system, might be gainfully employed within reservoir operating models that adapt the reservoir operation as a function of the climate condition. This study develops a Stochastic Dynamic Programming (SDP) approach that can incorporate climate indices using a Hidden Markov Model. The model simulates the climatic regime as a hidden state following a Markov chain, with the state transitions driven by variation in climatic indices, such as the Southern Oscillation Index. Time series analysis of recorded streamflow data reveals the parameters of separate autoregressive models that describe the inflow to the reservoir under three representative climate states ("normal", "wet", "dry"). These models then define inflow transition probabilities for use in a classic SDP approach. The key advantage of the Hidden Markov Model is that it allows conditioning the operating policy not only on the reservoir storage and the antecedent inflow, but also on the climate condition, thus potentially allowing adaptability to a broader range of climate conditions. In practice, the reservoir operator would effect a water release tailored to a specific climate state based on available teleconnection data and forecasts. The approach is demonstrated on the operation of a realistic, stylised water reservoir with carry-over capacity in South-East Australia. Here teleconnections relating
Monitoring time-varying parameters in an autoregression
Carsoule, Frédéric; Franses, Philip Hans
1999-01-01
textabstractWe develop a sequential testing approach for a structural change in the parameters of an autoregression, which amounts to a monitoring procedure with a controlled asymptotic size as we repeat the test. Our method can be used as a general misspecification test. We apply our method to monthly US industrial production in order to investigate if its autoregressive behavior and/or its innovation variance have changed during the twentieth century.
Inference of High-dimensional Autoregressive Generalized Linear Models
Hall, Eric C.; Raskutti, Garvesh; Willett, Rebecca
2016-01-01
Vector autoregressive models characterize a variety of time series in which linear combinations of current and past observations can be used to accurately predict future observations. For instance, each element of an observation vector could correspond to a different node in a network, and the parameters of an autoregressive model would correspond to the impact of the network structure on the time series evolution. Often these models are used successfully in practice to learn the structure of...
On the range of validity of the autoregressive sieve bootstrap
Kreiss, Jens-Peter; Paparoditis, Efstathios; Politis, Dimitris N.
2012-01-01
We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve bootstrap is valid for stationary processes possessing a general Wold-type autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is everywhere positive....
Sensitivity of hidden Markov models
Mitrophanov, Alexander Yu.; Lomsadze, Alexandre; Borodovsky, Mark
2005-01-01
We derive a tight perturbation bound for hidden Markov models. Using this bound, we show that, in many cases, the distribution of a hidden Markov model is considerably more sensitive to perturbations in the emission probabilities than to perturbations in the transition probability matrix and the initial distribution of the underlying Markov chain. Our approach can also be used to assess the sensitivity of other stochastic models, such as mixture processes and semi-Markov ...
A new Markov Binomial distribution.
Omey, Edward; Minkova, Leda D.
2011-01-01
In this paper, we introduce a two state homogeneous Markov chain and define a geometric distribution related to this Markov chain. We define also the negative binomial distribution similar to the classical case and call it NB related to interrupted Markov chain. The new binomial distribution is related to the interrupted Markov chain. Some characterization properties of the Geometric distributions are given. Recursion formulas and probability mass functions for the NB distribution and the new...
On Markov Chains and Filtrations
Spreij, Peter
1997-01-01
In this paper we rederive some well known results for continuous time Markov processes that live on a finite state space.Martingale techniques are used throughout the paper. Special attention is paid to the construction of a continuous timeMarkov process, when we start from a discrete time Markov chain. The Markov property here holds with respect tofiltrations that need not be minimal.
CONVERGENCE OF MARKOV CHAIN APPROXIMATIONS TO STOCHASTIC REACTION DIFFUSION EQUATIONS
Kouritzin, Michael A.; Hongwei Long
2001-01-01
In the context of simulating the transport of a chemical or bacterial contaminant through a moving sheet of water, we extend a well-established method of approximating reaction-diffusion equations with Markov chains by allowing convection, certain Poisson measure driving sources and a larger class of reaction functions. Our alterations also feature dramatically slower Markov chain state change rates often yielding a ten to one-hundred-fold simulation speed increase over the previous version o...
The Kernel Adaptive Autoregressive-Moving-Average Algorithm.
Li, Kan; Príncipe, José C
2016-02-01
In this paper, we present a novel kernel adaptive recurrent filtering algorithm based on the autoregressive-moving-average (ARMA) model, which is trained with recurrent stochastic gradient descent in the reproducing kernel Hilbert spaces. This kernelized recurrent system, the kernel adaptive ARMA (KAARMA) algorithm, brings together the theories of adaptive signal processing and recurrent neural networks (RNNs), extending the current theory of kernel adaptive filtering (KAF) using the representer theorem to include feedback. Compared with classical feedforward KAF methods, the KAARMA algorithm provides general nonlinear solutions for complex dynamical systems in a state-space representation, with a deferred teacher signal, by propagating forward the hidden states. We demonstrate its capabilities to provide exact solutions with compact structures by solving a set of benchmark nondeterministic polynomial-complete problems involving grammatical inference. Simulation results show that the KAARMA algorithm outperforms equivalent input-space recurrent architectures using first- and second-order RNNs, demonstrating its potential as an effective learning solution for the identification and synthesis of deterministic finite automata. PMID:25935049
The comparison study among several data transformations in autoregressive modeling
Setiyowati, Susi; Waluyo, Ramdhani Try
2015-12-01
In finance, the adjusted close of stocks are used to observe the performance of a company. The extreme prices, which may increase or decrease drastically, are often become particular concerned since it can impact to bankruptcy. As preventing action, the investors have to observe the future (forecasting) stock prices comprehensively. For that purpose, time series analysis could be one of statistical methods that can be implemented, for both stationary and non-stationary processes. Since the variability process of stocks prices tend to large and also most of time the extreme values are always exist, then it is necessary to do data transformation so that the time series models, i.e. autoregressive model, could be applied appropriately. One of popular data transformation in finance is return model, in addition to ratio of logarithm and some others Tukey ladder transformation. In this paper these transformations are applied to AR stationary models and non-stationary ARCH and GARCH models through some simulations with varying parameters. As results, this work present the suggestion table that shows transformations behavior for some condition of parameters and models. It is confirmed that the better transformation is obtained, depends on type of data distributions. In other hands, the parameter conditions term give significant influence either.
Benchmarking of a Markov multizone model of contaminant transport.
Jones, Rachael M; Nicas, Mark
2014-10-01
A Markov chain model previously applied to the simulation of advection and diffusion process of gaseous contaminants is extended to three-dimensional transport of particulates in indoor environments. The model framework and assumptions are described. The performance of the Markov model is benchmarked against simple conventional models of contaminant transport. The Markov model is able to replicate elutriation predictions of particle deposition with distance from a point source, and the stirred settling of respirable particles. Comparisons with turbulent eddy diffusion models indicate that the Markov model exhibits numerical diffusion in the first seconds after release, but over time accurately predicts mean lateral dispersion. The Markov model exhibits some instability with grid length aspect when turbulence is incorporated by way of the turbulent diffusion coefficient, and advection is present. However, the magnitude of prediction error may be tolerable for some applications and can be avoided by incorporating turbulence by way of fluctuating velocity (e.g. turbulence intensity). PMID:25143517
Partially Hidden Markov Models
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Rissanen, Jorma
1996-01-01
Partially Hidden Markov Models (PHMM) are introduced. They differ from the ordinary HMM's in that both the transition probabilities of the hidden states and the output probabilities are conditioned on past observations. As an illustration they are applied to black and white image compression where...
Partially Hidden Markov Models
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Rissanen, Jorma
1996-01-01
Partially Hidden Markov Models (PHMM) are introduced. They differ from the ordinary HMM's in that both the transition probabilities of the hidden states and the output probabilities are conditioned on past observations. As an illustration they are applied to black and white image compression wher...
DEFF Research Database (Denmark)
Kohlenbach, Ulrich Wilhelm
We show that the so-called weak Markov's principle (WMP) which states that every pseudo-positive real number is positive is underivable in E-HA + AC. Since allows one to formalize (atl eastl arge parts of) Bishop's constructive mathematics, this makes it unlikely that WMP can be proved within the...
Lopes, Sílvia R. C.; Prass, Taiane S.
2014-05-01
Here we present a theoretical study on the main properties of Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedastic (FIEGARCH) processes. We analyze the conditions for the existence, the invertibility, the stationarity and the ergodicity of these processes. We prove that, if { is a FIEGARCH(p,d,q) process then, under mild conditions, { is an ARFIMA(q,d,0) with correlated innovations, that is, an autoregressive fractionally integrated moving average process. The convergence order for the polynomial coefficients that describes the volatility is presented and results related to the spectral representation and to the covariance structure of both processes { and { are discussed. Expressions for the kurtosis and the asymmetry measures for any stationary FIEGARCH(p,d,q) process are also derived. The h-step ahead forecast for the processes {, { and { are given with their respective mean square error of forecast. The work also presents a Monte Carlo simulation study showing how to generate, estimate and forecast based on six different FIEGARCH models. The forecasting performance of six models belonging to the class of autoregressive conditional heteroskedastic models (namely, ARCH-type models) and radial basis models is compared through an empirical application to Brazilian stock market exchange index.
Robust filtering and prediction for systems with embedded finite-state Markov-Chain dynamics
International Nuclear Information System (INIS)
This research developed new methodologies for the design of robust near-optimal filters/predictors for a class of system models that exhibit embedded finite-state Markov-chain dynamics. These methodologies are developed through the concepts and methods of stochastic model building (including time-series analysis), game theory, decision theory, and filtering/prediction for linear dynamic systems. The methodology is based on the relationship between the robustness of a class of time-series models and quantization which is applied to the time series as part of the model identification process. This relationship is exploited by utilizing the concept of an equivalence, through invariance of spectra, between the class of Markov-chain models and the class of autoregressive moving average (ARMA) models. This spectral equivalence permits a straightforward implementation of the desirable robust properties of the Markov-chain approximation in a class of models which may be applied in linear-recursive form in a linear Kalman filter/predictor structure. The linear filter/predictor structure is shown to provide asymptotically optimal estimates of states which represent one or more integrations of the Markov-chain state. The development of a new saddle-point theorem for a game based on the Markov-chain model structure gives rise to a technique for determining a worst case Markov-chain process, upon which a robust filter/predictor design if based
Smith, R. M.
1991-01-01
Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the behavior of the system with a continuous-time Markov chain, where a reward rate is associated with each state. In a reliability/availability model, upstates may have reward rate 1 and down states may have reward rate zero associated with them. In a queueing model, the number of jobs of certain type in a given state may be the reward rate attached to that state. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Expected steady-state reward rate and expected instantaneous reward rate are clearly useful measures of the Markov reward model. More generally, the distribution of accumulated reward or time-averaged reward over a finite time interval may be determined from the solution of the Markov reward model. This information is of great practical significance in situations where the workload can be well characterized (deterministically, or by continuous functions e.g., distributions). The design process in the development of a computer system is an expensive and long term endeavor. For aerospace applications the reliability of the computer system is essential, as is the ability to complete critical workloads in a well defined real time interval. Consequently, effective modeling of such systems must take into account both performance and reliability. This fact motivates our use of Markov reward models to aid in the development and evaluation of fault tolerant computer systems.
Cohomological dimension of Markov compacta
Dranishnikov, Alexander
2006-01-01
We rephrase Gromov's definition of Markov compacta, introduce a subclass of Markov compacta defined by one building block and study cohomological dimensions of these compacta. We show that for a Markov compactum $X$, $\\dim_{\\Z_{(p)}}X=\\dim_{\\Q}X$ for all but finitely many primes $p$ where $\\Z_{(p)}$ is the localization of $\\Z$ at $p$. We construct Markov compacta of arbitrarily large dimension having $\\dim_{\\Q}X=1$ as well as Markov compacta of arbitrary large rational dimension with $\\dim_{\\...
Mixture latent autoregressive models for longitudinal data
Bartolucci, Francesco; Pennoni, Fulvia
2011-01-01
Many relevant statistical and econometric models for the analysis of longitudinal data include a latent process to account for the unobserved heterogeneity between subjects in a dynamic fashion. Such a process may be continuous (typically an AR(1)) or discrete (typically a Markov chain). In this paper, we propose a model for longitudinal data which is based on a mixture of AR(1) processes with different means and correlation coefficients, but with equal variances. This model belongs to the class of models based on a continuous latent process, and then it has a natural interpretation in many contexts of application, but it is more flexible than other models in this class, reaching a goodness-of-fit similar to that of a discrete latent process model, with a reduced number of parameters. We show how to perform maximum likelihood estimation of the proposed model by the joint use of an Expectation-Maximisation algorithm and a Newton-Raphson algorithm, implemented by means of recursions developed in the hidden Mark...
Variance bounding Markov chains
Roberts, Gareth O.; Jeffrey S. Rosenthal
2008-01-01
We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L2 functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Peskun order. We close with some applications to Metropolis–Hastings algorithms.
Energy Technology Data Exchange (ETDEWEB)
Nicoulaud-Gouin, V.; Giacalone, M.; Gonze, M.A. [Institut de Radioprotection et de Surete Nucleaire-PRP-ENV/SERIS/LM2E (France); Martin-Garin, A.; Garcia-Sanchez, L. [IRSN-PRP-ENV/SERIS/L2BT (France)
2014-07-01
, distinguishes instantaneous (K{sub d}1) and first-order kinetics of sorption and desorption processes (λ{sub fix}, λ{sub rem}), each having potentially a limited sorption capacity. A Soil-Plant Deposition Model describing the weeds contamination in {sup 137}Cs, {sup 134}Cs and {sup 131}I, with in situ measures in the Fukushima prefecture (Gonze et al. submitted to this conference). This model considers two foliage pools and a root pool, and describes foliar biomass growth with a Verhulst model. One prerequisite for calibration is model identifiability. Here, we showed that there are not unique parameter values corresponding to a data set. However, sharp distributions were found when several data sets were involved. One numerical difficulty of Markov Chains is to check convergence. It was here examined with Raftery and Lewis diagnostic, Gelman and Rubin plots, and simulation trails. Failing to converge may indicate that the model is not adapted to the observations. The Bayes factor was used to decide between competing models, which applies even if they are not nested. For most data series, EK model was preferable to the nested K{sub d} approach. An Empirical Dynamical Model -consisting of two exponential functions- was compared to the Soil-Plant Deposition Model, by distinguishing site-specific parameters and invariant parameters between stations, in order to study the goodness-of-fit of the Soil-Plant Deposition Model. (authors)
International Nuclear Information System (INIS)
instantaneous (Kd1) and first-order kinetics of sorption and desorption processes (λfix, λrem), each having potentially a limited sorption capacity. A Soil-Plant Deposition Model describing the weeds contamination in 137Cs, 134Cs and 131I, with in situ measures in the Fukushima prefecture (Gonze et al. submitted to this conference). This model considers two foliage pools and a root pool, and describes foliar biomass growth with a Verhulst model. One prerequisite for calibration is model identifiability. Here, we showed that there are not unique parameter values corresponding to a data set. However, sharp distributions were found when several data sets were involved. One numerical difficulty of Markov Chains is to check convergence. It was here examined with Raftery and Lewis diagnostic, Gelman and Rubin plots, and simulation trails. Failing to converge may indicate that the model is not adapted to the observations. The Bayes factor was used to decide between competing models, which applies even if they are not nested. For most data series, EK model was preferable to the nested Kd approach. An Empirical Dynamical Model -consisting of two exponential functions- was compared to the Soil-Plant Deposition Model, by distinguishing site-specific parameters and invariant parameters between stations, in order to study the goodness-of-fit of the Soil-Plant Deposition Model. (authors)
Markov or not Markov - this should be a question
Bickenbach, Frank; Bode, Eckhardt
2002-01-01
Although it is well known that Markov process theory, frequently applied in the literature on income convergence, imposes some very restrictive assumptions upon the data generating process, these assumptions have generally been taken for granted so far. The present paper proposes, resp. recalls chi-square tests of the Markov property, of spatial independence, and of homogeneity across time and space to assess the reliability of estimated Markov transition matrices. As an illustration we show ...
A complex autoregressive model and application to monthly temperature forecasts
Directory of Open Access Journals (Sweden)
X. Gu
2005-11-01
Full Text Available A complex autoregressive model was established based on the mathematic derivation of the least squares for the complex number domain which is referred to as the complex least squares. The model is different from the conventional way that the real number and the imaginary number are separately calculated. An application of this new model shows a better forecast than forecasts from other conventional statistical models, in predicting monthly temperature anomalies in July at 160 meteorological stations in mainland China. The conventional statistical models include an autoregressive model, where the real number and the imaginary number are separately disposed, an autoregressive model in the real number domain, and a persistence-forecast model.
Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity
Directory of Open Access Journals (Sweden)
Isao Ishida
2015-01-01
Full Text Available We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500 and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility.
A Mixture Innovation Heterogeneous Autoregressive Model for Structural Breaks and Long Memory
DEFF Research Database (Denmark)
Nonejad, Nima
We propose a flexible model to describe nonlinearities and long-range dependence in time series dynamics. Our model is an extension of the heterogeneous autoregressive model. Structural breaks occur through mixture distributions in state innovations of linear Gaussian state space models. Monte...... Carlo simulations evaluate the properties of the estimation procedures. Results show that the proposed model is viable and flexible for purposes of forecasting volatility. Model uncertainty is accounted for by employing Bayesian model averaging. Bayesian model averaging provides very competitive...... forecasts compared to any single model specification. It provides further improvements when we average over nonlinear specifications....
A Score Type Test for General Autoregressive Models in Time Series
Institute of Scientific and Technical Information of China (English)
Jian-hong Wu; Li-xing Zhu
2007-01-01
This paper is devoted to the goodness-of-fit test for the general autoregressive models in time series. By averaging for the weighted residuals, we construct a score type test which is asymptotically standard chi-squared under the null and has some desirable power properties under the alternatives. Specifically, the test is sensitive to alternatives and can detect the alternatives approaching, along a direction, the null at a rate that is arbitrarily close to n-1/2. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. The performance of the tests is evaluated through simulation studies.
Distribusi Markov-Binomial Negatif
Widyasari, Rina
2015-01-01
The way to find a new distribution of random variables is defining the distribution which associated with Markov chain. In this research, researcher defines all the random variables identically independent distributed negative binomial distribution and form a Markov chain. Suppose that Xn is a sequence of Bernoulli trials that if 1 occurs means ”success” and 0 occurs means ”failure”. Nb(s) defined as random variables sth success in n trials. Each trial form a Markov chain, in n...
Contribution to ECDIS Reliability using Markov Model
Sumić, Dean; Peraković, Dragan; Jurčević, Marinko
2014-01-01
An Integrated Bridge System (IBS) contains a fully duplicated Electronic Chart Display and Information System (ECDIS). Although duplication should increase system reliability, reliability and availability are not improved. Proper ECDIS maintenance includes updating both: the information system and the provided chart system. This procedure, in practice, tends to decrease reliability and availability. A Markov ECDIS simulation model is given. A new design concept is presented and proposed. The ...
Markov Chains For Testing Redundant Software
White, Allan L.; Sjogren, Jon A.
1990-01-01
Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
Bayesian Posterior Distributions Without Markov Chains
Cole, Stephen R.; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B.
2012-01-01
Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976–1983) assessing the relation between residential ex...
Institute of Scientific and Technical Information of China (English)
Xiaoyun MO; Jieming ZHOU; Hui OU; Xiangqun YANG
2013-01-01
Given a new Double-Markov risk model DM =(μ,Q,v,H; Y,Z) and Double-Markov risk process U ={U(t),t ≥ 0}.The ruin or survival problem is addressed.Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained.Recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained.The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.
Barczy, Matyas; Pap, Gyula
2010-01-01
In this paper the asymptotic behavior of conditional least squares estimators of the autoregressive parameter for nonprimitive unstable integer-valued autoregressive models of order 2 (INAR(2)) is described.
The cointegrated vector autoregressive model with general deterministic terms
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
In the cointegrated vector autoregression (CVAR) literature, deterministic terms have until now been analyzed on a case-by-case, or as-needed basis. We give a comprehensive unified treatment of deterministic terms in the additive model X(t)= Z(t) + Y(t), where Z(t) belongs to a large class...
Weak Convergence of the Residual Empirical Process in Explosive Autoregression
Koul, Hira L.; Levental, Shlomo
1989-01-01
This paper proves the weak convergence of the residual empirical process in an explosive autoregression model to the Brownian bridge. As an application the Kolmogorov-Smirnov goodness-of-fit test for testing that the errors have a specified distribution is shown to be asymptotically distribution-free.
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d-b; where d ≥ b > 1/2 are parameters to be estimated. We model the data X1,...,XT given the initial val...
Likelihood inference for a nonstationary fractional autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Ørregård Nielsen, Morten
2010-01-01
This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data X1,.....
Likelihood Inference for a Nonstationary Fractional Autoregressive Model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
This paper discusses model based inference in an autoregressive model for fractional processes based on the Gaussian likelihood. The model allows for the process to be fractional of order d or d - b; where d = b > 1/2 are parameters to be estimated. We model the data X¿, ..., X¿ given the initial...
Nonlinear autoregressive models with heavy-tailed innovation
Institute of Scientific and Technical Information of China (English)
JIN Yang; AN Hongzhi
2005-01-01
In this paper, we discuss the relationship between the stationary marginal tail probability and the innovation's tail probability of nonlJnear autoregressive models. We show that under certain conditions that ensure the stationarity and ergodicity, one dimension stationary marginal distribution has the heavy-tailed probability property with the same index as that of the innovation's tail probability.
Limit theorems for bifurcating integer-valued autoregressive processes
Blandin, Vassili
2012-01-01
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with the quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales.
New GPS-aided SINU System Modeling using an Autoregressive Model
Directory of Open Access Journals (Sweden)
Chot Hun Lim
2015-09-01
Full Text Available Stochastic error in the Micro-Electro-Mechanical-System (MEMS Strapdown Inertial Navigation Unit (SINU is the primary issue causing sensors to be unable to operate as a standalone device. Conventional implementation of MEMS SINU fuses measurement with a global positioning system (GPS through a Kalman filter in order to achieve long-term accuracy. Such integration is known as a GPS-aided SINU system, and its estimation accuracy relies on how precise the stochastic error prediction is in Kalman filtering operation. In this paper, a comprehensive study on stochastic error modeling and analysis through a Gauss- Markov (GM model and autoregressive (AR model are presented. A wavelet denoising technique is introduced prior to error modeling to remove the MEMS SINU's high frequency noise. Without a wavelet denoising technique, neither the GM model nor AR model can be utilized to represent the stochastic error of SINU. Next, details of the Kalman filter implementation to accommodate the AR model are presented. The modeling outcomes are implemented on an unmanned aerial vehicle (UAV for on-board motion sensing. The experimental results show that AR model implementation, compared to a conventional GM model, significantly reduced the estimated errors while preserving the position, velocity and orientation measurements.
Nonlinear Markov processes: Deterministic case
Energy Technology Data Exchange (ETDEWEB)
Frank, T.D. [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States)], E-mail: till.frank@uconn.edu
2008-10-06
Deterministic Markov processes that exhibit nonlinear transition mechanisms for probability densities are studied. In this context, the following issues are addressed: Markov property, conditional probability densities, propagation of probability densities, multistability in terms of multiple stationary distributions, stability analysis of stationary distributions, and basin of attraction of stationary distribution.
Markov Random Field Surface Reconstruction
DEFF Research Database (Denmark)
Paulsen, Rasmus Reinhold; Bærentzen, Jakob Andreas; Larsen, Rasmus
2010-01-01
A method for implicit surface reconstruction is proposed. The novelty in this paper is the adaption of Markov Random Field regularization of a distance field. The Markov Random Field formulation allows us to integrate both knowledge about the type of surface we wish to reconstruct (the prior) and...
Nonlinear Markov processes: Deterministic case
International Nuclear Information System (INIS)
Deterministic Markov processes that exhibit nonlinear transition mechanisms for probability densities are studied. In this context, the following issues are addressed: Markov property, conditional probability densities, propagation of probability densities, multistability in terms of multiple stationary distributions, stability analysis of stationary distributions, and basin of attraction of stationary distribution
An interlacing theorem for reversible Markov chains
International Nuclear Information System (INIS)
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
R. Maity; Prasad, D.
2011-01-01
In this paper, Split Markov Process (SMP) is developed to assess one-step-ahead variation of daily rainfall at a rain gauge station. SMP is an advancement of general Markov Process (MP) and specially developed for probabilistic assessment of change in daily rainfall magnitude. The approach is based on a first-order Markov chain to simulate daily rainfall variation at a point through state/sub-state Transitional Probability Matrix (TPM). Th...
Tornadoes and related damage costs: statistical modeling with a semi-Markov approach
Chiara Corini; Guglielmo D'Amico; Filippo Petroni; Flavio Prattico; Raimondo Manca
2015-01-01
We propose a statistical approach to tornadoes modeling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modeling the tornadoes intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornadoes intensity into six states, it is possible to model the tornadoes intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reprod...
Markov chains theory and applications
Sericola, Bruno
2013-01-01
Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest.The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...
Parameter Estimation for Generalized Brownian Motion with Autoregressive Increments
Fendick, Kerry
2011-01-01
This paper develops methods for estimating parameters for a generalization of Brownian motion with autoregressive increments called a Brownian ray with drift. We show that a superposition of Brownian rays with drift depends on three types of parameters - a drift coefficient, autoregressive coefficients, and volatility matrix elements, and we introduce methods for estimating each of these types of parameters using multidimensional times series data. We also cover parameter estimation in the contexts of two applications of Brownian rays in the financial sphere: queuing analysis and option valuation. For queuing analysis, we show how samples of queue lengths can be used to estimate the conditional expectation functions for the length of the queue and for increments in its net input and lost potential output. For option valuation, we show how the Black-Scholes-Merton formula depends on the price of the security on which the option is written through estimates not only of its volatility, but also of a coefficient ...
Bias-corrected estimation in potentially mildly explosive autoregressive models
DEFF Research Database (Denmark)
Haufmann, Hendrik; Kruse, Robinson
This paper provides a comprehensive Monte Carlo comparison of different finite-sample bias-correction methods for autoregressive processes. We consider classic situations where the process is either stationary or exhibits a unit root. Importantly, the case of mildly explosive behaviour is studied...... indirect inference approach oers a valuable alternative to other existing techniques. Its performance (measured by its bias and root mean squared error) is balanced and highly competitive across many different settings. A clear advantage is its applicability for mildly explosive processes. In an empirical...... application to a long annual US Debt/GDP series we consider rolling window estimation of autoregressive models. We find substantial evidence for time-varying persistence and periods of explosiveness during the Civil War and World War II. During the recent years, the series is nearly explosive again. Further...
On the range of validity of the autoregressive sieve bootstrap
Kreiss, Jens-Peter; Politis, Dimitris N; 10.1214/11-AOS900
2012-01-01
We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve bootstrap is valid for stationary processes possessing a general Wold-type autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is everywhere positive. Our main theorem provides a simple and effective tool in assessing whether the AR-sieve bootstrap is asymptotically valid in any given situation. In effect, the large-sample distribution of the statistic in question must only depend on the first and second order moments of the process; prominent examples include the sample mean and the spectral density. As a counterexample, we show how the AR-sieve bootstrap is not always valid for the sample autocovariance even when the underlying process is linear.
Compressing redundant information in Markov chains
Aletti, Giacomo
2006-01-01
Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is hence defined and tested on some classical problems.
Directory of Open Access Journals (Sweden)
D. G. Partridge
2012-03-01
Full Text Available This paper presents a novel approach to investigate cloud-aerosol interactions by coupling a Markov chain Monte Carlo (MCMC algorithm to an adiabatic cloud parcel model. Despite the number of numerical cloud-aerosol sensitivity studies previously conducted few have used statistical analysis tools to investigate the global sensitivity of a cloud model to input aerosol physiochemical parameters. Using numerically generated cloud droplet number concentration (CDNC distributions (i.e. synthetic data as cloud observations, this inverse modelling framework is shown to successfully estimate the correct calibration parameters, and their underlying posterior probability distribution.
The employed analysis method provides a new, integrative framework to evaluate the global sensitivity of the derived CDNC distribution to the input parameters describing the lognormal properties of the accumulation mode aerosol and the particle chemistry. To a large extent, results from prior studies are confirmed, but the present study also provides some additional insights. There is a transition in relative sensitivity from very clean marine Arctic conditions where the lognormal aerosol parameters representing the accumulation mode aerosol number concentration and mean radius and are found to be most important for determining the CDNC distribution to very polluted continental environments (aerosol concentration in the accumulation mode >1000 cm^{−3} where particle chemistry is more important than both number concentration and size of the accumulation mode.
The competition and compensation between the cloud model input parameters illustrates that if the soluble mass fraction is reduced, the aerosol number concentration, geometric standard deviation and mean radius of the accumulation mode must increase in order to achieve the same CDNC distribution.
This study demonstrates that inverse modelling provides a flexible, transparent and
Decision analysis in clinical radiology by means of Markov modeling
International Nuclear Information System (INIS)
Markov models (Multistate transition models) are mathematical tools to simulate a cohort of individuals followed over time to assess the prognosis resulting from different strategies. They are applied on the assumption that persons are in one of a finite number of states of health (Markov states). Each condition is given a transition probability as well as an incremental value. Probabilities may be chosen constant or varying over time due to predefined rules. Time horizon is divided into equal increments (Markov cycles). The model calculates quality-adjusted life expectancy employing real-life units and values and summing up the length of time spent in each health state adjusted for objective outcomes and subjective appraisal. This sort of modeling prognosis for a given patient is analogous to utility in common decision trees. Markov models can be evaluated by matrix algebra, probabilistic cohort simulation and Monte Carlo simulation. They have been applied to assess the relative benefits and risks of a limited number of diagnostic and therapeutic procedures in radiology. More interventions should be submitted to Markov analyses in order to elucidate their cost-effectiveness. (orig.)
CICAAR - Convolutive ICA with an Auto-Regressive Inverse Model
DEFF Research Database (Denmark)
Dyrholm, Mads; Hansen, Lars Kai
2004-01-01
We invoke an auto-regressive IIR inverse model for convolutive ICA and derive expressions for the likelihood and its gradient. We argue that optimization will give a stable inverse. When there are more sensors than sources the mixing model parameters are estimated in a second step by least square...... estimation. We demonstrate the method on synthetic data and finally separate speech and music in a real room recording....
Structural vector autoregressions: Theory of identification and algorithms for inference
Rubio-Ramírez, Juan F.; Waggoner, Daniel F.; Zha, Tao
2008-01-01
Structural vector autoregressions (SVARs) are widely used for policy analysis and to provide stylized facts for dynamic general equilibrium models. Yet there have been no workable rank conditions to ascertain whether an SVAR is globally identified. When identifying restrictions such as long-run restrictions are imposed on impulse responses, there have been no efficient algorithms for small-sample estimation and inference. To fill these important gaps in the literature, this paper makes four c...
Robust estimation of nonstationary, fractionally integrated, autoregressive, stochastic volatility
Mark J. Jensen
2015-01-01
Empirical volatility studies have discovered nonstationary, long-memory dynamics in the volatility of the stock market and foreign exchange rates. This highly persistent, infinite variance - but still mean reverting - behavior is commonly found with nonparametric estimates of the fractional differencing parameter d, for financial volatility. In this paper, a fully parametric Bayesian estimator, robust to nonstationarity, is designed for the fractionally integrated, autoregressive, stochastic ...
A Simple Cointegrating Rank Test Without Vector Autoregression
Mototsugu Shintani
2000-01-01
This paper proposes a fully nonparametric test for cointegrating rank which does not require estimation of a vector autoregressive model. The test exploits the fact that the degeneracy in the moment matrix of the variables with mixed integration order corresponds to the notion of cointegration. With an appropriate standardization, the test statistics are shown to have a nuisance parameter free limiting distribution and to be consistent under reasonable conditions. Monte Carlo experiments also...
Interest rate pass-through estimates from vector autoregressive models
Burgstaller, Johann
2005-01-01
The empirical literature on interest rate transmission presents diverse and sometimes conflicting estimates. By discussing methodological and specification-related issues, the results of this paper contribute to the understanding of these differences. Eleven Austrian bank lending and deposit rates are utilized to illustrate the pass-through of impulses from monetary policy and banks’ cost of funds. Results from vector autoregressions suggest that the long-run pass-through is higher for moveme...
Adaptive Estimation of Autoregressive Models with Time-Varying Variances
Ke-Li Xu; Phillips, Peter C. B.
2006-01-01
Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of th...
Forecasting with time-varying vector autoregressive models
Triantafyllopoulos, K.
2008-01-01
The purpose of this paper is to propose a time-varying vector autoregressive model (TV-VAR) for forecasting multivariate time series. The model is casted into a state-space form that allows flexible description and analysis. The volatility covariance matrix of the time series is modelled via inverted Wishart and singular multivariate beta distributions allowing a fully conjugate Bayesian inference. Model performance and model comparison is done via the likelihood function, sequential Bayes fa...
Testing exact rational expectations in cointegrated vector autoregressive models
DEFF Research Database (Denmark)
Johansen, Søren; Swensen, Anders Rygh
1999-01-01
This paper considers the testing of restrictions implied by rational expectations hypotheses in a cointegrated vector autoregressive model for I(1) variables. If the rational expectations involve one-step-ahead observations only and the coefficients are known, an explicit parameterization of the ...... restrictions is found, and the maximum-likelihood estimator is derived by regression and reduced rank regression. An application is given to a present value model....
Asymptotic results for bifurcating random coefficient autoregressive processes
Blandin, Vassili
2012-01-01
The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and the inheritance, we establish the almost sure convergence of our estimators, as well as a quadratic strong law and central limit theorems. Our study mostly relies on limit theorems for vector-valued martingales.
UV Index Modeling by Autoregressive Distributed Lag (ADL Model)
Alexandre Boleira Lopo; Maria Helena Constantino Spyrides; Paulo Sérgio Lucio; Javier Sigró
2014-01-01
The objective of this work is to model statistically the ultraviolet radiation index (UV Index) to make forecast (extrapolate) and analyze trends. The task is relevant, due to increased UV flux and high rate of cases non-melanoma skin cancer in northeast of Brazil. The methodology utilized an Autoregressive Distributed Lag model (ADL) or Dynamic Linear Regression model. The monthly data of UV index were measured in east coast of the Brazilian Northeast (City of Natal-Rio G...
Stock price forecasting: autoregressive modelling and fuzzy neural network
Marcek, Dusan
2000-01-01
Most models for the time series of stock prices have centered on autoregressive (AR) processes. Traditionaly, fundamantal Box-Jenkins analysis [3] have been the mainstream methodology used to develop time series models. Next, we briefly describe the develop a classical AR model for stock price forecasting. Then a fuzzy regression model is then introduced Following this description, an artificial fuzzy neural network based on B-spline member ship function is presented as an alternative to ...
CICAAR - Convolutive ICA with an Auto-Regressive Inverse Model
Dyrholm, Mads; Hansen, Lars Kai
2004-01-01
We invoke an auto-regressive IIR inverse model for convolutive ICA and derive expressions for the likelihood and its gradient. We argue that optimization will give a stable inverse. When there are more sensors than sources the mixing model parameters are estimated in a second step by least squares estimation. We demonstrate the method on synthetic data and finally separate speech and music in a real room recording.
Dynamic modeling of presence of occupants using inhomogeneous Markov chains
DEFF Research Database (Denmark)
Andersen, Philip Hvidthøft Delff; Iversen, Anne; Madsen, Henrik;
2014-01-01
time of day, and by use of a filter of the observations it is able to capture per-employee sequence dynamics. Simulations using this method are compared with simulations using homogeneous Markov chains and show far better ability to reproduce key properties of the data. The method is based on...... inhomogeneous Markov chains with where the transition probabilities are estimated using generalized linear models with polynomials, B-splines, and a filter of passed observations as inputs. For treating the dispersion of the data series, a hierarchical model structure is used where one model is for low presence...
Accurate determination of phase arrival times using autoregressive likelihood estimation
Directory of Open Access Journals (Sweden)
G. Kvaerna
1994-06-01
Full Text Available We have investigated the potential automatic use of an onset picker based on autoregressive likelihood estimation. Both a single component version and a three component version of this method have been tested on data from events located in the Khibiny Massif of the Kola peninsula, recorded at the Apatity array, the Apatity three component station and the ARCESS array. Using this method, we have been able to estimate onset times to an accuracy (standard deviation of about 0.05 s for P-phases and 0.15 0.20 s for S phases. These accuracies are as good as for analyst picks, and are considerably better than the accuracies of the current onset procedure used for processing of regional array data at NORSAR. In another application, we have developed a generic procedure to reestimate the onsets of all types of first arriving P phases. By again applying the autoregressive likelihood technique, we have obtained automatic onset times of a quality such that 70% of the automatic picks are within 0.1 s of the best manual pick. For the onset time procedure currently used at NORSAR, the corresponding number is 28%. Clearly, automatic reestimation of first arriving P onsets using the autoregressive likelihood technique has the potential of significantly reducing the retiming efforts of the analyst.
IDENTIFICATION OF PERIODIC AUTOREGRESSIVE MOVING-AVERAGE TIME SERIES MODELS WITH R
Directory of Open Access Journals (Sweden)
Hazem I. El Shekh Ahmed
2014-01-01
Full Text Available Periodic autoregressive moving average PARMA process extend the classical autoregressive moving average ARMA process by allowing the parameters to vary with seasons. Model identification is the identification of a possible model based on an available realization, i.e., determining the type of the model with appropriate orders. The Periodic Autocorrelation Function (PeACF and the Periodic Partial Autocorrelation Function (PePACF serve as useful indicators of the correlation or of the dependence between the values of the series so that they play an important role in model identification. The identification is based on the cut-off property of the Periodic Autocorrelation Function (PeACF. We derive an explicit expression for the asymptotic variance of the sample PeACF to be used in establishing its bands. Therefore, we will get in this study a new structure of the periodic autocorrelation function which depends directly to the variance that will derived to be used in establishing its bands for the PMA process over the cut-off region and we have studied the theoretical side and we will apply some simulated examples with R which agrees well with the theoretical results.
Simulation of M/M/m Queuing Model Based on Markov State Transition Process%基于马尔科夫状态转移过程的M/M/m排队模型仿真
Institute of Scientific and Technical Information of China (English)
曹永荣; 韩瑞霞; 胡伟
2012-01-01
马尔科夫链是研究排队系统的主要方法,本文在现有M/M/m排队理论和排队系统仿真理论基础上,利用Matlab建立基于马尔科夫状态转移过程的M/M/m排队模型仿真程序.仿真程序在产生初始化参数设定后,利用时钟推进法来模拟空闲服务台和繁忙服务台情况下的服务流程,最后通过M/M/m模型特征描述的仿真计算,获得平均等待时间(E[W])、平均停机时间(E[ DT])、平均排队队长E[ Q]、系统中的平均客户数(E[L])和可能延迟的概率((Ⅱ))5项重要的特征描述.模拟次数设定为20 000次,模拟客户服务率和客户到达率相同,服务台在3～6个的排队系统,并将仿真结果与理论值以及Queue2.0的模拟结果相比较.最终结果显示E[W]、[DT]和H3项最重要指标的仿真结果和理论值都极为相近,误差范围小,本研究将为优先权排队系统的仿真研究提供理论依据.%Markov chain is the main method for the study of queuing systems. This paper integrates the existing theories of M/M/m queuing system and theories of queuing system simulation, and builds simulation program of M/M/m Queuing Model according to the Markov state transition process using Matlab. The simulation process is as follows. First of all, simulation program initializes the parameter settings, such as service time, the interval of customer arrival, the number of server etc. Secondly, promotes the program used time clock which is based on the arrival time of customers and the end time of service. Thirdly, simulates the free servers and busy servers process when a customer arrived, and recodes the corresponding data. Finally, calculate the M/M/m model's characterized descriptions , included in the average down time (E[ DT] ) , the average waiting time (E[ W]), the average number of queuing customer (E[(Q])＞ the average number of customers in the queuing system( E[ L]) and delay probability (Ⅱ) , based on the simulation formula. Sets the
Stability of Markov regenerative switched linear systems
Ogura, Masaki; Preciado, Victor M.
2015-01-01
In this paper, we give a necessary and sufficient condition for mean stability of switched linear systems having a Markov regenerative process as its switching signal. This class of switched linear systems, which we call Markov regenerative switched linear systems, contains Markov jump linear systems and semi-Markov jump linear systems as special cases. We show that a Markov regenerative switched linear system is $m$th mean stable if and only if a particular matrix is Schur stable, under the ...
Entropy: The Markov Ordering Approach
Gorban, A N; Judge, G
2010-01-01
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii) existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i) and (ii) are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the {\\em Markov order}). The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally "most random" distributions.
Raberto, Marco; Scalas, Enrico
2011-01-01
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The model consists in subordinating the Markov chain to the semi-Markov counting process. In simple words, this means that the chain transitions occur at random time instants called epochs. The model is quite rich and its possible connections with algebraic geometry are briefly discussed. Moreover, for the sake of simplicity, we focus on the space of undirected graphs with a fixed number of nodes. However, in an example, we present an interbank market model where it is meaningful to use directed graphs or even weighted graphs.
Bibliometric Application of Markov Chains.
Pao, Miranda Lee; McCreery, Laurie
1986-01-01
A rudimentary description of Markov Chains is presented in order to introduce its use to describe and to predict authors' movements among subareas of the discipline of ethnomusicology. Other possible applications are suggested. (Author)
Reviving Markov processes and applications
International Nuclear Information System (INIS)
In this dissertation we study a procedure which restarts a Markov process when the process is killed by some arbitrary multiplicative functional. The regenerative nature of this revival procedure is characterized through a Markov renewal equation. An interesting duality between the revival procedure and the classical killing operation is found. Under the condition that the multiplicative functional possesses an intensity, the generators of the revival process can be written down explicitly. An intimate connection is also found between the perturbation of the sample path of a Markov process and the perturbation of a generator (in Kato's sense). The applications of the theory include the study of the processes like piecewise-deterministic Markov process, virtual waiting time process and the first entrance decomposition (taboo probability)
One-Dimensional Markov Random Fields, Markov Chains and Topological Markov Fields
Chandgotia, N; G. Han; Marcus, B; Meyerovitch, T; Pavlov, R
2014-01-01
In this paper we show that any one-dimensional stationary, finite-valued Markov Random Field (MRF) is a Markov chain, without any mixing condition or condition on the support. Our proof makes use of two properties of the support $X$ of a finite-valued stationary MRF: 1) $X$ is non-wandering (this is a property of the support of any finite-valued stationary process) and 2) $X$ is a topological Markov field (TMF). The latter is a new property that sits in between the classes of shifts of finite...
A Markov Chain Estimator of Multivariate Volatility from High Frequency Data
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume; Lunde, Asger; Archakov, Ilya
We introduce a multivariate estimator of financial volatility that is based on the theory of Markov chains. The Markov chain framework takes advantage of the discreteness of high-frequency returns. We study the finite sample properties of the estimation in a simulation study and apply it to...
Directory of Open Access Journals (Sweden)
D. G. Partridge
2011-07-01
Full Text Available This paper presents a novel approach to investigate cloud-aerosol interactions by coupling a Markov Chain Monte Carlo (MCMC algorithm to a pseudo-adiabatic cloud parcel model. Despite the number of numerical cloud-aerosol sensitivity studies previously conducted few have used statistical analysis tools to investigate the sensitivity of a cloud model to input aerosol physiochemical parameters. Using synthetic data as observed values of cloud droplet number concentration (CDNC distribution, this inverse modelling framework is shown to successfully converge to the correct calibration parameters.
The employed analysis method provides a new, integrative framework to evaluate the sensitivity of the derived CDNC distribution to the input parameters describing the lognormal properties of the accumulation mode and the particle chemistry. To a large extent, results from prior studies are confirmed, but the present study also provides some additional insightful findings. There is a clear transition from very clean marine Arctic conditions where the aerosol parameters representing the mean radius and geometric standard deviation of the accumulation mode are found to be most important for determining the CDNC distribution to very polluted continental environments (aerosol concentration in the accumulation mode >1000 cm^{−3} where particle chemistry is more important than both number concentration and size of the accumulation mode.
The competition and compensation between the cloud model input parameters illustrate that if the soluble mass fraction is reduced, both the number of particles and geometric standard deviation must increase and the mean radius of the accumulation mode must increase in order to achieve the same CDNC distribution.
For more polluted aerosol conditions, with a reduction in soluble mass fraction the parameter correlation becomes weaker and more non-linear over the range of possible solutions
Markov chain modelling of pitting corrosion in underground pipelines
Energy Technology Data Exchange (ETDEWEB)
Caleyo, F. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)], E-mail: fcaleyo@gmail.com; Velazquez, J.C. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico); Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 La Habana (Cuba); Hallen, J.M. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)
2009-09-15
A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.
Markov chain modelling of pitting corrosion in underground pipelines
International Nuclear Information System (INIS)
A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.
Markov-switching model for nonstationary runoff conditioned on El Niño information
Gelati, E.; Madsen, H.; Rosbjerg, D.
2010-02-01
We define a Markov-modulated autoregressive model with exogenous input (MARX) to generate runoff scenarios using climatic information. Runoff parameterization is assumed to be conditioned on a hidden climate state following a Markov chain, where state transition probabilities are functions of the climatic input. MARX allows stochastic modeling of nonstationary runoff, as runoff anomalies are described by a mixture of autoregressive models with exogenous input, each one corresponding to a climate state. We apply MARX to inflow time series of the Daule Peripa reservoir (Ecuador). El Niño-Southern Oscillation (ENSO) information is used to condition runoff parameterization. Among the investigated ENSO indexes, the NINO 1+2 sea surface temperature anomalies and the trans-Niño index perform best as predictors. In the perspective of reservoir optimization at various time scales, MARX produces realistic long-term scenarios and short-term forecasts, especially when intense El Niño events occur. Low predictive ability is found for negative runoff anomalies, as no climatic index correlating properly with negative inflow anomalies has yet been identified.
Institute of Scientific and Technical Information of China (English)
郜红娟; 许丽君
2015-01-01
【目的】为探讨快速发展的山区未来土地利用变化规律。【方法】利用 CA-Markov 模型，以贵州省麻江县为例，利用1992年、2002年和2012年三期土地利用数据，模拟了2022年土地利用格局，并分析了土地利用格局演变特点。【结果】结果表明：到2022年研究区耕地、未利用地、草地不断下降，而林地、建设用地和水域将持续增加。耕地、林地、草地和未利用地破碎化下降，建设用地破碎度增加，水域破碎度变化不大；耕地、林地、草地、建设用地的景观形状趋于规则化，而未利用地景观形状复杂化增强，水域景观形状复杂性变化不大；除未利用地聚合度下降外，其他地类聚合度都呈增加趋势。研究区景观破碎度降低；景观形状复杂性下降，各景观类型面积比重不断趋于均衡化，聚集度增强。【结论】该模型对山区土地利用模拟具有较高精度，研究结果可为土地优化研究奠定基础。%Objective]In order to discuss the change of the future land-use in the mountainous re-gion of rapid development.[Method]Taking Majiang County of Guizhou province as the study area,in this paper we simulated the land use pattern in 2022 based on the land use data in 1992, 2002 and 2012,and then analyzed the evolution characteristics of the land use pattern using the CA-Markov model.[Results]The results show that:cultivated land,unused land,grassland of the study area in 2022 will decline,while woodland,construction land and water body will in-crease.Concerning the landscape fragmentation,cultivated land,woodland,grassland and unused land will decrease,while construction land will increase,but the water body has a little change. LSI of cultivated land,woodland,grassland,construction land tend to be in regularization,while LSI of unused land will become more complex,but LSI of water body has a little change.AI of all the land use types will increase
International Nuclear Information System (INIS)
We extend the concept of half life of an Ornstein–Uhlenbeck process to Lévy-driven continuous-time autoregressive moving average processes with stochastic volatility. The half life becomes state dependent, and we analyze its properties in terms of the characteristics of the process. An empirical example based on daily temperatures observed in Petaling Jaya, Malaysia, is presented, where the proposed model is estimated and the distribution of the half life is simulated. The stationarity of the dynamics yield futures prices which asymptotically tend to constant at an exponential rate when time to maturity goes to infinity. The rate is characterized by the eigenvalues of the dynamics. An alternative description of this convergence can be given in terms of our concept of half life. - Highlights: • The concept of half life is extended to Levy-driven continuous time autoregressive moving average processes • The dynamics of Malaysian temperatures are modeled using a continuous time autoregressive model with stochastic volatility • Forward prices on temperature become constant when time to maturity tends to infinity • Convergence in time to maturity is at an exponential rate given by the eigenvalues of the model temperature model
Gaussian Markov random fields theory and applications
Rue, Havard
2005-01-01
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.
Lopez, Gerardo; Favreau, Romeo; Smith, Colin; Costes, Evelyne; Prusinkiewicz, Premyslaw; DeJong, Theodore M.
2008-01-01
International audience L-PEACH is an L-system-based functional-structural model for simulating architectural growth and carbohydrate partitioning among individual organs in peach ( Prunus persica (L.) Batsch) trees. The original model provided a prototype for how tree architecture and carbon economy could be integrated but did not simulate peach tree architecture realistically. Moreover, evaluation of the functional characteristics of the individual organs and the whole-tree remained a lar...
State-feedback stabilization of Markov jump linear systems with randomly observed Markov states
Ogura, Masaki; Cetinkaya, Ahmet
2014-01-01
In this paper we study the state-feedback stabilization of a discrete-time Markov jump linear system when the observation of the Markov chain of the system, called the Markov state, is time-randomized by another Markov chain. Embedding the Markov state into an extended Markov chain, we transform the given system with time-randomized observations to another one having the enlarged Markov-state space but with so-called cluster observations of Markov states. Based on this transformation we propo...
Constructing Dynamic Event Trees from Markov Models
International Nuclear Information System (INIS)
In the probabilistic risk assessment (PRA) of process plants, Markov models can be used to model accurately the complex dynamic interactions between plant physical process variables (e.g., temperature, pressure, etc.) and the instrumentation and control system that monitors and manages the process. One limitation of this approach that has prevented its use in nuclear power plant PRAs is the difficulty of integrating the results of a Markov analysis into an existing PRA. In this paper, we explore a new approach to the generation of failure scenarios and their compilation into dynamic event trees from a Markov model of the system. These event trees can be integrated into an existing PRA using software tools such as SAPHIRE. To implement our approach, we first construct a discrete-time Markov chain modeling the system of interest by: (a) partitioning the process variable state space into magnitude intervals (cells), (b) using analytical equations or a system simulator to determine the transition probabilities between the cells through the cell-to-cell mapping technique, and, (c) using given failure/repair data for all the components of interest. The Markov transition matrix thus generated can be thought of as a process model describing the stochastic dynamic behavior of the finite-state system. We can therefore search the state space starting from a set of initial states to explore all possible paths to failure (scenarios) with associated probabilities. We can also construct event trees of arbitrary depth by tracing paths from a chosen initiating event and recording the following events while keeping track of the probabilities associated with each branch in the tree. As an example of our approach, we use the simple level control system often used as benchmark in the literature with one process variable (liquid level in a tank), and three control units: a drain unit and two supply units. Each unit includes a separate level sensor to observe the liquid level in the tank
Institute of Scientific and Technical Information of China (English)
马蕾; 罗建强; 黄克己; 叶瑞
2012-01-01
According to the leap characteristics of technical innovation diffusion,the influence of random factors is researched,and the technical diffusion model of technical innovation diffusion process is constructed based on the Markov chain.The simulation result of the diffusion model indicates that the expectation m（t） will be less,finally tend to zero,which along with the diffusion rate and the increase of number of within the industry enterprises,the magnitude of m（t） drop curve is bigger.Finally the technical innovation diffusion is prospected.%针对技术创新扩散呈现出来的跳跃性特点,研究了随机因素对技术创新扩散活动的影响,构建了基于Markov链的技术创新扩散模型,并对这一扩散模型进行仿真分析,结果发现,随着时间的推移,未采纳新技术的企业的期望值m（t）会越少,最后趋向于零,其中随着扩散率和行业内企业数目的增加,m（t）曲线下降的幅度越大。最后对技术创新扩散可拓展的研究方向进行了展望。
Data-driven Markov models and their application in the evaluation of adverse events in radiotherapy
Abler, Daniel; Davies, Jim; Dosanjh, Manjit; Jena, Raj; Kirkby, Norman; Peach, Ken
2013-01-01
Decision-making processes in medicine rely increasingly on modelling and simulation techniques; they are especially useful when combining evidence from multiple sources. Markov models are frequently used to synthesize the available evidence for such simulation studies, by describing disease and treatment progress, as well as associated factors such as the treatment's effects on a patient's life and the costs to society. When the same decision problem is investigated by multiple stakeholders, differing modelling assumptions are often applied, making synthesis and interpretation of the results difficult. This paper proposes a standardized approach towards the creation of Markov models. It introduces the notion of ‘general Markov models’, providing a common definition of the Markov models that underlie many similar decision problems, and develops a language for their specification. We demonstrate the application of this language by developing a general Markov model for adverse event analysis in radiotherapy ...
CLARK, Todd E.; Francesco Ravazzolo
2012-01-01
This paper compares alternative models of time-varying macroeconomic volatility on the basis of the accuracy of point and density forecasts of macroeconomic variables. In this analysis, we consider both Bayesian autoregressive and Bayesian vector autoregressive models that incorporate some form of time-varying volatility, precisely stochastic volatility (both with constant and time-varying autoregressive coeffi cients), stochastic volatility following a stationary AR process, stochastic volat...
On Markov parameters in system identification
Phan, Minh; Juang, Jer-Nan; Longman, Richard W.
1991-01-01
A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.
International Nuclear Information System (INIS)
Highlights: • An unsupervised clustering algorithm with a neural network model was explored. • The forecasting results of solar radiation time series and the comparison of their performance was simulated. • A new method was proposed combining k-means algorithm and NAR network to provide better prediction results. - Abstract: In this paper, we review our work for forecasting hourly global horizontal solar radiation based on the combination of unsupervised k-means clustering algorithm and artificial neural networks (ANN). k-Means algorithm focused on extracting useful information from the data with the aim of modeling the time series behavior and find patterns of the input space by clustering the data. On the other hand, nonlinear autoregressive (NAR) neural networks are powerful computational models for modeling and forecasting nonlinear time series. Taking the advantage of both methods, a new method was proposed combining k-means algorithm and NAR network to provide better forecasting results
Goodness-of-fit tests for vector autoregressive models in time series
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The paper proposes and studies some diagnostic tools for checking the goodness-of-fit of general parametric vector autoregressive models in time series. The resulted tests are asymptotically chi-squared under the null hypothesis and can detect the alternatives converging to the null at a parametric rate. The tests involve weight functions,which provides us with the flexibility to choose scores for enhancing power performance,especially under directional alternatives. When the alternatives are not directional,we construct asymptotically distribution-free maximin tests for a large class of alternatives. A possibility to construct score-based omnibus tests is discussed when the alternative is saturated. The power performance is also investigated. In addition,when the sample size is small,a nonparametric Monte Carlo test approach for dependent data is proposed to improve the performance of the tests. The algorithm is easy to implement. Simulation studies and real applications are carried out for illustration.
DEFF Research Database (Denmark)
Chon, K H; Hoyer, D; Armoundas, A A; Holstein-Rathlou, N H; Marsh, D J
1999-01-01
In this study, we introduce a new approach for estimating linear and nonlinear stochastic autoregressive moving average (ARMA) model parameters, given a corrupt signal, using artificial recurrent neural networks. This new approach is a two-step approach in which the parameters of the deterministic...... part of the stochastic ARMA model are first estimated via a three-layer artificial neural network (deterministic estimation step) and then reestimated using the prediction error as one of the inputs to the artificial neural networks in an iterative algorithm (stochastic estimation step). The prediction...... error is obtained by subtracting the corrupt signal of the estimated ARMA model obtained via the deterministic estimation step from the system output response. We present computer simulation examples to show the efficacy of the proposed stochastic recurrent neural network approach in obtaining accurate...
AN EXPONENTIAL INEQUALITY FOR AUTOREGRESSIVE PROCESSES IN ADAPTIVE TRACKING
Institute of Scientific and Technical Information of China (English)
Bernard BERCU
2007-01-01
A wide range of literature concerning classical asymptotic properties for linear models with adaptive control is available, such as strong laws of large numbers or central limit theorems.Unfortunately, in contrast with the situation without control, it appears to be impossible to find sharp asymptotic or nonasymptotic properties such as large deviation principles or exponential inequalities.Our purpose is to provide a first step towards that direction by proving a very simple exponential inequality for the standard least squares estimator of the unknown parameter of Gaussian autoregressive process in adaptive tracking.
Temporal aggregation in first order cointegrated vector autoregressive
DEFF Research Database (Denmark)
La Cour, Lisbeth Funding; Milhøj, Anders
2006-01-01
We study aggregation - or sample frequencies - of time series, e.g. aggregation from weekly to monthly or quarterly time series. Aggregation usually gives shorter time series but spurious phenomena, in e.g. daily observations, can on the other hand be avoided. An important issue is the effect of ...... aggregation on the adjustment coefficient in cointegrated systems. We study only first order vector autoregressive processes for n dimensional time series Xt, and we illustrate the theory by a two dimensional and a four dimensional model for prices of various grades of gasoline....
Temporal aggregation in first order cointegrated vector autoregressive models
DEFF Research Database (Denmark)
La Cour, Lisbeth Funding; Milhøj, Anders
We study aggregation - or sample frequencies - of time series, e.g. aggregation from weekly to monthly or quarterly time series. Aggregation usually gives shorter time series but spurious phenomena, in e.g. daily observations, can on the other hand be avoided. An important issue is the effect of ...... aggregation on the adjustment coefficient in cointegrated systems. We study only first order vector autoregressive processes for n dimensional time series Xt, and we illustrate the theory by a two dimensional and a four dimensional model for prices of various grades of gasoline...
Accurate determination of phase arrival times using autoregressive likelihood estimation
G. Kvaerna
1994-01-01
We have investigated the potential automatic use of an onset picker based on autoregressive likelihood estimation. Both a single component version and a three component version of this method have been tested on data from events located in the Khibiny Massif of the Kola peninsula, recorded at the Apatity array, the Apatity three component station and the ARCESS array. Using this method, we have been able to estimate onset times to an accuracy (standard deviation) of about 0.05 s for P-phases ...
Analysis of nonlinear systems using ARMA [autoregressive moving average] models
International Nuclear Information System (INIS)
While many vibration systems exhibit primarily linear behavior, a significant percentage of the systems encountered in vibration and model testing are mildly to severely nonlinear. Analysis methods for such nonlinear systems are not yet well developed and the response of such systems is not accurately predicted by linear models. Nonlinear ARMA (autoregressive moving average) models are one method for the analysis and response prediction of nonlinear vibratory systems. In this paper we review the background of linear and nonlinear ARMA models, and illustrate the application of these models to nonlinear vibration systems. We conclude by summarizing the advantages and disadvantages of ARMA models and emphasizing prospects for future development. 14 refs., 11 figs
Markov Networks in Evolutionary Computation
Shakya, Siddhartha
2012-01-01
Markov networks and other probabilistic graphical modes have recently received an upsurge in attention from Evolutionary computation community, particularly in the area of Estimation of distribution algorithms (EDAs). EDAs have arisen as one of the most successful experiences in the application of machine learning methods in optimization, mainly due to their efficiency to solve complex real-world optimization problems and their suitability for theoretical analysis. This book focuses on the different steps involved in the conception, implementation and application of EDAs that use Markov networks, and undirected models in general. It can serve as a general introduction to EDAs but covers also an important current void in the study of these algorithms by explaining the specificities and benefits of modeling optimization problems by means of undirected probabilistic models. All major developments to date in the progressive introduction of Markov networks based EDAs are reviewed in the book. Hot current researc...
Markov Models for Handwriting Recognition
Plotz, Thomas
2011-01-01
Since their first inception, automatic reading systems have evolved substantially, yet the recognition of handwriting remains an open research problem due to its substantial variation in appearance. With the introduction of Markovian models to the field, a promising modeling and recognition paradigm was established for automatic handwriting recognition. However, no standard procedures for building Markov model-based recognizers have yet been established. This text provides a comprehensive overview of the application of Markov models in the field of handwriting recognition, covering both hidden
A Markov-binomial distribution
Santos, J.; S. Van Gulck; OMEY, E.
2007-01-01
Let ${X_{i},igeq 1}$ denote a sequence of $left{ 0,1 ight} $%-variables and suppose that the sequence forms a {sc Markov} Chain. In the paperwe study the number of successes $S_{n}=X_{1}+X_{2}+cdots+X_{n}$ and we studythe number of experiments $Y(r)$ up to the $r$-$th$ success. In the i.i.d.case $S_{n}$ has a binomial distribution and $Y(r)$ has a negative binomialdistribution and the asymptotic behaviour is well known. In the more general{sc Markov} chain case, we prove a central limit theor...
Examples in Markov decision processes
Piunovskiy, A B
2012-01-01
This invaluable book provides approximately eighty examples illustrating the theory of controlled discrete-time Markov processes. Except for applications of the theory to real-life problems like stock exchange, queues, gambling, optimal search etc, the main attention is paid to counter-intuitive, unexpected properties of optimization problems. Such examples illustrate the importance of conditions imposed in the theorems on Markov Decision Processes. Many of the examples are based upon examples published earlier in journal articles or textbooks while several other examples are new. The aim was
Adaptive Partially Hidden Markov Models
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Rasmussen, Tage
1996-01-01
Partially Hidden Markov Models (PHMM) have recently been introduced. The transition and emission probabilities are conditioned on the past. In this report, the PHMM is extended with a multiple token version. The different versions of the PHMM are applied to bi-level image coding.......Partially Hidden Markov Models (PHMM) have recently been introduced. The transition and emission probabilities are conditioned on the past. In this report, the PHMM is extended with a multiple token version. The different versions of the PHMM are applied to bi-level image coding....
AUTOREGRESSIVE MODELLING OF MONTHLY RAINFALL IN SAKARYA BASIN
Directory of Open Access Journals (Sweden)
Meral BÜYÜKYILDIZ
2006-01-01
Full Text Available In this study, periodic autoregressive models were established to predict future behaviour of monthly rainfall data of Sakarya Basin which is one of the big and important basin in Turkey. Mathematical equations of the Periodic Autoregressive Models (PAR were also determined. Optimum models were selected based on Akaike Information Criterion (AIC. Although the parameters are calculated according to "maximum probability method" in AIC, "moments method" was used in this study; the comparison of the results of both mentioned parameter estimation methods was thought to be considered in another study's scope. The Port Manteau lack of fit test for the selected models have indicated that residuals are white noise. By using the selected models for the stations, 50 set of synthetic series which have the same length with the historical series for the monthly average rainfalls have been generated, and statistical characteristics (mean, standard deviation, autocorrelation structure of these synthetic series have been compared with statistical characteristics of historical series. By determining the stochastic models of monthly average rainfall of 25 stations, 4 different PAR models were obtained, namely as PAR(0, PAR(1, PAR(2 and PAR(3.
Series Arc Fault Detection Algorithm Based on Autoregressive Bispectrum Analysis
Directory of Open Access Journals (Sweden)
Kai Yang
2015-10-01
Full Text Available Arc fault is one of the most critical reasons for electrical fires. Due to the diversity, randomness and concealment of arc faults in low-voltage circuits, it is difficult for general methods to protect all loads from series arc faults. From the analysis of many series arc faults, a large number of high frequency signals generated in circuits are found. These signals are easily affected by Gaussian noise which is difficult to be eliminated as a result of frequency aliasing. Thus, a novel detection algorithm is developed to accurately detect series arc faults in this paper. Initially, an autoregressive model of the mixed high frequency signals is modelled. Then, autoregressive bispectrum analysis is introduced to analyze common series arc fault features. The phase information of arc fault signal is preserved using this method. The influence of Gaussian noise is restrained effectively. Afterwards, several features including characteristic frequency, fluctuation of phase angles, diffused distribution and incremental numbers of bispectrum peaks are extracted for recognizing arc faults. Finally, least squares support vector machine is used to accurately identify series arc faults from the load states based on these frequency features of bispectrum. The validity of the algorithm is experimentally verified obtaining arc fault detection rate above 97%.
Numerical research of the optimal control problem in the semi-Markov inventory model
International Nuclear Information System (INIS)
This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented
Infinite Structured Hidden Semi-Markov Models
Huggins, Jonathan H.; Wood, Frank
2014-01-01
This paper reviews recent advances in Bayesian nonparametric techniques for constructing and performing inference in infinite hidden Markov models. We focus on variants of Bayesian nonparametric hidden Markov models that enhance a posteriori state-persistence in particular. This paper also introduces a new Bayesian nonparametric framework for generating left-to-right and other structured, explicit-duration infinite hidden Markov models that we call the infinite structured hidden semi-Markov m...
Graph-Based Lossless Markov Lumpings
Geiger, Bernhard C.; Hofer-Temmel, Christoph
2015-01-01
We use results from zero-error information theory to determine the set of non-injective functions through which a Markov chain can be projected without losing information. These lumping functions can be found by clique partitioning of a graph related to the Markov chain. Lossless lumping is made possible by exploiting the (sufficiently sparse) temporal structure of the Markov chain. Eliminating edges in the transition graph of the Markov chain trades the required output alphabet size versus i...
Generating Semi-Markov Models Automatically
Johnson, Sally C.
1990-01-01
Abstract Semi-Markov Specification Interface to SURE Tool (ASSIST) program developed to generate semi-Markov model automatically from description in abstract, high-level language. ASSIST reads input file describing failure behavior of system in abstract language and generates Markov models in format needed for input to Semi-Markov Unreliability Range Evaluator (SURE) program (COSMIC program LAR-13789). Facilitates analysis of behavior of fault-tolerant computer. Written in PASCAL.
A canonical representation for aggregated Markov processes
Larget, Bret
1998-01-01
A deterministic function of a Markov process is called an aggregated Markov process. We give necessary and sufficient conditions for the equivalence of continuous-time aggregated Markov processes. For both discrete- and continuous-time, we show that any aggregated Markov process which satisfies mild regularity conditions can be directly converted to a canonical representation which is unique for each class of equivalent models, and furthermore, is a minimal parameterization ...
Annotations of two examples about Markov process
TANG, RONG
2013-01-01
In this paper, we discuss an incorrect example that a Markov process does not satisfy strong Markov property, and analyzes the reason of mistake. In the end, we point out it is not reasonable to define strong Markov property by using transition probability functions since transition probability functions might not be one and only.
On a Result for Finite Markov Chains
Kulathinal, Sangita; Ghosh, Lagnojita
2006-01-01
In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…
Markov state models of protein misfolding
Sirur, Anshul; De Sancho, David; Best, Robert B.
2016-02-01
Markov state models (MSMs) are an extremely useful tool for understanding the conformational dynamics of macromolecules and for analyzing MD simulations in a quantitative fashion. They have been extensively used for peptide and protein folding, for small molecule binding, and for the study of native ensemble dynamics. Here, we adapt the MSM methodology to gain insight into the dynamics of misfolded states. To overcome possible flaws in root-mean-square deviation (RMSD)-based metrics, we introduce a novel discretization approach, based on coarse-grained contact maps. In addition, we extend the MSM methodology to include "sink" states in order to account for the irreversibility (on simulation time scales) of processes like protein misfolding. We apply this method to analyze the mechanism of misfolding of tandem repeats of titin domains, and how it is influenced by confinement in a chaperonin-like cavity.
Markov state models of protein misfolding.
Sirur, Anshul; De Sancho, David; Best, Robert B
2016-02-21
Markov state models (MSMs) are an extremely useful tool for understanding the conformational dynamics of macromolecules and for analyzing MD simulations in a quantitative fashion. They have been extensively used for peptide and protein folding, for small molecule binding, and for the study of native ensemble dynamics. Here, we adapt the MSM methodology to gain insight into the dynamics of misfolded states. To overcome possible flaws in root-mean-square deviation (RMSD)-based metrics, we introduce a novel discretization approach, based on coarse-grained contact maps. In addition, we extend the MSM methodology to include "sink" states in order to account for the irreversibility (on simulation time scales) of processes like protein misfolding. We apply this method to analyze the mechanism of misfolding of tandem repeats of titin domains, and how it is influenced by confinement in a chaperonin-like cavity. PMID:26897000
Estimation and uncertainty of reversible Markov models
Trendelkamp-Schroer, Benjamin; Paul, Fabian; Noé, Frank
2015-01-01
Reversibility is a key concept in the theory of Markov models, simplified kinetic models for the conforma- tion dynamics of molecules. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model relies heavily on the reversibility property. The estimation of a reversible transition matrix from simulation data is therefore crucial to the successful application of the previously developed theory. In this work we discuss methods for the maximum likelihood estimation of transition matrices from finite simulation data and present a new algorithm for the estimation if reversibility with respect to a given stationary vector is desired. We also develop new methods for the Bayesian posterior inference of reversible transition matrices with and without given stationary vector taking into account the need for a suitable prior distribution preserving the meta-stable features of the observed process during posterior inference.
APPLICATION OF SECOND KIND MODEL OF AUTOREGRESSION FOR EXTRAPOLATION ECONOMIC TIME SEQUENCE
Odnolko, A.V.; National Aviation University, Kyiv
2012-01-01
For extrapolation of economic time sequence we can use the method of autoregression. Originally given method of autoregression is used for prediction of the time series values. We must know: the first few points of sequence and time interval.
Maximizing entropy over Markov processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis; Wasowski, Andrzej
The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity computat...
Markov Monitoring with Unknown States
Smyth, Padhraic
1993-01-01
Pattern recognition methods and hidden Markov models can be effective tools for online health monitoring of communications systems. Previous work has assumed that the states in the system model are exhaustive. This can be a significant drawback in real-world fault monitoring applications where it is difficult if not impossible to model all the possible fault states of the system in advance.
Maximizing Entropy over Markov Processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis; Wąsowski, Andrzej
The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity computat......The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... a reward function, a polynomial algorithm to verify the existence of an system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show...... how to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code....
Large deviations on Markov towers
International Nuclear Information System (INIS)
We give a sufficient condition to hold a full large deviation principle for Markov tower maps induced from return time functions. As an application of this result we show the large deviation principle of level 2 for some class of smooth dynamical systems with nonuniform hyperbolicity
Quantum Markov processes and applications in many-body systems
International Nuclear Information System (INIS)
This thesis is concerned with the investigation of quantum as well as classical Markov processes and their application in the field of strongly correlated many-body systems. A Markov process is a special kind of stochastic process, which is determined by an evolution that is independent of its history and only depends on the current state of the system. The application of Markov processes has a long history in the field of statistical mechanics and classical many-body theory. Not only are Markov processes used to describe the dynamics of stochastic systems, but they predominantly also serve as a practical method that allows for the computation of fundamental properties of complex many-body systems by means of probabilistic algorithms. The aim of this thesis is to investigate the properties of quantum Markov processes, i.e. Markov processes taking place in a quantum mechanical state space, and to gain a better insight into complex many-body systems by means thereof. Moreover, we formulate a novel quantum algorithm which allows for the computation of the thermal and ground states of quantum many-body systems. After a brief introduction to quantum Markov processes we turn to an investigation of their convergence properties. We find bounds on the convergence rate of the quantum process by generalizing geometric bounds found for classical processes. We generalize a distance measure that serves as the basis for our investigations, the chi-square divergence, to non-commuting probability spaces. This divergence allows for a convenient generalization of the detailed balance condition to quantum processes. We then devise the quantum algorithm that can be seen as the natural generalization of the ubiquitous Metropolis algorithm to simulate quantum many-body Hamiltonians. By this we intend to provide further evidence, that a quantum computer can serve as a fully-fledged quantum simulator, which is not only capable of describing the dynamical evolution of quantum systems, but
Multiensemble Markov models of molecular thermodynamics and kinetics.
Wu, Hao; Paul, Fabian; Wehmeyer, Christoph; Noé, Frank
2016-06-01
We introduce the general transition-based reweighting analysis method (TRAM), a statistically optimal approach to integrate both unbiased and biased molecular dynamics simulations, such as umbrella sampling or replica exchange. TRAM estimates a multiensemble Markov model (MEMM) with full thermodynamic and kinetic information at all ensembles. The approach combines the benefits of Markov state models-clustering of high-dimensional spaces and modeling of complex many-state systems-with those of the multistate Bennett acceptance ratio of exploiting biased or high-temperature ensembles to accelerate rare-event sampling. TRAM does not depend on any rate model in addition to the widely used Markov state model approximation, but uses only fundamental relations such as detailed balance and binless reweighting of configurations between ensembles. Previous methods, including the multistate Bennett acceptance ratio, discrete TRAM, and Markov state models are special cases and can be derived from the TRAM equations. TRAM is demonstrated by efficiently computing MEMMs in cases where other estimators break down, including the full thermodynamics and rare-event kinetics from high-dimensional simulation data of an all-atom protein-ligand binding model. PMID:27226302
Modeling corporate defaults: Poisson autoregressions with exogenous covariates (PARX)
DEFF Research Database (Denmark)
Agosto, Arianna; Cavaliere, Guiseppe; Kristensen, Dennis;
We develop a class of Poisson autoregressive models with additional covariates (PARX) that can be used to model and forecast time series of counts. We establish the time series properties of the models, including conditions for stationarity and existence of moments. These results are in turn used...... in the analysis of the asympotic properties of the maximum-likelihood estimators of the models. The PARX class of models is used to analyse the time series properties of monthly corporate defaults in the US in the period 1982-2011 using financial and economic variables as exogeneous covariates...... years economic and financial factors at the macro level are capable to explain a large portion of the correlation of US firms defaults over time....
Implementing Modifed Burg Algorithms in Multivariate Subset Autoregressive Modeling
Directory of Open Access Journals (Sweden)
A. Alexandre Trindade
2003-02-01
Full Text Available The large number of parameters in subset vector autoregressive models often leads one to procure fast, simple, and efficient alternatives or precursors to maximum likelihood estimation. We present the solution of the multivariate subset Yule-Walker equations as one such alternative. In recent work, Brockwell, Dahlhaus, and Trindade (2002, show that the Yule-Walker estimators can actually be obtained as a special case of a general recursive Burg-type algorithm. We illustrate the structure of this Algorithm, and discuss its implementation in a high-level programming language. Applications of the Algorithm in univariate and bivariate modeling are showcased in examples. Univariate and bivariate versions of the Algorithm written in Fortran 90 are included in the appendix, and their use illustrated.
Likelihood inference for a fractionally cointegrated vector autoregressive model
DEFF Research Database (Denmark)
Johansen, Søren; Nielsen, Morten Ørregaard
We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X_{t} to be fractional of order d and cofractional of order d-b; that is, there exist vectors β for which β......′X_{t} is fractional of order d-b. The parameters d and b satisfy either d≥b≥1/2, d=b≥1/2, or d=d_{0}≥b≥1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2≤b≤d≤d_{1} for any d_{1}≥d_{0}. To this end, we consider the conditional likelihood as a...... Gaussian. We also find the asymptotic distribution of the likelihood ratio test for cointegration rank, which is a functional of fractional Brownian motion of type II....
Testing stability in a spatial unilateral autoregressive model
Baran, Sándor; Sikolya, Kinga
2012-01-01
Least squares estimator of the stability parameter $\\varrho := |\\alpha| + |\\beta|$ for a spatial unilateral autoregressive process $X_{k,\\ell}=\\alpha X_{k-1,\\ell}+\\beta X_{k,\\ell-1}+\\varepsilon_{k,\\ell}$ is investigated. Asymptotic normality with a scaling factor $n^{5/4}$ is shown in the unstable case, i.e., when $\\varrho = 1$, in contrast to the AR(p) model $X_k=\\alpha_1 X_{k-1}+... +\\alpha_p X_{k-p}+ \\varepsilon_k$, where the least squares estimator of the stability parameter $\\varrho :=\\alpha_1 + ... + \\alpha_p$ is not asymptotically normal in the unstable, i.e., in the unit root case.
Parameter estimation in a spatial unit root autoregressive model
Baran, Sándor
2011-01-01
Spatial autoregressive model $X_{k,\\ell}=\\alpha X_{k-1,\\ell}+\\beta X_{k,\\ell-1}+\\gamma X_{k-1,\\ell-1}+\\epsilon_{k,\\ell}$ is investigated in the unit root case, that is when the parameters are on the boundary of the domain of stability that forms a tetrahedron with vertices $(1,1,-1), \\ (1,-1,1),\\ (-1,1,1)$ and $(-1,-1,-1)$. It is shown that the limiting distribution of the least squares estimator of the parameters is normal and the rate of convergence is $n$ when the parameters are in the faces or on the edges of the tetrahedron, while on the vertices the rate is $n^{3/2}$.
Unit root vector autoregression with volatility induced stationarity
DEFF Research Database (Denmark)
Rahbek, Anders; Nielsen, Heino Bohn
stationarity despite such unit-roots. Specifically, the model bridges vector autoregressions and multivariate ARCH models in which residuals are replaced by levels lagged. An empirical illustration using recent US term structure data is given in which the individual interest rates have unit roots, have......We propose a discrete-time multivariate model where lagged levels of the process enter both the conditional mean and the conditional variance. This way we allow for the empirically observed persistence in time series such as interest rates, often implying unit-roots, while at the same time maintain...... no finite first-order moments, but remain strictly stationary and ergodic, while they co-move in the sense that their spread has no unit root. The model thus allows for volatility induced stationarity, and the paper shows conditions under which the multivariate process is strictly stationary...
Unit Root Vector Autoregression with volatility Induced Stationarity
DEFF Research Database (Denmark)
Rahbek, Anders; Nielsen, Heino Bohn
stationarity despite such unit-roots. Specifically, the model bridges vector autoregressions and multivariate ARCH models in which residuals are replaced by levels lagged. An empirical illustration using recent US term structure data is given in which the individual interest rates have unit roots, have......We propose a discrete-time multivariate model where lagged levels of the process enter both the conditional mean and the conditional variance. This way we allow for the empirically observed persistence in time series such as interest rates, often implying unit-roots, while at the same time maintain...... no finite first-order moments, but remain strictly stationary and ergodic, while they co-move in the sense that their spread has no unit root. The model thus allows for volatility induced stationarity, and the paper shows conditions under which the multivariate process is strictly stationary...
Drought Patterns Forecasting using an Auto-Regressive Logistic Model
del Jesus, M.; Sheffield, J.; Méndez Incera, F. J.; Losada, I. J.; Espejo, A.
2014-12-01
Drought is characterized by a water deficit that may manifest across a large range of spatial and temporal scales. Drought may create important socio-economic consequences, many times of catastrophic dimensions. A quantifiable definition of drought is elusive because depending on its impacts, consequences and generation mechanism, different water deficit periods may be identified as a drought by virtue of some definitions but not by others. Droughts are linked to the water cycle and, although a climate change signal may not have emerged yet, they are also intimately linked to climate.In this work we develop an auto-regressive logistic model for drought prediction at different temporal scales that makes use of a spatially explicit framework. Our model allows to include covariates, continuous or categorical, to improve the performance of the auto-regressive component.Our approach makes use of dimensionality reduction (principal component analysis) and classification techniques (K-Means and maximum dissimilarity) to simplify the representation of complex climatic patterns, such as sea surface temperature (SST) and sea level pressure (SLP), while including information on their spatial structure, i.e. considering their spatial patterns. This procedure allows us to include in the analysis multivariate representation of complex climatic phenomena, as the El Niño-Southern Oscillation. We also explore the impact of other climate-related variables such as sun spots. The model allows to quantify the uncertainty of the forecasts and can be easily adapted to make predictions under future climatic scenarios. The framework herein presented may be extended to other applications such as flash flood analysis, or risk assessment of natural hazards.
Markov Equivalences for Subclasses of Loopless Mixed Graphs
Sadeghi, Kayvan
2011-01-01
In this paper we discuss four problems regarding Markov equivalences for subclasses of loopless mixed graphs. We classify these four problems as finding conditions for internal Markov equivalence, which is Markov equivalence within a subclass, for external Markov equivalence, which is Markov equivalence between subclasses, for representational Markov equivalence, which is the possibility of a graph from a subclass being Markov equivalent to a graph from another subclass, and finding algorithm...
Markov Tracking for Agent Coordination
Washington, Richard; Lau, Sonie (Technical Monitor)
1998-01-01
Partially observable Markov decision processes (POMDPs) axe an attractive representation for representing agent behavior, since they capture uncertainty in both the agent's state and its actions. However, finding an optimal policy for POMDPs in general is computationally difficult. In this paper we present Markov Tracking, a restricted problem of coordinating actions with an agent or process represented as a POMDP Because the actions coordinate with the agent rather than influence its behavior, the optimal solution to this problem can be computed locally and quickly. We also demonstrate the use of the technique on sequential POMDPs, which can be used to model a behavior that follows a linear, acyclic trajectory through a series of states. By imposing a "windowing" restriction that restricts the number of possible alternatives considered at any moment to a fixed size, a coordinating action can be calculated in constant time, making this amenable to coordination with complex agents.
Characteristics of the transmission of autoregressive sub-patterns in financial time series
Gao, Xiangyun; An, Haizhong; Fang, Wei; Huang, Xuan; Li, Huajiao; Zhong, Weiqiong
2014-09-01
There are many types of autoregressive patterns in financial time series, and they form a transmission process. Here, we define autoregressive patterns quantitatively through an econometrical regression model. We present a computational algorithm that sets the autoregressive patterns as nodes and transmissions between patterns as edges, and then converts the transmission process of autoregressive patterns in a time series into a network. We utilised daily Shanghai (securities) composite index time series to study the transmission characteristics of autoregressive patterns. We found statistically significant evidence that the financial market is not random and that there are similar characteristics between parts and whole time series. A few types of autoregressive sub-patterns and transmission patterns drive the oscillations of the financial market. A clustering effect on fluctuations appears in the transmission process, and certain non-major autoregressive sub-patterns have high media capabilities in the financial time series. Different stock indexes exhibit similar characteristics in the transmission of fluctuation information. This work not only proposes a distinctive perspective for analysing financial time series but also provides important information for investors.
Markov state models and molecular alchemy
Schütte, Christof; Nielsen, Adam; Weber, Marcus
2015-01-01
In recent years, Markov state models (MSMs) have attracted a considerable amount of attention with regard to modelling conformation changes and associated function of biomolecular systems. They have been used successfully, e.g. for peptides including time-resolved spectroscopic experiments, protein function and protein folding , DNA and RNA, and ligand-receptor interaction in drug design and more complicated multivalent scenarios. In this article, a novel reweighting scheme is introduced that allows to construct an MSM for certain molecular system out of an MSM for a similar system. This permits studying how molecular properties on long timescales differ between similar molecular systems without performing full molecular dynamics simulations for each system under consideration. The performance of the reweighting scheme is illustrated for simple test cases, including one where the main wells of the respective energy landscapes are located differently and an alchemical transformation of butane to pentane where the dimension of the state space is changed.
Markov processes for stochastic modeling
Ibe, Oliver
2008-01-01
Markov processes are used to model systems with limited memory. They are used in many areas including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. This book, which is written for upper level undergraduate and graduate students, and researchers, presents a unified presentat
Markov processes characterization and convergence
Ethier, Stewart N
2009-01-01
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists."[A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference."-American Scientist"There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings."-Zentralblatt f?r Mathematik und ihre Grenzgebiete/Mathematics Abstracts"Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook."-Journal of Statistical PhysicsMarkov Proce...
Statistical significance test for transition matrices of atmospheric Markov chains
Vautard, Robert; Mo, Kingtse C.; Ghil, Michael
1990-01-01
Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.
Criterion of Semi-Markov Dependent Risk Model
Institute of Scientific and Technical Information of China (English)
Xiao Yun MO; Xiang Qun YANG
2014-01-01
A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi-Markov dependent risk model are obtained. The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model.
Bayesian Fine-Scale Mapping of Disease Loci, by Hidden Markov Models
Morris, A P; Whittaker, J C; Balding, D. J.
2000-01-01
We present a new multilocus method for the fine-scale mapping of genes contributing to human diseases. The method is designed for use with multiple biallelic markers—in particular, single-nucleotide polymorphisms for which high-density genetic maps will soon be available. We model disease-marker association in a candidate region via a hidden Markov process and allow for correlation between linked marker loci. Using Markov-chain–Monte Carlo simulation methods, we obtain posterior distributions...
Offline and online detection of damage using autoregressive models and artificial neural networks
Omenzetter, Piotr; de Lautour, Oliver R.
2007-04-01
Developed to study long, regularly sampled streams of data, time series analysis methods are being increasingly investigated for the use of Structural Health Monitoring. In this research, Autoregressive (AR) models are used in conjunction with Artificial Neural Networks (ANNs) for damage detection, localisation and severity assessment. In the first reported experimental exercise, AR models were used offline to fit the acceleration time histories of a 3-storey test structure in undamaged and various damaged states when excited by earthquake motion simulated on a shake table. Damage was introduced into the structure by replacing the columns with those of a thinner thickness. Analytical models of the structure in both damaged and undamaged states were also developed and updated using experimental data in order to determine structural stiffness. The coefficients of AR models were used as damage sensitive features and input into an ANN to build a relationship between them and the remaining structural stiffness. In the second, analytical exercise, a system with gradually progressing damage was numerically simulated and acceleration AR models with exogenous inputs were identified recursively. A trained ANN was then required to trace the structural stiffness online. The results for the offline and online approach showed the efficiency of using AR coefficient as damage sensitive features and good performance of the ANNs for damage detection, localization and quantification.
Spectral methods for quantum Markov chains
International Nuclear Information System (INIS)
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
The Entropy of Conditional Markov Trajectories
Kafsi, Mohamed; Grossglauser, Matthias; Thiran, Patrick
2012-01-01
To quantify the randomness of Markov trajectories with fixed initial and final states, Ekroot and Cover proposed a closed-form expression for the entropy of trajectories of an irreducible finite state Markov chain. Numerous applications, including the study of random walks on graphs, require the computation of the entropy of Markov trajectories conditioned on a set of intermediate states. However, the expression of Ekroot and Cover does not allow for computing this quantity. In this paper, we...
Continuously monitored barrier options under Markov processes
Aleksandar Mijatovic; Martijn Pistorius
2009-01-01
In this paper we present an algorithm for pricing barrier options in one-dimensional Markov models. The approach rests on the construction of an approximating continuous-time Markov chain that closely follows the dynamics of the given Markov model. We illustrate the method by implementing it for a range of models, including a local Levy process and a local volatility jump-diffusion. We also provide a convergence proof and error estimates for this algorithm.
An Adaptively Constructed Algebraic Multigrid Preconditioner for Irreducible Markov Chains
Brannick, James; Kahl, Karsten; Sokolovic, Sonja
2014-01-01
The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a natural choice for solving these systems. In this paper we investigate extensions and improvements of the bootstrap algebraic multigrid framework for solving these systems. This is achieved by reworking the bootstrap setup process to use singular vectors i...
Markov process functionals in finance and insurance
Institute of Scientific and Technical Information of China (English)
GENG Xian-min; LI Liang
2009-01-01
The Maxkov property of Maxkov process functionals which axe frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Maxkov property of some important Markov process functionals axe presented, the following conclusions are obtained: the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent incre-ments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Maxkov process being still a Maxkov process are given.
Barbu, Vlad
2008-01-01
Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. This book concerns with the estimation of discrete-time semi-Markov and hidden semi-Markov processes
Dinamika Pada Rantai Markov Dengan Dua Komponen (Dinamika On Two Compotent Markov Chains)
Yakub, Riki
2010-01-01
Dinamika pada rantai Markov dengan dua komponen dipengaruhi oleh nilai eigen dari matriks probabilitas transisinya serta keadaan awal yang diberikan. Berdasarkan nilai λ2 yang diperoleh, dinamika pada rantai Markov dengan dua komponen dapat dikelompokkan menjadi 3 bagian utama. Yaitu: a. Dinamika pada rantai Markov dengan dua komponen jika nilai 0
An algebraic method for constructing stable and consistent autoregressive filters
International Nuclear Information System (INIS)
In this paper, we introduce an algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth. By stable, we refer to the classical stability condition for the AR model. By consistent, we refer to the classical consistency constraints of Adams–Bashforth methods of order-two. One attractive feature of this algebraic method is that the model parameters can be obtained without directly knowing any training data set as opposed to many standard, regression-based parameterization methods. It takes only long-time average statistics as inputs. The proposed method provides a discretization time step interval which guarantees the existence of stable and consistent AR model and simultaneously produces the parameters for the AR models. In our numerical examples with two chaotic time series with different characteristics of decaying time scales, we find that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models. These encouraging results are robust across wide ranges of discretization times, observation times, and observation noise variances. Finally, we also find that the proposed model produces an improved short-time prediction relative to the linear regression-based AR-models in forecasting a data set that characterizes the variability of the Madden–Julian Oscillation, a dominant tropical atmospheric wave pattern
Prediction of municipal solid waste generation using nonlinear autoregressive network.
Younes, Mohammad K; Nopiah, Z M; Basri, N E Ahmad; Basri, H; Abushammala, Mohammed F M; Maulud, K N A
2015-12-01
Most of the developing countries have solid waste management problems. Solid waste strategic planning requires accurate prediction of the quality and quantity of the generated waste. In developing countries, such as Malaysia, the solid waste generation rate is increasing rapidly, due to population growth and new consumption trends that characterize society. This paper proposes an artificial neural network (ANN) approach using feedforward nonlinear autoregressive network with exogenous inputs (NARX) to predict annual solid waste generation in relation to demographic and economic variables like population number, gross domestic product, electricity demand per capita and employment and unemployment numbers. In addition, variable selection procedures are also developed to select a significant explanatory variable. The model evaluation was performed using coefficient of determination (R(2)) and mean square error (MSE). The optimum model that produced the lowest testing MSE (2.46) and the highest R(2) (0.97) had three inputs (gross domestic product, population and employment), eight neurons and one lag in the hidden layer, and used Fletcher-Powell's conjugate gradient as the training algorithm. PMID:26573690
No-reference image sharpness assessment in autoregressive parameter space.
Gu, Ke; Zhai, Guangtao; Lin, Weisi; Yang, Xiaokang; Zhang, Wenjun
2015-10-01
In this paper, we propose a new no-reference (NR)/blind sharpness metric in the autoregressive (AR) parameter space. Our model is established via the analysis of AR model parameters, first calculating the energy- and contrast-differences in the locally estimated AR coefficients in a pointwise way, and then quantifying the image sharpness with percentile pooling to predict the overall score. In addition to the luminance domain, we further consider the inevitable effect of color information on visual perception to sharpness and thereby extend the above model to the widely used YIQ color space. Validation of our technique is conducted on the subsets with blurring artifacts from four large-scale image databases (LIVE, TID2008, CSIQ, and TID2013). Experimental results confirm the superiority and efficiency of our method over existing NR algorithms, the stateof-the-art blind sharpness/blurriness estimators, and classical full-reference quality evaluators. Furthermore, the proposed metric can be also extended to stereoscopic images based on binocular rivalry, and attains remarkably high performance on LIVE3D-I and LIVE3D-II databases. PMID:26054063
A fuzzy-autoregressive model of daily river flows
Greco, Roberto
2012-06-01
A model for the identification of daily river flows has been developed, consisting of the combination of an autoregressive model with a fuzzy inference system. The AR model is devoted to the identification of base flow, supposed to be described by linear laws. The fuzzy model identifies the surface runoff, by applying a small set of linguistic statements, deriving from the knowledge of the physical features of the nonlinear rainfall-runoff transformation, to the inflow entering the river basin. The model has been applied to the identification of the daily flow series of river Volturno at Cancello-Arnone (Southern Italy), with a drainage basin of around 5560 km2, observed between 1970 and 1974. The inflow was estimated on the basis of daily precipitations registered during the same years at six rain gauges located throughout the basin. The first two years were used for model training, the remaining three for the validation. The obtained results show that the proposed model provides good predictions of either low river flows or high floods, although the analysis of residuals, which do not turn out to be a white noise, indicates that the cause and effect relationship between rainfall and runoff is not completely identified by the model.
Entropy Rate for Hidden Markov Chains with rare transitions
Peres, Yuval; Quas, Anthony
2010-01-01
We consider Hidden Markov Chains obtained by passing a Markov Chain with rare transitions through a noisy memoryless channel. We obtain asymptotic estimates for the entropy of the resulting Hidden Markov Chain as the transition rate is reduced to zero.
Schmidt games and Markov partitions
International Nuclear Information System (INIS)
Let T be a C2-expanding self-map of a compact, connected, C∞, Riemannian manifold M. We correct a minor gap in the proof of a theorem from the literature: the set of points whose forward orbits are nondense has full Hausdorff dimension. Our correction allows us to strengthen the theorem. Combining the correction with Schmidt games, we generalize the theorem in dimension one: given a point x0 in M, the set of points whose forward orbit closures miss x0 is a winning set. Finally, our key lemma, the no matching lemma, may be of independent interest in the theory of symbolic dynamics or the theory of Markov partitions
Markov constant and quantum instabilities
Pelantová, Edita; Starosta, Štěpán; Znojil, Miloslav
2016-04-01
For a qualitative analysis of spectra of certain two-dimensional rectangular-well quantum systems several rigorous methods of number theory are shown productive and useful. These methods (and, in particular, a generalization of the concept of Markov constant known in Diophantine approximation theory) are shown to provide a new mathematical insight in the phenomenologically relevant occurrence of anomalies in the spectra. Our results may inspire methodical innovations ranging from the description of the stability properties of metamaterials and of certain hiddenly unitary quantum evolution models up to the clarification of the mechanisms of occurrence of ghosts in quantum cosmology.
Markov Process of Muscle Motors
Kondratiev, Yu; Pirogov, S
2007-01-01
We study a Markov random process describing a muscle molecular motor behavior. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spend an exponential time depending on the state. The thin filament moves at its velocity proportional to average of all displacements of all motors. We assume that the time which a motor stays at the bound state does not depend on its displacement. Then one can find an exact solution of a non-linear equation appearing in the limit of infinite number of the motors.
Estimating hidden semi-Markov chains from discrete sequences.
Guédon, Yann
2003-01-01
International audience This article addresses the estimation of hidden semi-Markov chains from nonstationary discrete sequences. Hidden semi-Markov chains are particularly useful to model the succession of homogeneous zones or segments along sequences. A discrete hidden semi-Markov chain is composed of a nonobservable state process, which is a semi-Markov chain, and a discrete output process. Hidden semi-Markov chains generalize hidden Markov chains and enable the modeling of various durat...
An increment type set-indexed Markov property
Balança, Paul
2012-01-01
In this article is introduced and studied a set-indexed Markov property named C-Markov. This new definition fulfils one important expectation for a Markov property: there exists a natural set-indexed generalization of the concept of transition operator which leads to characterization and construction theorems for C-Markov processes. Several other usual Markovian notions, including Feller and strong Markov properties, can also be developed in this framework. Actually, the C-Markov property tur...
Conditional Markov Chains Part II: Consistency and Copulae
Bielecki, Tomasz R.; Jakubowski, Jacek; Niewęgłowski, Mariusz
2015-01-01
In this paper we continue the study of conditional Markov chains (CMCs) with finite state spaces, that we initiated in Bielecki, Jakubowski and Niew\\k{e}g\\l owski (2015). Here, we turn our attention to the study of Markov consistency and Markov copulae with regard to CMCs, and thus we follow up on the study of Markov consistency and Markov copulae for ordinary Markov chains that we presented in Bielecki, Jakubowski and Niew\\k{e}g\\l owski (2013).
Modeling gene expression regulatory networks with the sparse vector autoregressive model
Directory of Open Access Journals (Sweden)
Miyano Satoru
2007-08-01
Full Text Available Abstract Background To understand the molecular mechanisms underlying important biological processes, a detailed description of the gene products networks involved is required. In order to define and understand such molecular networks, some statistical methods are proposed in the literature to estimate gene regulatory networks from time-series microarray data. However, several problems still need to be overcome. Firstly, information flow need to be inferred, in addition to the correlation between genes. Secondly, we usually try to identify large networks from a large number of genes (parameters originating from a smaller number of microarray experiments (samples. Due to this situation, which is rather frequent in Bioinformatics, it is difficult to perform statistical tests using methods that model large gene-gene networks. In addition, most of the models are based on dimension reduction using clustering techniques, therefore, the resulting network is not a gene-gene network but a module-module network. Here, we present the Sparse Vector Autoregressive model as a solution to these problems. Results We have applied the Sparse Vector Autoregressive model to estimate gene regulatory networks based on gene expression profiles obtained from time-series microarray experiments. Through extensive simulations, by applying the SVAR method to artificial regulatory networks, we show that SVAR can infer true positive edges even under conditions in which the number of samples is smaller than the number of genes. Moreover, it is possible to control for false positives, a significant advantage when compared to other methods described in the literature, which are based on ranks or score functions. By applying SVAR to actual HeLa cell cycle gene expression data, we were able to identify well known transcription factor targets. Conclusion The proposed SVAR method is able to model gene regulatory networks in frequent situations in which the number of samples is
Noe, Frank; Prinz, Jan-Hendrik; Plattner, Nuria
2013-01-01
Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dynamics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has therefore been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase- space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecula...
Regeneration and Fixed-Width Analysis of Markov Chain Monte Carlo Algorithms
Latuszynski, Krzysztof
2009-07-01
In the thesis we take the split chain approach to analyzing Markov chains and use it to establish fixed-width results for estimators obtained via Markov chain Monte Carlo procedures (MCMC). Theoretical results include necessary and sufficient conditions in terms of regeneration for central limit theorems for ergodic Markov chains and a regenerative proof of a CLT version for uniformly ergodic Markov chains with E_{π}f^2< infty. To obtain asymptotic confidence intervals for MCMC estimators, strongly consistent estimators of the asymptotic variance are essential. We relax assumptions required to obtain such estimators. Moreover, under a drift condition, nonasymptotic fixed-width results for MCMC estimators for a general state space setting (not necessarily compact) and not necessarily bounded target function f are obtained. The last chapter is devoted to the idea of adaptive Monte Carlo simulation and provides convergence results and law of large numbers for adaptive procedures under path-stability condition for transition kernels.
Indexed semi-Markov process for wind speed modeling.
Petroni, F.; D'Amico, G.; Prattico, F.
2012-04-01
-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. In a previous work we proposed different semi-Markov models, showing their ability to reproduce the autocorrelation structures of wind speed data. In that paper we showed also that the autocorrelation is higher with respect to the Markov model. Unfortunately this autocorrelation was still too small compared to the empirical one. In order to overcome the problem of low autocorrelation, in this paper we propose an indexed semi-Markov model. More precisely we assume that wind speed is described by a discrete time homogeneous semi-Markov process. We introduce a memory index which takes into account the periods of different wind activities. With this model the statistical characteristics of wind speed are faithfully reproduced. The wind is a very unstable phenomenon characterized by a sequence of lulls and sustained speeds, and a good wind generator must be able to reproduce such sequences. To check the validity of the predictive semi-Markovian model, the persistence of synthetic winds were calculated, then averaged and computed. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic generation of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating
Siggiridou, Elsa
2015-01-01
Granger causality has been used for the investigation of the inter-dependence structure of the underlying systems of multi-variate time series. In particular, the direct causal effects are commonly estimated by the conditional Granger causality index (CGCI). In the presence of many observed variables and relatively short time series, CGCI may fail because it is based on vector autoregressive models (VAR) involving a large number of coefficients to be estimated. In this work, the VAR is restricted by a scheme that modifies the recently developed method of backward-in-time selection (BTS) of the lagged variables and the CGCI is combined with BTS. Further, the proposed approach is compared favorably to other restricted VAR representations, such as the top-down strategy, the bottom-up strategy, and the least absolute shrinkage and selection operator (LASSO), in terms of sensitivity and specificity of CGCI. This is shown by using simulations of linear and nonlinear, low and high-dimensional systems and different t...
Autoregressive Prediction with Rolling Mechanism for Time Series Forecasting with Small Sample Size
Directory of Open Access Journals (Sweden)
Zhihua Wang
2014-01-01
Full Text Available Reasonable prediction makes significant practical sense to stochastic and unstable time series analysis with small or limited sample size. Motivated by the rolling idea in grey theory and the practical relevance of very short-term forecasting or 1-step-ahead prediction, a novel autoregressive (AR prediction approach with rolling mechanism is proposed. In the modeling procedure, a new developed AR equation, which can be used to model nonstationary time series, is constructed in each prediction step. Meanwhile, the data window, for the next step ahead forecasting, rolls on by adding the most recent derived prediction result while deleting the first value of the former used sample data set. This rolling mechanism is an efficient technique for its advantages of improved forecasting accuracy, applicability in the case of limited and unstable data situations, and requirement of little computational effort. The general performance, influence of sample size, nonlinearity dynamic mechanism, and significance of the observed trends, as well as innovation variance, are illustrated and verified with Monte Carlo simulations. The proposed methodology is then applied to several practical data sets, including multiple building settlement sequences and two economic series.
Data-driven Markov models and their application in the evaluation of adverse events in radiotherapy
International Nuclear Information System (INIS)
Decision-making processes in medicine rely increasingly on modelling and simulation techniques; they are especially useful when combining evidence from multiple sources. Markov models are frequently used to synthesize the available evidence for such simulation studies, by describing disease and treatment progress, as well as associated factors such as the treatment's effects on a patient's life and the costs to society. When the same decision problem is investigated by multiple stakeholders, differing modelling assumptions are often applied, making synthesis and interpretation of the results difficult. This paper proposes a standardized approach towards the creation of Markov models. It introduces the notion of 'general Markov models', providing a common definition of the Markov models that underlie many similar decision problems, and develops a language for their specification. We demonstrate the application of this language by developing a general Markov model for adverse event analysis in radiotherapy and argue that the proposed method can automate the creation of Markov models from existing data. The approach has the potential to support the radiotherapy community in conducting systematic analyses involving predictive modelling of existing and upcoming radiotherapy data. We expect it to facilitate the application of modelling techniques in medical decision problems beyond the field of radiotherapy, and to improve the comparability of their results. (author)
Detecting Structural Breaks using Hidden Markov Models
DEFF Research Database (Denmark)
Ntantamis, Christos
Testing for structural breaks and identifying their location is essential for econometric modeling. In this paper, a Hidden Markov Model (HMM) approach is used in order to perform these tasks. Breaks are defined as the data points where the underlying Markov Chain switches from one state to another...
Building Simple Hidden Markov Models. Classroom Notes
Ching, Wai-Ki; Ng, Michael K.
2004-01-01
Hidden Markov models (HMMs) are widely used in bioinformatics, speech recognition and many other areas. This note presents HMMs via the framework of classical Markov chain models. A simple example is given to illustrate the model. An estimation method for the transition probabilities of the hidden states is also discussed.
Using Games to Teach Markov Chains
Johnson, Roger W.
2003-01-01
Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…
Markov-modulated diffusion risk models
Bäuerle, Nicole; Kötter, Mirko
2009-01-01
In this paper we consider Markov-modulated diffusion risk reserve processes. Using diffusion approximation we show the relation to classical Markov-modulated risk reserve processes. In particular we derive a representation for the adjustment coefficient and prove some comparison results. Among others we show that increasing the volatility of the diffusion increases the probability of ruin.
Inhomogeneous Markov point processes by transformation
DEFF Research Database (Denmark)
Jensen, Eva B. Vedel; Nielsen, Linda Stougaard
2000-01-01
We construct parametrized models for point processes, allowing for both inhomogeneity and interaction. The inhomogeneity is obtained by applying parametrized transformations to homogeneous Markov point processes. An interesting model class, which can be constructed by this transformation approach......, is that of exponential inhomogeneous Markov point processes. Statistical inference For such processes is discussed in some detail....
Semi-Markov Unreliability-Range Evaluator
Butler, Ricky W.
1988-01-01
Reconfigurable, fault-tolerant systems modeled. Semi-Markov unreliability-range evaluator (SURE) computer program is software tool for analysis of reliability of reconfigurable, fault-tolerant systems. Based on new method for computing death-state probabilities of semi-Markov model. Computes accurate upper and lower bounds on probability of failure of system. Written in PASCAL.
Generators of quantum Markov semigroups
Androulakis, George; Ziemke, Matthew
2015-08-01
Quantum Markov Semigroups (QMSs) originally arose in the study of the evolutions of irreversible open quantum systems. Mathematically, they are a generalization of classical Markov semigroups where the underlying function space is replaced by a non-commutative operator algebra. In the case when the QMS is uniformly continuous, theorems due to the works of Lindblad [Commun. Math. Phys. 48, 119-130 (1976)], Stinespring [Proc. Am. Math. Soc. 6, 211-216 (1955)], and Kraus [Ann. Phys. 64, 311-335 (1970)] imply that the generator of the semigroup has the form L ( A ) = ∑ n = 1 ∞ Vn ∗ A V n + G A + A G ∗ , where Vn and G are elements of the underlying operator algebra. In the present paper, we investigate the form of the generators of QMSs which are not necessarily uniformly continuous and act on the bounded operators of a Hilbert space. We prove that the generators of such semigroups have forms that reflect the results of Lindblad and Stinespring. We also make some progress towards forms reflecting Kraus' result. Finally, we look at several examples to clarify our findings and verify that some of the unbounded operators we are using have dense domains.
Inferring animal densities from tracking data using Markov chains.
Directory of Open Access Journals (Sweden)
Hal Whitehead
Full Text Available The distributions and relative densities of species are keys to ecology. Large amounts of tracking data are being collected on a wide variety of animal species using several methods, especially electronic tags that record location. These tracking data are effectively used for many purposes, but generally provide biased measures of distribution, because the starts of the tracks are not randomly distributed among the locations used by the animals. We introduce a simple Markov-chain method that produces unbiased measures of relative density from tracking data. The density estimates can be over a geographical grid, and/or relative to environmental measures. The method assumes that the tracked animals are a random subset of the population in respect to how they move through the habitat cells, and that the movements of the animals among the habitat cells form a time-homogenous Markov chain. We illustrate the method using simulated data as well as real data on the movements of sperm whales. The simulations illustrate the bias introduced when the initial tracking locations are not randomly distributed, as well as the lack of bias when the Markov method is used. We believe that this method will be important in giving unbiased estimates of density from the growing corpus of animal tracking data.
Testing the Markov hypothesis in fluid flows
Meyer, Daniel W.; Saggini, Frédéric
2016-05-01
Stochastic Markov processes are used very frequently to model, for example, processes in turbulence and subsurface flow and transport. Based on the weak Chapman-Kolmogorov equation and the strong Markov condition, we present methods to test the Markov hypothesis that is at the heart of these models. We demonstrate the capabilities of our methodology by testing the Markov hypothesis for fluid and inertial particles in turbulence, and fluid particles in the heterogeneous subsurface. In the context of subsurface macrodispersion, we find that depending on the heterogeneity level, Markov models work well above a certain scale of interest for media with different log-conductivity correlation structures. Moreover, we find surprising similarities in the velocity dynamics of the different media considered.
REPRESENTING MARKOV CHAINS WITH TRANSITION DIAGRAMS
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Farida Kachapova
2013-01-01
Full Text Available Stochastic processes have many useful applications and are taught in several university programmes. Students often encounter difficulties in learning stochastic processes and Markov chains, in particular. In this article we describe a teaching strategy that uses transition diagrams to represent a Markov chain and to re-define properties of its states in simple terms of directed graphs. This strategy utilises the studentsâ intuition and makes the learning of complex concepts about Markov chains faster and easier. The method is illustrated by worked examples. The described strategy helps students to master properties of finite Markov chains, so they have a solid basis for the study of infinite Markov chains and other stochastic processes.
Classification Using Markov Blanket for Feature Selection
DEFF Research Database (Denmark)
Zeng, Yifeng; Luo, Jian
Selecting relevant features is in demand when a large data set is of interest in a classification task. It produces a tractable number of features that are sufficient and possibly improve the classification performance. This paper studies a statistical method of Markov blanket induction algorithm...... for filtering features and then applies a classifier using the Markov blanket predictors. The Markov blanket contains a minimal subset of relevant features that yields optimal classification performance. We experimentally demonstrate the improved performance of several classifiers using a Markov...... blanket induction as a feature selection method. In addition, we point out an important assumption behind the Markov blanket induction algorithm and show its effect on the classification performance....
Kepler AutoRegressive Planet Search: Initial Results
Caceres, Gabriel; Feigelson, Eric; Jogesh Babu, G.; Bahamonde, Natalia; Bertin, Karine; Christen, Alejandra; Curé, Michel; Meza, Cristian
2015-08-01
The statistical analysis procedures of the Kepler AutoRegressive Planet Search (KARPS) project are applied to a portion of the publicly available Kepler light curve data for the full 4-year mission duration. Tests of the methods have been made on a subset of Kepler Objects of Interest (KOI) systems, classified both as planetary `candidates' and `false positives' by the Kepler Team, as well as a random sample of unclassified systems. We find that the ARMA-type modeling successfully reduces the stellar variability, by a factor of 10 or more in active stars and by smaller factors in more quiescent stars. A typical quiescent Kepler star has an interquartile range (IQR) of ~10 e-/sec, which may improve slightly after modeling, while those with IQR ranging from 20 to 50 e-/sec, have improvements from 20% up to 70%. High activity stars (IQR exceeding 100) markedly improve, but visual inspection of the residual series shows that significant deviations from Gaussianity remain for many of them. Although the reduction in stellar signal is encouraging, it is important to note that the transit signal is also altered in the resulting residual time series. The periodogram derived from our Transit Comb Filter (TCF) is most effective for shorter period planets with quick ingress/egress times (relative to Kepler's 29-minute sample rate). We do not expect high sensitivity to periods of hundreds of days. Our findings to date on real-data tests of the KARPS methodology will be discussed including confirmation of some Kepler Team `candidate' planets, no confirmation of some `candidate' and `false positive' sytems, and suggestions of mischosen harmonics in the Kepler Team periodograms. We also present cases of new possible planetary signals.
Multivariate longitudinal data analysis with mixed effects hidden Markov models.
Raffa, Jesse D; Dubin, Joel A
2015-09-01
Multiple longitudinal responses are often collected as a means to capture relevant features of the true outcome of interest, which is often hidden and not directly measurable. We outline an approach which models these multivariate longitudinal responses as generated from a hidden disease process. We propose a class of models which uses a hidden Markov model with separate but correlated random effects between multiple longitudinal responses. This approach was motivated by a smoking cessation clinical trial, where a bivariate longitudinal response involving both a continuous and a binomial response was collected for each participant to monitor smoking behavior. A Bayesian method using Markov chain Monte Carlo is used. Comparison of separate univariate response models to the bivariate response models was undertaken. Our methods are demonstrated on the smoking cessation clinical trial dataset, and properties of our approach are examined through extensive simulation studies. PMID:25761965
Multiple testing for neuroimaging via hidden Markov random field.
Shu, Hai; Nan, Bin; Koeppe, Robert
2015-09-01
Traditional voxel-level multiple testing procedures in neuroimaging, mostly p-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based procedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation-maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimer's or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimer's Disease Neuroimaging Initiative. PMID:26012881
Geometric allocation approaches in Markov chain Monte Carlo
International Nuclear Information System (INIS)
The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the selection of candidate states, the optimization of transition kernel, algorithm for choosing a configuration according to the transition probabilities. We show that the unconventional approaches based on the geometric allocation of probabilities or weights can improve the dynamics and scaling of the Monte Carlo simulation in several aspects. Particularly, the approach using the irreversible kernel can reduce or sometimes completely eliminate the rejection of trial move in the Markov chain. We also discuss how the space-time interchange technique together with Walker's method of aliases can reduce the computational time especially for the case where the number of candidates is large, such as models with long-range interactions
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Bindu Abraham
2014-05-01
Full Text Available In this paper we analyze DAR(1/D/s Queue with Discrete Mittag-Leffler [DML(α] as marginal distribution. Simulation study of the sample path of the arrival process is conducted. For this queueing system, the stationary distribution of the system size and the waiting time distribution of an arbitrary packet is obtained with the help of matrix analytic methods and Markov regenerative theory. The quantitative effect of the stationary distribution on system size, waiting time and the autocorrelation function as well as the parameters of the input traffic is illustrated empirically. The model is applied to a real data on the passenger arrivals at a subway bus terminal in Santiago de Chile and is established that the model well suits this data.
Wang, Yiyi; Kockelman, Kara M
2013-11-01
This work examines the relationship between 3-year pedestrian crash counts across Census tracts in Austin, Texas, and various land use, network, and demographic attributes, such as land use balance, residents' access to commercial land uses, sidewalk density, lane-mile densities (by roadway class), and population and employment densities (by type). The model specification allows for region-specific heterogeneity, correlation across response types, and spatial autocorrelation via a Poisson-based multivariate conditional auto-regressive (CAR) framework and is estimated using Bayesian Markov chain Monte Carlo methods. Least-squares regression estimates of walk-miles traveled per zone serve as the exposure measure. Here, the Poisson-lognormal multivariate CAR model outperforms an aspatial Poisson-lognormal multivariate model and a spatial model (without cross-severity correlation), both in terms of fit and inference. Positive spatial autocorrelation emerges across neighborhoods, as expected (due to latent heterogeneity or missing variables that trend in space, resulting in spatial clustering of crash counts). In comparison, the positive aspatial, bivariate cross correlation of severe (fatal or incapacitating) and non-severe crash rates reflects latent covariates that have impacts across severity levels but are more local in nature (such as lighting conditions and local sight obstructions), along with spatially lagged cross correlation. Results also suggest greater mixing of residences and commercial land uses is associated with higher pedestrian crash risk across different severity levels, ceteris paribus, presumably since such access produces more potential conflicts between pedestrian and vehicle movements. Interestingly, network densities show variable effects, and sidewalk provision is associated with lower severe-crash rates. PMID:24036167
Markov Chain Monte Carlo Estimation of Item Parameters for the Generalized Graded Unfolding Model
de la Torre, Jimmy; Stark, Stephen; Chernyshenko, Oleksandr S.
2006-01-01
The authors present a Markov Chain Monte Carlo (MCMC) parameter estimation procedure for the generalized graded unfolding model (GGUM) and compare it to the marginal maximum likelihood (MML) approach implemented in the GGUM2000 computer program, using simulated and real personality data. In the simulation study, test length, number of response…
Teaching Markov Chain Monte Carlo: Revealing the Basic Ideas behind the Algorithm
Stewart, Wayne; Stewart, Sepideh
2014-01-01
For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper…
Stochastic modeling of pitting corrosion in underground pipelines using Markov chains
Energy Technology Data Exchange (ETDEWEB)
Velazquez, J.C.; Caleyo, F.; Hallen, J.M.; Araujo, J.E. [Instituto Politecnico Nacional (IPN), Mexico D.F. (Mexico). Escuela Superior de Ingenieria Quimica e Industrias Extractivas (ESIQIE); Valor, A. [Universidad de La Habana, La Habana (Cuba)
2009-07-01
A non-homogenous, linear growth (pure birth) Markov process, with discrete states in continuous time, has been used to model external pitting corrosion in underground pipelines. The transition probability function for the pit depth is obtained from the analytical solution of the forward Kolmogorov equations for this process. The parameters of the transition probability function between depth states can be identified from the observed time evolution of the mean of the pit depth distribution. Monte Carlo simulations were used to predict the time evolution of the mean value of the pit depth distribution in soils with different physicochemical characteristics. The simulated distributions have been used to create an empirical Markov-chain-based stochastic model for predicting the evolution of pitting corrosion from the observed properties of the soil in contact with the pipeline. Real- life case studies, involving simulated and measured pit depth distributions are presented to illustrate the application of the proposed Markov chains model. (author)
Revisiting Causality in Markov Chains
Shojaee, Abbas
2016-01-01
Identifying causal relationships is a key premise of scientific research. The growth of observational data in different disciplines along with the availability of machine learning methods offers the possibility of using an empirical approach to identifying potential causal relationships, to deepen our understandings of causal behavior and to build theories accordingly. Conventional methods of causality inference from observational data require a considerable length of time series data to capture cause-effect relationship. We find that potential causal relationships can be inferred from the composition of one step transition rates to and from an event. Also known as Markov chain, one step transition rates are a commonly available resource in different scientific disciplines. Here we introduce a simple, effective and computationally efficient method that we termed 'Causality Inference using Composition of Transitions CICT' to reveal causal structure with high accuracy. We characterize the differences in causes,...
Tornadoes and related damage costs: statistical modeling with a semi-Markov approach
Corini, Chiara; Petroni, Filippo; Prattico, Flavio; Manca, Raimondo
2015-01-01
We propose a statistical approach to tornadoes modeling for predicting and simulating occurrences of tornadoes and accumulated cost distributions over a time interval. This is achieved by modeling the tornadoes intensity, measured with the Fujita scale, as a stochastic process. Since the Fujita scale divides tornadoes intensity into six states, it is possible to model the tornadoes intensity by using Markov and semi-Markov models. We demonstrate that the semi-Markov approach is able to reproduce the duration effect that is detected in tornadoes occurrence. The superiority of the semi-Markov model as compared to the Markov chain model is also affirmed by means of a statistical test of hypothesis. As an application we compute the expected value and the variance of the costs generated by the tornadoes over a given time interval in a given area. he paper contributes to the literature by demonstrating that semi-Markov models represent an effective tool for physical analysis of tornadoes as well as for the estimati...
Hidden Markov models estimation and control
Elliott, Robert J; Moore, John B
1995-01-01
As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics. In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filte
Markov chains models, algorithms and applications
Ching, Wai-Ki; Ng, Michael K; Siu, Tak-Kuen
2013-01-01
This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods
Finite Markov processes and their applications
Iosifescu, Marius
2007-01-01
A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic ch
Coding with partially hidden Markov models
DEFF Research Database (Denmark)
Forchhammer, Søren; Rissanen, J.
Partially hidden Markov models (PHMM) are introduced. They are a variation of the hidden Markov models (HMM) combining the power of explicit conditioning on past observations and the power of using hidden states. (P)HMM may be combined with arithmetic coding for lossless data compression. A general....... The PHMM structure and the conditions of the convergence proof allows for application of the PHMM to image coding. Relations between the PHMM and hidden Markov models (HMM) are treated. Results of coding bi-level images with the PHMM coding scheme is given. The results indicate that the PHMM can adapt...
Stationary Probability Vectors of Higher-order Markov Chains
Li, Chi-Kwong; Zhang, Shixiao
2013-01-01
We consider the higher-order Markov Chain, and characterize the second order Markov chains admitting every probability distribution vector as a stationary vector. The result is used to construct Markov chains of higher-order with the same property. We also study conditions under which the set of stationary vectors of the Markov chain has a certain affine dimension.
Markov Chain Order estimation with Conditional Mutual Information
Papapetrou, Maria; 10.1016/j.physa.2012.12.017.
2013-01-01
We introduce the Conditional Mutual Information (CMI) for the estimation of the Markov chain order. For a Markov chain of $K$ symbols, we define CMI of order $m$, $I_c(m)$, as the mutual information of two variables in the chain being $m$ time steps apart, conditioning on the intermediate variables of the chain. We find approximate analytic significance limits based on the estimation bias of CMI and develop a randomization significance test of $I_c(m)$, where the randomized symbol sequences are formed by random permutation of the components of the original symbol sequence. The significance test is applied for increasing $m$ and the Markov chain order is estimated by the last order for which the null hypothesis is rejected. We present the appropriateness of CMI-testing on Monte Carlo simulations and compare it to the Akaike and Bayesian information criteria, the maximal fluctuation method (Peres-Shields estimator) and a likelihood ratio test for increasing orders using $\\phi$-divergence. The order criterion of...
Discrimination between earthquakes and explosions using Markov Length Scale (MLS)
International Nuclear Information System (INIS)
Full text: In this paper, the Markov length (time) scale are regarded as the discriminating tools to classify the natural seismic events (earthquakes) from the artificial ones (nuclear explosions) based on the seismic signals recorded at teleseismic distances. The bulk of our novel is to improve the obtained numerical results using this advance technique. For the Markov length scale, by testing the different types of seismic features, we have shown the potential application of this method to discriminate the classes. During the above study, we found out that the Markov length scale (MLS) has been used in a fully innovative manner in this work. Here the MLS detects the type of the source whenever a natural or artificial source changes the nature of the background noise of the seismograms. During the above study, we found out that MLS is sometimes capable to alarm the further natural seismological events just a little before the onset. So the application of MLS in seismic prediction is also studied through the simulated experiments. (author)
MCMC simulation of GARCH model to forecast network traffic load
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Akhter Raza Syed
2012-05-01
Full Text Available The performance of a computer network can be enhanced by increasing number of servers, upgrading the hardware, and gaining additional bandwidth but this solution require the huge amount to invest. In contrast to increasing the bandwidth and hardware resources, network traffic modeling play a significant role in enhancing the network performance. As the emphasis of telecommunication service providers shifted towards the high-speed networks providing integrated services at a prescribed Quality of Service (QoS, the role of accurate traffic models in network design and network simulation becomes ever more crucial. We analyze a traffic volume time series of internet requests made to a workstation. This series exhibits a long-range dependence and self-similarity in large time scale and exhibits multifractal in small time scale. In this paper, for this time series, we proposed Generalized Autoregressive Conditional Heteroscedastic, (GARCH model, and practical techniques for model fitting, Markov Chain Monte Carlo simulation and forecasting issues are demonstrated. The proposed model provides us simple and accurate approach for simulating internet data traffic patterns.
Mission reliability of semi-Markov systems under generalized operational time requirements
International Nuclear Information System (INIS)
Mission reliability of a system depends on specific criteria for mission success. To evaluate the mission reliability of some mission systems that do not need to work normally for the whole mission time, two types of mission reliability for such systems are studied. The first type corresponds to the mission requirement that the system must remain operational continuously for a minimum time within the given mission time interval, while the second corresponds to the mission requirement that the total operational time of the system within the mission time window must be greater than a given value. Based on Markov renewal properties, matrix integral equations are derived for semi-Markov systems. Numerical algorithms and a simulation procedure are provided for both types of mission reliability. Two examples are used for illustration purposes. One is a one-unit repairable Markov system, and the other is a cold standby semi-Markov system consisting of two components. By the proposed approaches, the mission reliability of systems with time redundancy can be more precisely estimated to avoid possible unnecessary redundancy of system resources. - Highlights: • Two types of mission reliability under generalized requirements are defined. • Equations for both types of reliability are derived for semi-Markov systems. • Numerical methods are given for solving both types of reliability. • Simulation procedure is given for estimating both types of reliability. • Verification of the numerical methods is given by the results of simulation
Limit theorems for Markov random fields
International Nuclear Information System (INIS)
Markov Random Fields (MRF's) have been extensively applied in Statistical Mechanics as well as in Bayesian Image Analysis. MRF's are a special class of dependent random variables located at the vertices of a graph whose joint distribution includes a parameter called the temperature. When the number of vertices of the graph tends to infinity, the normalized distribution of statistics based on these random variables converge in distribution. It can happen that for certain values of the temperature, that the rate of growth of these normalizing constants change drastically. This feature is generally used to explain the phenomenon of phase transition as understood by physicist. In this dissertation the author will show that this drastic change in normalizing constants occurs even in the relatively smooth case when all the random variables are Gaussian. Hence any image analytic MRF ought to be checked for such discontinuous behavior before any analysis is performed. Mixed limit theorems in Bayesian Image Analysis seek to replace intensive simulations of MRF's with limit theorems that approximate the distribution of the MRF's as the number of sites increases. The problem of deriving mixed limit theorems for MRF's on a one dimensional lattice graph with an acceptor function that has a second moment has been studied by Chow. A mixed limit theorem for the integer lattice graph is derived when the acceptor function does not have a second moment as for instance when the acceptor function is a symmetric stable density of index 0 < α < 2
Chattopadhyay, Goutami; 10.1140/epjp/i2012-12043-9
2012-01-01
This study reports a statistical analysis of monthly sunspot number time series and observes non homogeneity and asymmetry within it. Using Mann-Kendall test a linear trend is revealed. After identifying stationarity within the time series we generate autoregressive AR(p) and autoregressive moving average (ARMA(p,q)). Based on minimization of AIC we find 3 and 1 as the best values of p and q respectively. In the next phase, autoregressive neural network (AR-NN(3)) is generated by training a generalized feedforward neural network (GFNN). Assessing the model performances by means of Willmott's index of second order and coefficient of determination, the performance of AR-NN(3) is identified to be better than AR(3) and ARMA(3,1).
A Note on the Properties of Generalised Separable Spatial Autoregressive Process
Directory of Open Access Journals (Sweden)
Mahendran Shitan
2009-01-01
Full Text Available Spatial modelling has its applications in many fields like geology, agriculture, meteorology, geography, and so forth. In time series a class of models known as Generalised Autoregressive (GAR has been introduced by Peiris (2003 that includes an index parameter δ. It has been shown that the inclusion of this additional parameter aids in modelling and forecasting many real data sets. This paper studies the properties of a new class of spatial autoregressive process of order 1 with an index. We will call this a Generalised Separable Spatial Autoregressive (GENSSAR Model. The spectral density function (SDF, the autocovariance function (ACVF, and the autocorrelation function (ACF are derived. The theoretical ACF and SDF plots are presented as three-dimensional figures.
Chattopadhyay, Goutami; Chattopadhyay, Surajit
2012-04-01
This study reports a statistical analysis of monthly sunspot number time series and observes nonhomogeneity and asymmetry within it. Using the Mann-Kendall test a linear trend is revealed. After identifying stationarity within the time series we generate autoregressive AR( p) and autoregressive moving average (ARMA( p, q) . Based on the minimization of AIC we find 3 and 1 as the best values for p and q , respectively. In the next phase, autoregressive neural network (AR-NN(3)) is generated by training a generalized feedforward neural network (GFNN). Assessing the model performances by means of Willmott's index of second order and the coefficient of determination, the performance of AR-NN(3) is identified to be better than AR(3) and ARMA(3,1).
International Nuclear Information System (INIS)
We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)
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Frank, T D [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States)
2008-07-18
We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)
Markov chains and decision processes for engineers and managers
Sheskin, Theodore J
2010-01-01
Markov Chain Structure and ModelsHistorical NoteStates and TransitionsModel of the WeatherRandom WalksEstimating Transition ProbabilitiesMultiple-Step Transition ProbabilitiesState Probabilities after Multiple StepsClassification of StatesMarkov Chain StructureMarkov Chain ModelsProblemsReferencesRegular Markov ChainsSteady State ProbabilitiesFirst Passage to a Target StateProblemsReferencesReducible Markov ChainsCanonical Form of the Transition MatrixTh
What does a generic Markov operator look like
Vershik, A.
2005-01-01
We consider generic i.e., forming an everywhere dense massive subset classes of Markov operators in the space $L^2(X,\\mu)$ with a finite continuous measure. Since there is a canonical correspondence that associates with each Markov operator a multivalued measure-preserving transformation (i.e., a polymorphism), as well as a stationary Markov chain, we can also speak about generic polymorphisms and generic Markov chains. The most important and inexpected generic properties of Markov operators ...
On invariant measures of nonlinear Markov processes
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N. U. Ahmed
1993-01-01
Full Text Available We consider a nonlinear (in the sense of McKean Markov process described by a stochastic differential equations in Rd. We prove the existence and uniqueness of invariant measures of such process.
Transition Probability Estimates for Reversible Markov Chains
Telcs, Andras
2000-01-01
This paper provides transition probability estimates of transient reversible Markov chains. The key condition of the result is the spatial symmetry and polynomial decay of the Green's function of the chain.
Variational Perturbation Theory for Markov Processes
Kleinert, Hagen; Pelster, Axel; Mihai V. Putz
2002-01-01
We develop a convergent variational perturbation theory for conditional probability densities of Markov processes. The power of the theory is illustrated by applying it to the diffusion of a particle in an anharmonic potential.
Generalized crested products of Markov chains
D'Angeli, Daniele
2010-01-01
We define a finite Markov chain, called generalized crested product, which naturally appears as a generalization of the first crested product of Markov chains. A complete spectral analysis is developed and the $k$-step transition probability is given. It is important to remark that this Markov chain describes a more general version of the classical Ehrenfest diffusion model. As a particular case, one gets a generalization of the classical Insect Markov chain defined on the ultrametric space. Finally, an interpretation in terms of representation group theory is given, by showing the correspondence between the spectral decomposition of the generalized crested product and the Gelfand pairs associated with the generalized wreath product of permutation groups.
Generated dynamics of Markov and quantum processes
Janßen, Martin
2016-01-01
This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state. Quantum processes apply to systems where all variables, that control reversibility, are taken as relevant variables, while Markov processes emerge when some of those variables cannot be followed and are thus irrelevant for the dynamic description. Their absence renders the dynamic irreversible. A further aim is to demonstrate that almost any subdiscipline of theoretical physics can conceptually be put in...
On A Markov Game with Incomplete Information
Hörner, Johannes; Rosenberg, Dinah; Solan, Eilon; Vieille, Nicolas
2006-01-01
We consider an example of a Markov game with lack of information on one side, that was first introduced by Renault (2002). We compute both the value and optimal strategies for a range of parameter values.
Statistical semantic processing using Markov logic
Meza-Ruiz, Ivan Vladimir
2009-01-01
Markov Logic (ML) is a novel approach to Natural Language Processing tasks [Richardson and Domingos, 2006; Riedel, 2008]. It is a Statistical Relational Learning language based on First Order Logic (FOL) and Markov Networks (MN). It allows one to treat a task as structured classification. In this work, we investigate ML for the semantic processing tasks of Spoken Language Understanding (SLU) and Semantic Role Labelling (SRL). Both tasks consist of identifying a semantic represe...
Interacting Particle Markov Chain Monte Carlo
Rainforth, Tom; Naesseth, Christian A.; Lindsten, Fredrik; Paige, Brooks; van de Meent, Jan-Willem; Doucet, Arnaud; Wood, Frank
2016-01-01
We introduce interacting particle Markov chain Monte Carlo (iPMCMC), a PMCMC method that introduces a coupling between multiple standard and conditional sequential Monte Carlo samplers. Like related methods, iPMCMC is a Markov chain Monte Carlo sampler on an extended space. We present empirical results that show significant improvements in mixing rates relative to both non-interacting PMCMC samplers and a single PMCMC sampler with an equivalent total computational budget. An additional advant...
Markov Processes linking Thermodynamics and Turbulence
Nickelsen, Daniel
2015-01-01
This PhD thesis deals with the Markov picture of developed turbulence from the theoretical point of view. The thesis consists of two parts. The first part introduces stochastic thermodynamics, the second part aims at transferring the concepts of stochastic thermodynamics to developed turbulence. / Central in stochastic thermodynamics are Markov processes. An elementary example is Brownian motion. In contrast to macroscopic thermodynamics, the work done and the entropy produced for single traj...
Markov processes and parabolic partial differential equations
Bossy, Mireille; Champagnat, Nicolas
2010-01-01
In the first part of this article, we present the main tools and definitions of Markov processes' theory: transition semigroups, Feller processes, infinitesimal generator, Kolmogorov's backward and forward equations and Feller diffusion. We also give several classical examples including stochastic differential equations (SDEs) and backward SDEs (BSDEs). The second part of this article is devoted to the links between Markov processes and parabolic partial differential equations (PDEs). In part...
Stochastic relations foundations for Markov transition systems
Doberkat, Ernst-Erich
2007-01-01
Collecting information previously scattered throughout the vast literature, including the author's own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition systems. After an introduction to the basic mathematical tools from topology, measure theory, and categories, the book examines the central topics of congruences and morphisms, applies these to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. The author views developments from the general
Understanding Markov-switching rational expectations models
Roger E.A. Farmer; Daniel F. Waggoner; Zha, Tao
2009-01-01
We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models, and we develop an algorithm to check these conditions in practice. We use three examples, based on the new Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov switching with forward-looking rational expectations models and allows an applied researcher to construc...
Semi-Markov Unreliability Range Evaluator
Butler, Ricky W.; Boerschlein, David P.
1993-01-01
Semi-Markov Unreliability Range Evaluator, SURE, computer program is software tool for analysis of reconfigurable, fault-tolerant systems. Traditional reliability analyses based on aggregates of fault-handling and fault-occurrence models. SURE provides efficient means for calculating accurate upper and lower bounds for probabilities of death states for large class of semi-Markov mathematical models, and not merely those reduced to critical-pair architectures.
Quantum Markov Chain Mixing and Dissipative Engineering
DEFF Research Database (Denmark)
Kastoryano, Michael James
2012-01-01
This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state of the sy....... Finally, we consider three independent tasks of dissipative engineering: dissipatively preparing a maximally entangled state of two atoms trapped in an optical cavity, dissipative preparation of graph states, and dissipative quantum computing construction.......This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state...... (stationary states). The aim of Markov chain mixing is to obtain (upper and/or lower) bounds on the number of steps it takes for the Markov chain to reach a stationary state. The natural quantum extensions of these notions are density matrices and quantum channels. We set out to develop a general mathematical...
Is First-Order Vector Autoregressive Model Optimal for fMRI Data?
Ting, Chee-Ming; Seghouane, Abd-Krim; Khalid, Muhammad Usman; Salleh, Sh-Hussain
2015-09-01
We consider the problem of selecting the optimal orders of vector autoregressive (VAR) models for fMRI data. Many previous studies used model order of one and ignored that it may vary considerably across data sets depending on different data dimensions, subjects, tasks, and experimental designs. In addition, the classical information criteria (IC) used (e.g., the Akaike IC (AIC)) are biased and inappropriate for the high-dimensional fMRI data typically with a small sample size. We examine the mixed results on the optimal VAR orders for fMRI, especially the validity of the order-one hypothesis, by a comprehensive evaluation using different model selection criteria over three typical data types--a resting state, an event-related design, and a block design data set--with varying time series dimensions obtained from distinct functional brain networks. We use a more balanced criterion, Kullback's IC (KIC) based on Kullback's symmetric divergence combining two directed divergences. We also consider the bias-corrected versions (AICc and KICc) to improve VAR model selection in small samples. Simulation results show better small-sample selection performance of the proposed criteria over the classical ones. Both bias-corrected ICs provide more accurate and consistent model order choices than their biased counterparts, which suffer from overfitting, with KICc performing the best. Results on real data show that orders greater than one were selected by all criteria across all data sets for the small to moderate dimensions, particularly from small, specific networks such as the resting-state default mode network and the task-related motor networks, whereas low orders close to one but not necessarily one were chosen for the large dimensions of full-brain networks. PMID:26161816
Perspective: Markov models for long-timescale biomolecular dynamics
International Nuclear Information System (INIS)
Molecular dynamics simulations have the potential to provide atomic-level detail and insight to important questions in chemical physics that cannot be observed in typical experiments. However, simply generating a long trajectory is insufficient, as researchers must be able to transform the data in a simulation trajectory into specific scientific insights. Although this analysis step has often been taken for granted, it deserves further attention as large-scale simulations become increasingly routine. In this perspective, we discuss the application of Markov models to the analysis of large-scale biomolecular simulations. We draw attention to recent improvements in the construction of these models as well as several important open issues. In addition, we highlight recent theoretical advances that pave the way for a new generation of models of molecular kinetics
Perspective: Markov Models for Long-Timescale Biomolecular Dynamics
Schwantes, Christian R; Pande, Vijay S
2014-01-01
Molecular dynamics simulations have the potential to provide atomic-level detail and insight to important questions in chemical physics that cannot be observed in typical experiments. However, simply generating a long trajectory is insufficient, as researchers must be able to transform the data in a simulation trajectory into specific scientific insights. Although this analysis step has often been taken for granted, it deserves further attention as large-scale simulations become increasingly routine. In this perspective, we discuss the application of Markov models to the analysis of large-scale biomolecular simulations. We draw attention to recent improvements in the construction of these models as well as several important open issues. In addition, we highlight recent theoretical advances that pave the way for a new generation of models of molecular kinetics.
International Nuclear Information System (INIS)
A new approach to the problem of modelling and predicting respiration motion has been implemented. This is a dual-component model, which describes the respiration motion as a non-periodic time series superimposed onto a periodic waveform. A periodic autoregressive moving average algorithm has been used to define a mathematical model of the periodic and non-periodic components of the respiration motion. The periodic components of the motion were found by projecting multiple inhale-exhale cycles onto a common subspace. The component of the respiration signal that is left after removing this periodicity is a partially autocorrelated time series and was modelled as an autoregressive moving average (ARMA) process. The accuracy of the periodic ARMA model with respect to fluctuation in amplitude and variation in length of cycles has been assessed. A respiration phantom was developed to simulate the inter-cycle variations seen in free-breathing and coached respiration patterns. At ±14% variability in cycle length and maximum amplitude of motion, the prediction errors were 4.8% of the total motion extent for a 0.5 s ahead prediction, and 9.4% at 1.0 s lag. The prediction errors increased to 11.6% at 0.5 s and 21.6% at 1.0 s when the respiration pattern had ±34% variations in both these parameters. Our results have shown that the accuracy of the periodic ARMA model is more strongly dependent on the variations in cycle length than the amplitude of the respiration cycles
Markov chain model for particle migration at the repository scale
International Nuclear Information System (INIS)
A model for particle migration at multiple scales is developed using the Markov chain probability model. The goal of the model is to enable analyses of radionuclide migration at the repository scale based on the information obtained in smaller-scale detailed analyses by other models. Geologic domain is divided into an array of compartments, and particle migration is simulated by transitions from one compartment to another based on transition probabilities. Nuclide transport in hypothetical repository with heterogeneous flow due to random connectivity between compartments is demonstrated. In the comparison with the analytical continuum model of mass transport, the results from the present model show a good agreement. (author)
Free energies from dynamic weighted histogram analysis using unbiased Markov state model.
Rosta, Edina; Hummer, Gerhard
2015-01-13
The weighted histogram analysis method (WHAM) is widely used to obtain accurate free energies from biased molecular simulations. However, WHAM free energies can exhibit significant errors if some of the biasing windows are not fully equilibrated. To account for the lack of full equilibration, we develop the dynamic histogram analysis method (DHAM). DHAM uses a global Markov state model to obtain the free energy along the reaction coordinate. A maximum likelihood estimate of the Markov transition matrix is constructed by joint unbiasing of the transition counts from multiple umbrella-sampling simulations along discretized reaction coordinates. The free energy profile is the stationary distribution of the resulting Markov matrix. For this matrix, we derive an explicit approximation that does not require the usual iterative solution of WHAM. We apply DHAM to model systems, a chemical reaction in water treated using quantum-mechanics/molecular-mechanics (QM/MM) simulations, and the Na(+) ion passage through the membrane-embedded ion channel GLIC. We find that DHAM gives accurate free energies even in cases where WHAM fails. In addition, DHAM provides kinetic information, which we here use to assess the extent of convergence in each of the simulation windows. DHAM may also prove useful in the construction of Markov state models from biased simulations in phase-space regions with otherwise low population. PMID:26574225
Semi-Markov adjunction to the Computer-Aided Markov Evaluator (CAME)
Rosch, Gene; Hutchins, Monica A.; Leong, Frank J.; Babcock, Philip S., IV
1988-01-01
The rule-based Computer-Aided Markov Evaluator (CAME) program was expanded in its ability to incorporate the effect of fault-handling processes into the construction of a reliability model. The fault-handling processes are modeled as semi-Markov events and CAME constructs and appropriate semi-Markov model. To solve the model, the program outputs it in a form which can be directly solved with the Semi-Markov Unreliability Range Evaluator (SURE) program. As a means of evaluating the alterations made to the CAME program, the program is used to model the reliability of portions of the Integrated Airframe/Propulsion Control System Architecture (IAPSA 2) reference configuration. The reliability predictions are compared with a previous analysis. The results bear out the feasibility of utilizing CAME to generate appropriate semi-Markov models to model fault-handling processes.
DEFF Research Database (Denmark)
Holt, Matthew T.; Teräsvirta, Timo
This paper examines trends in annual temperature data for the northern and southern hemisphere (1850-2010) by using variants of the shifting-mean autoregressive (SM-AR) model of Gonzalez and Terasvirta (2008). Univariate models are first fitted to each series by using the so called QuickShift me...
Asymptotic behavior of the variance of the EWMA statistic for autoregressive processes
Vermaat, T.M.B.; Meulen, van der, N.; Does, R.J.M.M.
2010-01-01
Asymptotic behavior of the variance of the EWMA statistic for autoregressive processes correspondance: Corresponding author. Tel.: +31 20 5255203; fax: +31 20 5255101. (Vermaat, M.B.) (Vermaat, M.B.) Institute for Business and Industrial Statistics of the University of Amsterdam--> , IBIS UvA--> - NETHERLANDS (Vermaat, M.B.) Institute for Business and Industrial Statistics of the University of Amst...
Data-Driven Inference on Sign Restrictions in Bayesian Structural Vector Autoregression
DEFF Research Database (Denmark)
Lanne, Markku; Luoto, Jani
Sign-identified structural vector autoregressive (SVAR) models have recently become popular. However, the conventional approach to sign restrictions only yields set identification, and implicitly assumes an informative prior distribution of the impulse responses whose influence does not vanish as...... methods by two empirical applications to U.S. macroeconomic data....
The Performance of Multilevel Growth Curve Models under an Autoregressive Moving Average Process
Murphy, Daniel L.; Pituch, Keenan A.
2009-01-01
The authors examined the robustness of multilevel linear growth curve modeling to misspecification of an autoregressive moving average process. As previous research has shown (J. Ferron, R. Dailey, & Q. Yi, 2002; O. Kwok, S. G. West, & S. B. Green, 2007; S. Sivo, X. Fan, & L. Witta, 2005), estimates of the fixed effects were unbiased, and Type I…
de Vries, SO; Fidler, [No Value; Kuipers, WD; Hunink, MGM
1998-01-01
The purpose of this study was to develop a model that predicts the outcome of supervised exercise for intermittent claudication. The authors present an example of the use of autoregressive logistic regression for modeling observed longitudinal data. Data were collected from 329 participants in a six
de Vries, S.O.; Fidler, V.; Kuipers, W.D.; Hunink, M.G.
1998-01-01
The purpose of this study was to develop a model that predicts the outcome of supervised exercise for intermittent claudication. The authors present an example of the use of autoregressive logistic regression for modeling observed longitudinal data. Data were collected from 329 participants in a six
DEFF Research Database (Denmark)
Kock, Anders Bredahl
2015-01-01
We show that the adaptive Lasso is oracle efficient in stationary and nonstationary autoregressions. This means that it estimates parameters consistently, selects the correct sparsity pattern, and estimates the coefficients belonging to the relevant variables at the same asymptotic efficiency as if...
On the Oracle Property of the Adaptive LASSO in Stationary and Nonstationary Autoregressions
DEFF Research Database (Denmark)
Kock, Anders Bredahl
We show that the Adaptive LASSO is oracle efficient in stationary and non-stationary autoregressions. This means that it estimates parameters consistently, selects the correct sparsity pattern, and estimates the coefficients belonging to the relevant variables at the same asymptotic efficiency as...
2003-01-01
Abstract: In this note we consider testing of a type of linear restrictions implied by rational expectations hypotheses in a cointegrated vector autoregressive model for I(1) variables when there in addition is a restriction on the deterministic drift term. Keywords: VAR model, cointegration, restricted drift term, rational expectations
Enhanced modeling via network theory: Adaptive sampling of Markov state models
Bowman, Gregory R; Ensign, Daniel L.; Pande, Vijay S.
2010-01-01
Computer simulations can complement experiments by providing insight into molecular kinetics with atomic resolution. Unfortunately, even the most powerful supercomputers can only simulate small systems for short timescales, leaving modeling of most biologically relevant systems and timescales intractable. In this work, however, we show that molecular simulations driven by adaptive sampling of networks called Markov State Models (MSMs) can yield tremendous time and resource savings, allowing p...
Grinfeld, Michael; Knight, Philip A.; Wade, Andrew R.
2012-01-01
We study a class of Markovian systems of N elements taking values in [0,1] that evolve in discrete time t via randomized replacement rules based on the ranks of the elements. These rank-driven processes are inspired by variants of the Bak-Sneppen model of evolution, in which the system represents an evolutionary `fitness landscape' and which is famous as a simple model displaying self-organized criticality. Our main results are concerned with long-time large- N asymptotics for the general model in which, at each time step, K randomly chosen elements are discarded and replaced by independent U[0,1] variables, where the ranks of the elements to be replaced are chosen, independently at each time step, according to a distribution κ N on {1,2,…, N} K . Our main results are that, under appropriate conditions on κ N , the system exhibits threshold behavior at s ∗∈[0,1], where s ∗ is a function of κ N , and the marginal distribution of a randomly selected element converges to U[ s ∗,1] as t→∞ and N→∞. Of this class of models, results in the literature have previously been given for special cases only, namely the `mean-field' or `random neighbor' Bak-Sneppen model. Our proofs avoid the heuristic arguments of some of the previous work and use Foster-Lyapunov ideas. Our results extend existing results and establish their natural, more general context. We derive some more specialized results for the particular case where K=2. One of our technical tools is a result on convergence of stationary distributions for families of uniformly ergodic Markov chains on increasing state-spaces, which may be of independent interest.
Hidden Markov Model Application to Transfer The Trader Online Forex Brokers
Directory of Open Access Journals (Sweden)
Farida Suharleni
2012-05-01
Full Text Available Hidden Markov Model is elaboration of Markov chain, which is applicable to cases that can’t directly observe. In this research, Hidden Markov Model is used to know trader’s transition to broker forex online. In Hidden Markov Model, observed state is observable part and hidden state is hidden part. Hidden Markov Model allows modeling system that contains interrelated observed state and hidden state. As observed state in trader’s transition to broker forex online is category 1, category 2, category 3, category 4, category 5 by condition of every broker forex online, whereas as hidden state is broker forex online Marketiva, Masterforex, Instaforex, FBS and Others. First step on application of Hidden Markov Model in this research is making construction model by making a probability of transition matrix (A from every broker forex online. Next step is making a probability of observation matrix (B by making conditional probability of five categories, that is category 1, category 2, category 3, category 4, category 5 by condition of every broker forex online and also need to determine an initial state probability (π from every broker forex online. The last step is using Viterbi algorithm to find hidden state sequences that is broker forex online sequences which is the most possible based on model and observed state that is the five categories. Application of Hidden Markov Model is done by making program with Viterbi algorithm using Delphi 7.0 software with observed state based on simulation data. Example: By the number of observation T = 5 and observed state sequences O = (2,4,3,5,1 is found hidden state sequences which the most possible with observed state O as following : where X1 = FBS, X2 = Masterforex, X3 = Marketiva, X4 = Others, and X5 = Instaforex.
Directory of Open Access Journals (Sweden)
F. Oriani
2014-03-01
Full Text Available The Direct Sampling technique, belonging to the family of multiple-point statistics, is proposed as a non-parametric alternative to the classical autoregressive and Markov-chain based models for daily rainfall time-series simulation. The algorithm makes use of the patterns contained inside the training image (the past rainfall record to reproduce the complexity of the signal without inferring its prior statistical model: the time-series is simulated by sampling the training dataset where a sufficiently similar neighborhood exists. The advantage of this approach is the capability of simulating complex statistical relations by respecting the similarity of the patterns at different scales. The technique is applied to daily rainfall records from different climate settings, using a standard setup and without performing any optimization of the parameters. The results show that the overall statistics as well as the dry/wet spells patterns are simulated accurately. Also the extremes at the higher temporal scale are reproduced exhaustively, reducing the well known problem of over-dispersion.
Zipf exponent of trajectory distribution in the hidden Markov model
Bochkarev, V. V.; Lerner, E. Yu
2014-03-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.
Performance Modeling of Communication Networks with Markov Chains
Mo, Jeonghoon
2010-01-01
This book is an introduction to Markov chain modeling with applications to communication networks. It begins with a general introduction to performance modeling in Chapter 1 where we introduce different performance models. We then introduce basic ideas of Markov chain modeling: Markov property, discrete time Markov chain (DTMe and continuous time Markov chain (CTMe. We also discuss how to find the steady state distributions from these Markov chains and how they can be used to compute the system performance metric. The solution methodologies include a balance equation technique, limiting probab
Zipf exponent of trajectory distribution in the hidden Markov model
International Nuclear Information System (INIS)
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different
Finesso, L; Spreij, P
2010-01-01
We propose a two-step algorithm for the construction of a Hidden Markov Model (HMM) of assigned size, i.e. cardinality of the state space of the underlying Markov chain, whose $n$-dimensional distribution is closest in divergence to a given distribution. The algorithm is based on the factorization of a pseudo Hankel matrix, defined in terms of the given distribution, into the product of a tall and a wide nonnegative matrix. The implementation is based on the nonnegative matrix factorization (NMF) algorithm. To evaluate the performance of our algorithm we produced some numerical simulations in the context of HMM order reduction.
The Fracture Mechanical Markov Chain Fatigue Model Compared with Empirical Data
DEFF Research Database (Denmark)
Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard
The applicability of the FMF-model (Fracture Mechanical Markov Chain Fatigue Model) introduced in Gansted, L., R. Brincker and L. Pilegaard Hansen (1991) is tested by simulations and compared with empirical data. Two sets of data have been used, the Virkler data (aluminium alloy) and data...... established at the Laboratory of Structural Engineering at Aalborg University, the AUC-data, (mild steel). The model, which is based on the assumption, that the crack propagation process can be described by a discrete Space Markov theory, is applicable to constant as well as random loading. It is shown that...
Directory of Open Access Journals (Sweden)
Zi Ye
2012-10-01
Full Text Available Measuring particle size distribution through calculating light scattering intensity is a typical inverse problem. This paper builds an inverse mathematical model based on Mie scattering, deduces the inversion formulas for particle size, and calculates the relative coefficients through programming with built-in functions in MATLAB. In order to improve the accuracy and noise immunity of particle size distribution measurement, the development of stochastic inversion algorithm: an inverse problem model based on Markov chain algorithm is proposed. Results of numerical simulation are added acceptable noise indicate that the algorithm of Markov chain has strong noise immunity and can meet the requirements of on-line measurement.
Weighted-indexed semi-Markov models for modeling financial returns
International Nuclear Information System (INIS)
In this paper we propose a new stochastic model based on a generalization of semi-Markov chains for studying the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted-indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series such as the first-passage-time distributions and the persistence of volatility. The model is applied to data from the Italian and German stock markets from 1 January 2007 until the end of December 2010. (paper)
Formal Reasoning About Finite-State Discrete-Time Markov Chains in HOL
Institute of Scientific and Technical Information of China (English)
Liya Liu; Osman Hasan; Sofiène Tahar
2013-01-01
Markov chains are extensively used in modeling different aspects of engineering and scientific systems,such as performance of algorithms and reliability of systems.Different techniques have been developed for analyzing Markovian models,for example,Markov Chain Monte Carlo based simulation,Markov Analyzer,and more recently probabilistic modelchecking.However,these techniques either do not guarantee accurate analysis or are not scalable.Higher-order-logic theorem proving is a formal method that has the ability to overcome the above mentioned limitations.However,it is not mature enough to handle all sorts of Markovian models.In this paper,we propose a formalization of Discrete-Time Markov Chain (DTMC) that facilitates formal reasoning about time-homogeneous finite-state discrete-time Markov chain.In particular,we provide a formal verification on some of its important properties,such as joint probabilities,Chapman-Kolmogorov equation,reversibility property,using higher-order logic.To demonstrate the usefulness of our work,we analyze two applications:a simplified binary communication channel and the Automatic Mail Quality Measurement protocol.
A hidden Markov Model for image fusion and their joint segmentation in medical image computing
Féron, O; Feron, Olivier; Mohammad-Djafari, Ali
2004-01-01
In this work we propose a Bayesian framework for fully automated image fusion and their joint segmentation. More specifically, we consider the case where we have observed images of the same object through different image processes or through different spectral bands. The objective of this work is then to propose a coherent approach to combine these data sets and obtain a segmented image which can be considered as the fusion result of these observations. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently, with common hidden classification label variables which are modeled by the Potts Markov Random Field. We propose an appropriate Markov Chain Monte Carlo (MCMC) algorithm to implement the method and show some simulation results and applications.
A Hidden Markov model for Bayesian data fusion of multivariate signals
Féron, O; Feron, Olivier; Mohammad-Djafari, Ali
2004-01-01
In this work we propose a Bayesian framework for data fusion of multivariate signals which arises in imaging systems. More specifically, we consider the case where we have observed two images of the same object through two different imaging processes. The objective of this work is then to propose a coherent approach to combine these data sets to obtain a segmented image which can be considered as the fusion result of these two images. The proposed approach is based on a Hidden Markov Modeling (HMM) of the images with common segmentation, or equivalently, with common hidden classification label variables which is modeled by the Potts Markov Random Field. We propose then an appropriate Markov Chain Monte Carlo (MCMC) algorithm to implement the method and show some simulation results and applications.
Projected metastable Markov processes and their estimation with observable operator models
International Nuclear Information System (INIS)
The determination of kinetics of high-dimensional dynamical systems, such as macromolecules, polymers, or spin systems, is a difficult and generally unsolved problem — both in simulation, where the optimal reaction coordinate(s) are generally unknown and are difficult to compute, and in experimental measurements, where only specific coordinates are observable. Markov models, or Markov state models, are widely used but suffer from the fact that the dynamics on a coarsely discretized state spaced are no longer Markovian, even if the dynamics in the full phase space are. The recently proposed projected Markov models (PMMs) are a formulation that provides a description of the kinetics on a low-dimensional projection without making the Markovianity assumption. However, as yet no general way of estimating PMMs from data has been available. Here, we show that the observed dynamics of a PMM can be exactly described by an observable operator model (OOM) and derive a PMM estimator based on the OOM learning
LISA data analysis using Markov chain Monte Carlo methods
International Nuclear Information System (INIS)
The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low-frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground based gravitational wave astronomy. LISA data analysis requires the identification of individual signals from a data stream containing an unknown number of overlapping signals. Because of the signal overlaps, a global fit to all the signals has to be performed in order to avoid biasing the solution. However, performing such a global fit requires the exploration of an enormous parameter space with a dimension upwards of 50 000. Markov Chain Monte Carlo (MCMC) methods offer a very promising solution to the LISA data analysis problem. MCMC algorithms are able to efficiently explore large parameter spaces, simultaneously providing parameter estimates, error analysis, and even model selection. Here we present the first application of MCMC methods to simulated LISA data and demonstrate the great potential of the MCMC approach. Our implementation uses a generalized F-statistic to evaluate the likelihoods, and simulated annealing to speed convergence of the Markov chains. As a final step we supercool the chains to extract maximum likelihood estimates, and estimates of the Bayes factors for competing models. We find that the MCMC approach is able to correctly identify the number of signals present, extract the source parameters, and return error estimates consistent with Fisher information matrix predictions
Markov dynamic models for long-timescale protein motion.
Chiang, Tsung-Han
2010-06-01
Molecular dynamics (MD) simulation is a well-established method for studying protein motion at the atomic scale. However, it is computationally intensive and generates massive amounts of data. One way of addressing the dual challenges of computation efficiency and data analysis is to construct simplified models of long-timescale protein motion from MD simulation data. In this direction, we propose to use Markov models with hidden states, in which the Markovian states represent potentially overlapping probabilistic distributions over protein conformations. We also propose a principled criterion for evaluating the quality of a model by its ability to predict long-timescale protein motions. Our method was tested on 2D synthetic energy landscapes and two extensively studied peptides, alanine dipeptide and the villin headpiece subdomain (HP-35 NleNle). One interesting finding is that although a widely accepted model of alanine dipeptide contains six states, a simpler model with only three states is equally good for predicting long-timescale motions. We also used the constructed Markov models to estimate important kinetic and dynamic quantities for protein folding, in particular, mean first-passage time. The results are consistent with available experimental measurements.
On multitarget pairwise-Markov models
Mahler, Ronald
2015-05-01
Single- and multi-target tracking are both typically based on strong independence assumptions regarding both the target states and sensor measurements. In particular, both are theoretically based on the hidden Markov chain (HMC) model. That is, the target process is a Markov chain that is observed by an independent observation process. Since HMC assumptions are invalid in many practical applications, the pairwise Markov chain (PMC) model has been proposed as a way to weaken those assumptions. In this paper it is shown that the PMC model can be directly generalized to multitarget problems. Since the resulting tracking filters are computationally intractable, the paper investigates generalizations of the cardinalized probability hypothesis density (CPHD) filter to applications with PMC models.
Planning in Markov Stochastic Task Domains
Directory of Open Access Journals (Sweden)
Yong Lin
2010-10-01
Full Text Available In decision theoretic planning, a challenge for Markov decision processes (MDPs and partially observable Markov decision processes (POMDPs is, many problem domains contain big state spaces and complex tasks, which will result in poor solution performance. We develop a task analysis and modeling (TAM approach, in which the (POMDP model is separated into a task view and an action view. In the task view, TAM models the problem domain using a task equivalence model, with task-dependent abstract states and observations. We provide a learning algorithm to obtain the parameter values of task equivalence models. We present three typical examples to explain the TAM approach. Experimental results indicate our approach can greatly improve the computational capacity of task planning in Markov stochastic domains.
The ensemble of random Markov matrices
International Nuclear Information System (INIS)
The ensemble of random Markov matrices is introduced as a set of Markov or stochastic matrices with the maximal Shannon entropy. The statistical properties of the stationary distribution π, the average entropy growth rate h and the second-largest eigenvalue ν across the ensemble are studied. It is shown and heuristically proven that the entropy growth rate and second-largest eigenvalue of Markov matrices scale on average with the dimension of the matrices d as h∼log(O(d)) and |ν|∼d−1/2, respectively, yielding the asymptotic relation hτc∼1/2 between the entropy h and the correlation decay time τ = −1/log|ν|. Additionally, the correlation between h and τc is analysed; it decreases with increasing dimension d
Markov decision processes in artificial intelligence
Sigaud, Olivier
2013-01-01
Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision problems under uncertainty as well as Reinforcement Learning problems. Written by experts in the field, this book provides a global view of current research using MDPs in Artificial Intelligence. It starts with an introductory presentation of the fundamental aspects of MDPs (planning in MDPs, Reinforcement Learning, Partially Observable MDPs, Markov games and the use of non-classical criteria). Then it presents more advanced research trends in the domain and gives some concrete examples using illustr
Entropy Computation in Partially Observed Markov Chains
Desbouvries, François
2006-11-01
Let X = {Xn}n∈N be a hidden process and Y = {Yn}n∈N be an observed process. We assume that (X,Y) is a (pairwise) Markov Chain (PMC). PMC are more general than Hidden Markov Chains (HMC) and yet enable the development of efficient parameter estimation and Bayesian restoration algorithms. In this paper we propose a fast (i.e., O(N)) algorithm for computing the entropy of {Xn}n=0N given an observation sequence {yn}n=0N.
On approximation of Markov binomial distributions
Xia, Aihua; Zhang, Mei
2009-01-01
For a Markov chain $\\mathbf{X}=\\{X_i,i=1,2,...,n\\}$ with the state space $\\{0,1\\}$, the random variable $S:=\\sum_{i=1}^nX_i$ is said to follow a Markov binomial distribution. The exact distribution of $S$, denoted $\\mathcal{L}S$, is very computationally intensive for large $n$ (see Gabriel [Biometrika 46 (1959) 454--460] and Bhat and Lal [Adv. in Appl. Probab. 20 (1988) 677--680]) and this paper concerns suitable approximate distributions for $\\mathcal{L}S$ when $\\mathbf{X}$ is stationary. We...
Markov Model Applied to Gene Evolution
Institute of Scientific and Technical Information of China (English)
季星来; 孙之荣
2001-01-01
The study of nucleotide substitution is very important both to our understanding of gene evolution and to reliable estimation of phylogenetic relationships. In this paper nucleotide substitution is assumed to be random and the Markov model is applied to the study of the evolution of genes. Then a non-linear optimization approach is proposed for estimating substitution in real sequences. This substitution is called the "Nucleotide State Transfer Matrix". One of the most important conclusions from this work is that gene sequence evolution conforms to the Markov process. Also, some theoretical evidences for random evolution are given from energy analysis of DNA replication.
Illumination Invariants Based on Markov Random Fields
Czech Academy of Sciences Publication Activity Database
Vácha, Pavel; Haindl, Michal
Vukovar, Croatia : In-Teh, 2010 - (Herout, A.), s. 253-272 ISBN 978-953-7619-90-9 R&D Projects: GA MŠk 1M0572; GA ČR GA102/08/0593 Grant ostatní: GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10750506 Keywords : illumination invariants * textural features * Markov random fields Subject RIV: BD - Theory of Information http://library.utia.cas.cz/separaty/2010/RO/vacha-illumination invariants based on markov random fields.pdf
Inhomogeneous Markov Models for Describing Driving Patterns
DEFF Research Database (Denmark)
Iversen, Jan Emil Banning; Møller, Jan Kloppenborg; Morales González, Juan Miguel; Madsen, Henrik
. Specically, an inhomogeneous Markov model that captures the diurnal variation in the use of a vehicle is presented. The model is dened by the time-varying probabilities of starting and ending a trip and is justied due to the uncertainty associated with the use of the vehicle. The model is tted to data...... collected from the actual utilization of a vehicle. Inhomogeneous Markov models imply a large number of parameters. The number of parameters in the proposed model is reduced using B-splines....
Noé, Frank; Wu, Hao; Prinz, Jan-Hendrik; Plattner, Nuria
2013-11-01
Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dynamics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has, therefore, been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase-space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecular observables of interest that are often computed from MSMs can be computed from HMMs/PMMs. The new framework is applicable to both, simulation and single-molecule experimental data. We demonstrate its versatility by applications to educative model systems, a 1 ms Anton MD simulation of the bovine pancreatic trypsin inhibitor protein, and an optical tweezer force probe trajectory of an RNA hairpin.
BEBERAPA SIFAT HASIL KALI KRONECKER RANTAI MARKOV BERDIMENSI HINGGA
Jaya, Andi Kresna
2014-01-01
Pada paper ini akan dibahas tentang Rantai Markov yang diperoleh dari perkalian kronecker dua Rantai Markov berdimensi hingga. Pembahasan akan diawali dengan beberapa definisi Rantai Markov dengan Matriks Peluang transisinya dan diagram transisi antar keadaannya. Demikian pula dengan hasil kali kroneckernya, akan diperlihatkan bagaimana Ruang keadaan, Matriks peluang transisi dan diagram transisi antar keadaannya. Hasil utama pembahasannya adalah beberapa sifat Rantai Markov hasil perkalian k...
Markov Chain Approximations to Singular Stable-like Processes
Xu, Fangjun
2012-01-01
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these chains to singular stable-like processes.
Indian Academy of Sciences (India)
Long Zhang; Guoliang Xiong; Hesheng Liu; Huijun Zou; Weizhong Guo
2010-04-01
A parametric time-frequency representation is presented based on timevarying autoregressive model (TVAR), followed by applications to non-stationary vibration signal processing. The identiﬁcation of time-varying model coefﬁcients and the determination of model order, are addressed by means of neural networks and genetic algorithms, respectively. Firstly, a simulated signal which mimic the rotor vibration during run-up stages was processed for a comparative study on TVAR and other non-parametric time-frequency representations such as Short Time Fourier Transform, Continuous Wavelet Transform, Empirical Mode Decomposition, Wigner–Ville Distribution and Choi–Williams Distribution, in terms of their resolutions, accuracy, cross term suppression as well as noise resistance. Secondly, TVAR was applied to analyse non-stationary vibration signals collected from a rotor test rig during run-up stages, with an aim to extract fault symptoms under non-stationary operating conditions. Simulation and experimental results demonstrate that TVAR is an effective solution to non-stationary signal analysis and has strong capability in signal time-frequency feature extraction.
Using Markov State Models to Study Self-Assembly
Perkett, Matthew R
2014-01-01
Markov state models (MSMs) have been demonstrated to be a powerful method for computationally studying intramolecular processes such as protein folding and macromolecular conformational changes. In this article, we present a new approach to construct MSMs that is applicable to modeling a broad class of multi-molecular assembly reactions. Distinct structures formed during assembly are distinguished by their undirected graphs, which are defined by strong subunit interactions. Spatial inhomogeneities of free subunits are accounted for using a recently developed Gaussian-based signature. Simplifications to this state identification are also investigated. The feasibility of this approach is demonstrated on two different coarse-grained models for virus self-assembly. We find good agreement between the dynamics predicted by the MSMs and long, unbiased simulations, and that the MSMs can reduce overall simulation time by orders of magnitude.
Markov chains with quasitoeplitz transition matrix
Directory of Open Access Journals (Sweden)
Alexander M. Dukhovny
1989-01-01
Full Text Available This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems, dams and inventories with feedback. Generating functions of transient and steady state probabilities are found by solving a special Riemann boundary value problem on the unit circle. A criterion of ergodicity is established.
Markov Chains with Stochastically Stationary Transition Probabilities
Orey, Steven
1991-01-01
Markov chains on a countable state space are studied under the assumption that the transition probabilities $(P_n(x,y))$ constitute a stationary stochastic process. An introductory section exposing some basic results of Nawrotzki and Cogburn is followed by four sections of new results.
Continuity Properties of Distances for Markov Processes
DEFF Research Database (Denmark)
Jaeger, Manfred; Mao, Hua; Larsen, Kim Guldstrand;
2014-01-01
In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and trace-based distances derived from standard Lp and Kullback-Leibler distances. Two desirable...
Pruning Boltzmann networks and hidden Markov models
DEFF Research Database (Denmark)
Pedersen, Morten With; Stork, D.
1996-01-01
Boltzmann chains and hidden Markov models (HMMs), we argue that our method can be applied to HMMs as well. We illustrate pruning on Boltzmann zippers, which are equivalent to two HMMs with cross-connection links. We verify that our second-order approximation preserves the rank ordering of weight saliencies...
Piecewise deterministic Markov processes : an analytic approach
Alkurdi, Taleb Salameh Odeh
2013-01-01
The subject of this thesis, piecewise deterministic Markov processes, an analytic approach, is on the border between analysis and probability theory. Such processes can either be viewed as random perturbations of deterministic dynamical systems in an impulsive fashion, or as a particular kind of sto
Metric on state space of Markov chain
Rozinas, M. R.
2010-01-01
We consider finite irreducible Markov chains. It was shown that mean hitting time from one state to another satisfies the triangle inequality. Hence, sum of mean hitting time between couple of states in both directions is a metric on the space of states.
Markov Random Fields on Triangle Meshes
DEFF Research Database (Denmark)
Andersen, Vedrana; Aanæs, Henrik; Bærentzen, Jakob Andreas;
2010-01-01
In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process labels...
Document Ranking Based upon Markov Chains.
Danilowicz, Czeslaw; Balinski, Jaroslaw
2001-01-01
Considers how the order of documents in information retrieval responses are determined and introduces a method that uses a probabilistic model of a document set where documents are regarded as states of a Markov chain and where transition probabilities are directly proportional to similarities between documents. (Author/LRW)
Asymptotic properties of quantum Markov chains
International Nuclear Information System (INIS)
The asymptotic dynamics of discrete quantum Markov chains generated by the most general physically relevant quantum operations is investigated. It is shown that it is confined to an attractor space in which the resulting quantum Markov chain is diagonalizable. A construction procedure of a basis of this attractor space and its associated dual basis of 1-forms is presented. It is applicable whenever a strictly positive quantum state exists which is contracted or left invariant by the generating quantum operation. Moreover, algebraic relations between the attractor space and Kraus operators involved in the definition of a quantum Markov chain are derived. This construction is not only expected to offer significant computational advantages in cases in which the dimension of the Hilbert space is large and the dimension of the attractor space is small, but it also sheds new light onto the relation between the asymptotic dynamics of discrete quantum Markov chains and fixed points of their generating quantum operations. Finally, we show that without any restriction our construction applies to all initial states whose support belongs to the so-called recurrent subspace. (paper)
Markov Chain Estimation of Avian Seasonal Fecundity
To explore the consequences of modeling decisions on inference about avian seasonal fecundity we generalize previous Markov chain (MC) models of avian nest success to formulate two different MC models of avian seasonal fecundity that represent two different ways to model renestin...
A Martingale Decomposition of Discrete Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard
We consider a multivariate time series whose increments are given from a homogeneous Markov chain. We show that the martingale component of this process can be extracted by a filtering method and establish the corresponding martingale decomposition in closed-form. This representation is useful for...
Manipulation and the causal Markov condition
Hausman, Daniel; Woodward, James
2004-01-01
This paper explores the relationship between a manipulability conception of causation and the causal Markov condition (CM). We argue that violations of CM also violate widely shared expectations—implicit in the manipulability conception—having to do with the absence of spontaneous correlations. They also violate expectations concerning the connection between independence or dependence relationships in the presence and absence of interventions.
Denumerable Markov decision chains: sensitive optimality criteria
A. Hordijk (Arie); R. Dekker (Rommert)
1991-01-01
textabstractIn this paper we investigate denumerable state semi-Markov decision chains with small interest rates. We consider average and Blackwell optimality and allow for multiple closed sets and unbounded immediate rewards. Our analysis uses the existence of a Laurent series expansion for the tot
Optimal dividend distribution under Markov regime switching
Z. Jiang; M. Pistorius
2012-01-01
We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a determini
Markov bridges, bisection and variance reduction
DEFF Research Database (Denmark)
Asmussen, Søren; Hobolth, Asger
this paper we firstly consider the problem of generating sample paths from a continuous-time Markov chain conditioned on the endpoints using a new algorithm based on the idea of bisection. Secondly we study the potential of the bisection algorithm for variance reduction. In particular, examples are...
Local stability in a transient Markov chain
Adan, Ivo; Foss, Sergey; Shneer, Seva; Weiss, Gideon
2015-01-01
We prove two lemmas with conditions that a system, which is described by a transient Markov chain, will display local stability. Examples of such systems include partly overloaded Jackson networks, partly overloaded polling systems, and overloaded multi-server queues with skill based service, under first come first served policy.
Bayesian analysis of Markov point processes
DEFF Research Database (Denmark)
Berthelsen, Kasper Klitgaard; Møller, Jesper
2006-01-01
Recently Møller, Pettitt, Berthelsen and Reeves introduced a new MCMC methodology for drawing samples from a posterior distribution when the likelihood function is only specified up to a normalising constant. We illustrate the method in the setting of Bayesian inference for Markov point processes...
A Metrized Duality Theorem for Markov Processes
DEFF Research Database (Denmark)
Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash
2014-01-01
We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...
Generalizing Markov Decision Processes to Imprecise Probabilities
Czech Academy of Sciences Publication Activity Database
Harmanec, David
2002-01-01
Roč. 105, - (2002), s. 199-213. ISSN 0378-3758 Grant ostatní: Ministry of Education(SG) RP960351 Institutional research plan: AV0Z1030915 Keywords : generalized Markov decission process * sequential decision making * interval utilities Subject RIV: BA - General Mathematics Impact factor: 0.385, year: 2002
One-Counter Markov Decision Processes
Brazdil, T.; Brozek, V.; Etessami, K.; Kucera, A.; Wojtczak, D.K.; Charikar, M.
2010-01-01
We study the computational complexity of central analysis problems for One-Counter Markov Decision Processes (OC-MDPs), a class of finitely-presented, countable-state MDPs. OC-MDPs are equivalent to a controlled extension of (discrete-time) Quasi-Birth-Death processes (QBDs), a stochastic model stud
Hidden Markov Models for Human Genes
DEFF Research Database (Denmark)
Baldi, Pierre; Brunak, Søren; Chauvin, Yves; Krogh, Anders Stærmose
We analyse the sequential structure of human genomic DNA by hidden Markov models. We apply models of widely different design: conventional left-right constructs and models with a built-in periodic architecture. The models are trained on segments of DNA sequences extracted such that they cover...
Semi-Markov Unreliability Range Evaluator (SURE)
Butler, R. W.
1989-01-01
Analysis tool for reconfigurable, fault-tolerant systems, SURE provides efficient way to calculate accurate upper and lower bounds for death state probabilities for large class of semi-Markov models. Calculated bounds close enough for use in reliability studies of ultrareliable computer systems. Written in PASCAL for interactive execution and runs on DEC VAX computer under VMS.
Hidden Markov models for labeled sequences
DEFF Research Database (Denmark)
Krogh, Anders Stærmose
A hidden Markov model for labeled observations, called a class HMM, is introduced and a maximum likelihood method is developed for estimating the parameters of the model. Instead of training it to model the statistics of the training sequences it is trained to optimize recognition. It resembles MMI...
Evaluation of Usability Utilizing Markov Models
Penedo, Janaina Rodrigues; Diniz, Morganna; Ferreira, Simone Bacellar Leal; Silveira, Denis S.; Capra, Eliane
2012-01-01
Purpose: The purpose of this paper is to analyze the usability of a remote learning system in its initial development phase, using a quantitative usability evaluation method through Markov models. Design/methodology/approach: The paper opted for an exploratory study. The data of interest of the research correspond to the possible accesses of users…
Proses Keputusan Markov Dengan Metode Pengiterasian Kebijakan
Syafitri, Rizky
2011-01-01
Pengambilan keputusan memerlukan beberapa pertimbangan analisis sehingga keputusan yang diambil dapat memuaskan dan optimal. Tulisan ini menguraikan salah satu metode pengambilan keputusan yaitu metode pengiterasian kebijakan (policy iteration) sebagai metode proses keputusan Markov berdasarkan pada model-model stokastik. Metode pengiterasian kebijakan merupakan suatu metode yang menggunakan pendekatan iterasi yang dimulai dari kebijakan mana saja, dan pada akhirnya akan men...
First Passage Probability Estimation of Wind Turbines by Markov Chain Monte Carlo
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.
2013-01-01
Markov Chain Monte Carlo simulation has received considerable attention within the past decade as reportedly one of the most powerful techniques for the first passage probability estimation of dynamic systems. A very popular method in this direction capable of estimating probability of rare event...... rotor equal to its nominal value. Finally Monte Carlo simulations are performed which allow assessment of the accuracy of the first passage probability estimation by the SS methods....
Batch means and spectral variance estimators in Markov chain Monte Carlo
Flegal, James M.; Jones, Galin L.
2008-01-01
Calculating a Monte Carlo standard error (MCSE) is an important step in the statistical analysis of the simulation output obtained from a Markov chain Monte Carlo experiment. An MCSE is usually based on an estimate of the variance of the asymptotic normal distribution. We consider spectral and batch means methods for estimating this variance. In particular, we establish conditions which guarantee that these estimators are strongly consistent as the simulation effort increases. In addition, fo...
Application of Hidden Markov Models and Hidden Semi-Markov Models to Financial Time Series
Bulla, Jan
2006-01-01
Hidden Markov Models (HMMs) and Hidden Semi-Markov Models (HSMMs) provide flexible, general-purpose models for univariate and multivariate time series. Although interest in HMMs and HSMMs has continuously increased during the past years, and numerous articles on theoretical and practical aspects have been published, several gaps remain. This thesis addresses some of them, divided into three main topics. 1. Computational issues in parameter estimation of stationary HMMs. The parameters of ...
Directory of Open Access Journals (Sweden)
Luis Gonzaga Baca Ruiz
2016-08-01
Full Text Available This paper addresses the problem of energy consumption prediction using neural networks over a set of public buildings. Since energy consumption in the public sector comprises a substantial share of overall consumption, the prediction of such consumption represents a decisive issue in the achievement of energy savings. In our experiments, we use the data provided by an energy consumption monitoring system in a compound of faculties and research centers at the University of Granada, and provide a methodology to predict future energy consumption using nonlinear autoregressive (NAR and the nonlinear autoregressive neural network with exogenous inputs (NARX, respectively. Results reveal that NAR and NARX neural networks are both suitable for performing energy consumption prediction, but also that exogenous data may help to improve the accuracy of predictions.
Institute of Scientific and Technical Information of China (English)
TIAN Lin-ya; HUA Xi-sheng
2007-01-01
To ensure the safety of buildings surrounding foundation pits, a study was made on a settlement monitoring and trend prediction method. A statistical testing method for analyzing the stability of a settlement monitoring datum has been discussed. According to a comprehensive survey, data of 16 stages at operating control point, were verified by a standard t test to determine the stability of the operating control point. A stationary auto-regression model, AR(p), used for the observation point settlement prediction has been investigated. Given the 16 stages of the settlement data at an observation point, the applicability of this model was analyzed. Settlement of last four stages was predicted using the stationary auto-regression model AR (1); the maximum difference between predicted and measured values was 0.6 mm,indicating good prediction results of the model. Hence, this model can be applied to settlement predictions for buildings surrounding foundation pits.
Medium- and Long-term Prediction of LOD Change by the Leap-step Autoregressive Model
Wang, Qijie
2015-08-01
The accuracy of medium- and long-term prediction of length of day (LOD) change base on combined least-square and autoregressive (LS+AR) deteriorates gradually. Leap-step autoregressive (LSAR) model can significantly reduce the edge effect of the observation sequence. Especially, LSAR model greatly improves the resolution of signals’ low-frequency components. Therefore, it can improve the efficiency of prediction. In this work, LSAR is used to forecast the LOD change. The LOD series from EOP 08 C04 provided by IERS is modeled by both the LSAR and AR models. The results of the two models are analyzed and compared. When the prediction length is between 10-30 days, the accuracy improvement is less than 10%. When the prediction length amounts to above 30 day, the accuracy improved obviously, with the maximum being around 19%. The results show that the LSAR model has higher prediction accuracy and stability in medium- and long-term prediction.
Medium- and Long-term Prediction of LOD Change with the Leap-step Autoregressive Model
Liu, Q. B.; Wang, Q. J.; Lei, M. F.
2015-09-01
It is known that the accuracies of medium- and long-term prediction of changes of length of day (LOD) based on the combined least-square and autoregressive (LS+AR) decrease gradually. The leap-step autoregressive (LSAR) model is more accurate and stable in medium- and long-term prediction, therefore it is used to forecast the LOD changes in this work. Then the LOD series from EOP 08 C04 provided by IERS (International Earth Rotation and Reference Systems Service) is used to compare the effectiveness of the LSAR and traditional AR methods. The predicted series resulted from the two models show that the prediction accuracy with the LSAR model is better than that from AR model in medium- and long-term prediction.
Probing turbulence intermittency via Auto-Regressive Moving-Average models
Faranda, Davide; Dubrulle, Berengere; Daviaud, Francois
2014-01-01
We suggest a new approach to probing intermittency corrections to the Kolmogorov law in turbulent flows based on the Auto-Regressive Moving-Average modeling of turbulent time series. We introduce a new index $\\Upsilon$ that measures the distance from a Kolmogorov-Obukhov model in the Auto-Regressive Moving-Average models space. Applying our analysis to Particle Image Velocimetry and Laser Doppler Velocimetry measurements in a von K\\'arm\\'an swirling flow, we show that $\\Upsilon$ is proportional to the traditional intermittency correction computed from the structure function. Therefore it provides the same information, using much shorter time series. We conclude that $\\Upsilon$ is a suitable index to reconstruct the spatial intermittency of the dissipation in both numerical and experimental turbulent fields.
Stefan Mittnik; Thorsten Neumann
2001-01-01
We analyze the dynamic relationship between public investment and output. Whereas existing empirical studies on the effects of public capital typically rely on single-equation models of the private sector, we investigate the role of public investment in an economy by examining impulse responses derived from vector autoregressions. Using data from six industrial countries, we specifically examine the following questions: does higher public investment lead to GDP increases; is there reverse cau...
Time-varying parameter auto-regressive models for autocovariance nonstationary time series
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, autocovariance nonstationary time series is clearly defined on a family of time series. We propose three types of TVPAR (time-varying parameter auto-regressive) models: the full order TVPAR model, the time-unvarying order TVPAR model and the time-varying order TV-PAR model for autocovariance nonstationary time series. Related minimum AIC (Akaike information criterion) estimations are carried out.
Time-varying parameter auto-regressive models for autocovariance nonstationary time series
Institute of Scientific and Technical Information of China (English)
FEI WanChun; BAI Lun
2009-01-01
In this paper,autocovariance nonstationary time series is clearly defined on a family of time series.We propose three types of TVPAR (time-varying parameter auto-regressive) models:the full order TVPAR model,the time-unvarying order TVPAR model and the time-varying order TVPAR model for autocovariance nonstationary time series.Related minimum AIC (Akaike information criterion) estimations are carried out.
Directory of Open Access Journals (Sweden)
A. R. Soltani
2006-05-01
Full Text Available Periodically correlated autoregressive nonstationary processes of finite order are considered. The corresponding Yule-Walker equations are applied to derive the generating functions of the covariance functions, what are called here the periodic covariance generating functions. We also provide closed formulas for the spectral densities by using the periodic covariance generating functions, which is a new technique in the spectral theory of periodically correlated processes.
Testing for rational bubbles in a co-explosive vector autoregression
DEFF Research Database (Denmark)
Engsted, Tom; Nielsen, Bent
We derive the parameter restrictions that a standard equity market model implies for a bivariate vector autoregression for stock prices and dividends, and we show how to test these restrictions using likelihood ratio tests. The restrictions, which imply that stock returns are unpredictable, are d...... analysed using a co-explosive framework. The methodology is illustrated using US stock prices and dividends for the period 1872-2000....
A graphical vector autoregressive modelling approach to the analysis of electronic diary data
Zipfel Stephan; Hartmann Mechthild; Friederich Hans-Christoph; Eichler Michael; Wild Beate; Herzog Wolfgang
2010-01-01
Abstract Background In recent years, electronic diaries are increasingly used in medical research and practice to investigate patients' processes and fluctuations in symptoms over time. To model dynamic dependence structures and feedback mechanisms between symptom-relevant variables, a multivariate time series method has to be applied. Methods We propose to analyse the temporal interrelationships among the variables by a structural modelling approach based on graphical vector autoregressive (...
Testing second order dynamics for autoregressive processes in presence of time-varying variance
Patilea, Valentin; Raïssi, Hamdi
2012-01-01
The volatility modeling for autoregressive univariate time series is considered. A benchmark approach is the stationary ARCH model of Engle (1982). Motivated by real data evidence, processes with non constant unconditional variance and ARCH effects have been recently introduced. We take into account such possible non stationarity and propose simple testing procedures for ARCH effects. Adaptive McLeod and Li's portmanteau and ARCH-LM tests for checking for second order dynamics are provided. T...
Two-dimensional minimum free energy autoregressive parametric modelling and spectral estimation
Kiernan, P.
1995-01-01
We present a new high resolution spectral estimation method. This method is a 2-D extension of the Minimum Free Energy (MFE) parameter estimation technique based on extension of the multidimensional Levinson method Our 2-D MFE technique determines autoregressive (AR) models for 2-D fields MFE-AR models may be used for 2-D spectral estimation. The performance of the technique for spectral estimation of closely spaced 2-D sinusoids in white noise is demonstrated by numerical example. Experi...
Helen Higgs; Andrew C. Worthington
2014-01-01
This paper models the price and income elasticity of retail finance in Australia using aggregate quarterly data and an autoregressive distributed lag (ARDL) approach. We particularly focus on the impact of the global financial crisis (GFC) from 2007 onwards on retail finance demand and analyse four submarkets (period analysed in brackets): owneroccupied housing loans (Sep 1985–June 2010), term loans (for motor vehicles, household goods and debt consolidation, etc.) (Dec 1988–Jun 2010), cre...
Eleftherios Giovanis
2014-01-01
The current study examines the turn of the month effect on stock returns in 20 countries. This will allow us to explore whether the seasonal patterns usually found in global data; America, Australia, Europe and Asia. Ordinary Least Squares (OLS) is problematic as it leads to unreliable estimations; because of the autocorrelation and Autoregressive Conditional Heteroskedasticity (ARCH) effects existence. For this reason Generalized GARCH models are estimated. Two approaches are followed. The f...
Chao, John C.; Phillips, Peter C.B.
1997-01-01
The current practice for determining the number of cointegrating vectors, or the cointegrating rank, in a vector autoregression (VAR) requires the investigator to perform a sequence of cointegration tests. However, as was shown in Johansen (1992), this type of sequential procedure does not lead to consistent estimation of the cointegrating rank. Moreover, these methods take as given the correct specification of the lag order of the VAR, though in actual applications the true lag length is rar...
Multivariate Portmanteau test for Autoregressive models with uncorrelated but nonindependent errors
Francq, Christian; Raïssi, Hamdi
2007-01-01
In this paper we consider estimation and test of fit for multiple autoregressive time series models with nonindependent innovations. We derive the asymptotic distribution of the residual autocorrelations. It is shown that this asymptotic distribution can be quite different for models with iid innovations and models in which the innovations exhibit conditional heteroscedasticity or other forms of dependence. Consequently, the usual chi-square distribution does not provide adequate approximatio...
A vector autoregression (VAR) model of housing starts and housing price in Hong Kong
Wong, Kin-man; 黃健文
2012-01-01
It is observed that there are many different models about housing price. Yet, this is relatively smaller number of studies about housing starts. This thesis is an empirical study to work out the relationship between housing starts, housing price and other economic and policy instrumental factors. To achieve this objective, a Vector Autoregression (VAR) model is built since there is inter-relationship between housing starts and housing price. By applying previous models filled with the res...
Efficient Market Hypothesis in South Africa: Evidence from a threshold autoregressive (TAR) model
Van Heerden, Dorathea; Rodrigues, Jose; Hockly, Dale; Lambert, Bongani; Taljard, Tjaart; Phiri, Andrew
2013-01-01
This study deviates from the conventional use of a linear approach in testing for the efficiency market hypothesis (EMH) for the Johannesburg Stock Exchange (JSE) between the periods 2001:01 to 2013:07. By making use of a threshold autoregressive (TAR) model and corresponding asymmetric unit root tests, our study demonstrates how the stock market indexes evolve as highly persistent, nonlinear process and yet for a majority of the time series under observation, the formal unit root tests rejec...
Determinants of Target Dividend Payout Ratio: A Panel Autoregressive Distributed Lag Analysis
Kartal Demirgüneþ
2015-01-01
The aim of this study is to find out the determinants of target dividend payout ratio (TDPR) of BIST - listed firms operating in the non-metallic products (cement) manufacturing industry in the period of 2002-2012. Through this aim, the short and long-run effects of factors related to profitability, liquidity, growth, risk, market expectations and taxation on TDPR is analyzed via panel autoregressive distributed lag analysis methodology. Empirical findings indicate that in the long-run, facto...
Autoregressive Prediction with Rolling Mechanism for Time Series Forecasting with Small Sample Size
Zhihua Wang; Yongbo Zhang; Huimin Fu
2014-01-01
Reasonable prediction makes significant practical sense to stochastic and unstable time series analysis with small or limited sample size. Motivated by the rolling idea in grey theory and the practical relevance of very short-term forecasting or 1-step-ahead prediction, a novel autoregressive (AR) prediction approach with rolling mechanism is proposed. In the modeling procedure, a new developed AR equation, which can be used to model nonstationary time series, is constructed in each predictio...
VECTOR AUTOREGRESSION EVIDENCE ON MONETARISM: A FOCUS ON SOME DEVELOPING ECONOMIES IN SOUTH ASIA
MUDABBER AHMED; U. L. G. RAO
2006-01-01
The objective of this paper is to test the validity of two views of monetarism in Bangladesh, India, and Pakistan. A Structural Vector Autoregressive (SVAR) model is developed and the objective is accomplished by conducting Granger causality tests and estimating variance decompositions and impulse response functions. The first view of monetarism that changes in the quantity of money cause, lead and are positively related to changes in prices at least in the medium to long time horizon is supp...
Entropy rate of continuous-state hidden Markov chains
Han, G; Marcus, B
2010-01-01
We prove that under mild positivity assumptions, the entropy rate of a continuous-state hidden Markov chain, observed when passing a finite-state Markov chain through a discrete-time continuous-output channel, is analytic as a function of the transition probabilities of the underlying Markov chain. We further prove that the entropy rate of a continuous-state hidden Markov chain, observed when passing a mixing finite-type constrained Markov chain through a discrete-time Gaussian channel, is sm...
Grey-Markov Model for Road Accidents Forecasting
Institute of Scientific and Technical Information of China (English)
李相勇; 严余松; 蒋葛夫
2003-01-01
In order to improve the forecasting precision of road accidents, by introducing Markov chains forecasting method, a grey-Markov model for forecasting road accidents is established based on grey forecasting method. The model combines the advantages of both grey forecasting method and Markov chains forecasting method, overcomes the influence of random fluctuation data on forecasting precision and widens the application scope of the grey forecasting. An application example is conducted to evaluate the grey-Markov model, which shows that the precision of the grey-Markov model is better than that of grey model in forecasting road accidents.
Study of Simplification of Markov Model for Analyzing System Dependability
Energy Technology Data Exchange (ETDEWEB)
Son, Gwang Seop; Kim, Dong Hoon; Choi, Jong Gyun [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2015-05-15
In this paper, we introduce the simplification methodology of the Markov model for analyzing system dependability using system failure rate concept. This system failure rate is the probability that the system is failed or unavailable given that the system was as good as at this time. Using this parameter, the Markov model of sub system can be replaced to the system failure rate and then this parameter just is considered in the Markov model of whole system. In this paper, we proposed the method to simplify the Markov model in complex system architecture. We define the system failure rate and using this parameter, the Markov model of system could be simplified.
On the Markov-Dyck shifts of vertex type
Matsumoto, Kengo
2014-01-01
For a given finite directed graph $G$, there are two types of Markov-Dyck shifts, the Markov-Dyck shift $D_G^V$ of vertex type and the Markov-Dyck shift $D_G^E$ of edge type. It is shown that, if $G$ does not have multi-edges, the former is a finite-to-one factor of the latter, and they have the same topological entropy. An expression for the zeta function of a Markov-Dyck shift of vertex type is given. It is different from that of the Markov-Dyck shift of edge type.
Study of Simplification of Markov Model for Analyzing System Dependability
International Nuclear Information System (INIS)
In this paper, we introduce the simplification methodology of the Markov model for analyzing system dependability using system failure rate concept. This system failure rate is the probability that the system is failed or unavailable given that the system was as good as at this time. Using this parameter, the Markov model of sub system can be replaced to the system failure rate and then this parameter just is considered in the Markov model of whole system. In this paper, we proposed the method to simplify the Markov model in complex system architecture. We define the system failure rate and using this parameter, the Markov model of system could be simplified
Dueker, Michael J.; Apostolos Serletis
2000-01-01
In this paper, we estimate (by maximum likelihood) the parameters of univariate fractionally integrated real exchange rate time series models, and test for autoregressive unit roots on the alternative of a covariance stationary long-memory process. We use quarterly dollar-based real exchange rates (since 1957) for seventeen OECD countries, and that the finding of unit autoregressive roots does not go away even with this more sophisticated alternative.
Holan, S.H.; Davis, G.M.; Wildhaber, M.L.; DeLonay, A.J.; Papoulias, D.M.
2009-01-01
The timing of spawning in fish is tightly linked to environmental factors; however, these factors are not very well understood for many species. Specifically, little information is available to guide recruitment efforts for endangered species such as the sturgeon. Therefore, we propose a Bayesian hierarchical model for predicting the success of spawning of the shovelnose sturgeon which uses both biological and behavioural (longitudinal) data. In particular, we use data that were produced from a tracking study that was conducted in the Lower Missouri River. The data that were produced from this study consist of biological variables associated with readiness to spawn along with longitudinal behavioural data collected by using telemetry and archival data storage tags. These high frequency data are complex both biologically and in the underlying behavioural process. To accommodate such complexity we developed a hierarchical linear regression model that uses an eigenvalue predictor, derived from the transition probability matrix of a two-state Markov switching model with generalized auto-regressive conditional heteroscedastic dynamics. Finally, to minimize the computational burden that is associated with estimation of this model, a parallel computing approach is proposed. ?? Journal compilation 2009 Royal Statistical Society.
Bayesian inference for Markov jump processes with informative observations.
Golightly, Andrew; Wilkinson, Darren J
2015-04-01
In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is straightforward, Bayesian inference typically proceeds through computationally intensive methods such as (particle) MCMC. Such methods ostensibly require the ability to simulate trajectories from the conditioned jump process. When observations are highly informative, use of the forward simulator is likely to be inefficient and may even preclude an exact (simulation based) analysis. We therefore propose three methods for improving the efficiency of simulating conditioned jump processes. A conditioned hazard is derived based on an approximation to the jump process, and used to generate end-point conditioned trajectories for use inside an importance sampling algorithm. We also adapt a recently proposed sequential Monte Carlo scheme to our problem. Essentially, trajectories are reweighted at a set of intermediate time points, with more weight assigned to trajectories that are consistent with the next observation. We consider two implementations of this approach, based on two continuous approximations of the MJP. We compare these constructs for a simple tractable jump process before using them to perform inference for a Lotka-Volterra system. The best performing construct is used to infer the parameters governing a simple model of motility regulation in Bacillus subtilis. PMID:25720091
MARKOV CHAIN PORTFOLIO LIQUIDITY OPTIMIZATION MODEL
Directory of Open Access Journals (Sweden)
Eder Oliveira Abensur
2014-05-01
Full Text Available The international financial crisis of September 2008 and May 2010 showed the importance of liquidity as an attribute to be considered in portfolio decisions. This study proposes an optimization model based on available public data, using Markov chain and Genetic Algorithms concepts as it considers the classic duality of risk versus return and incorporating liquidity costs. The work intends to propose a multi-criterion non-linear optimization model using liquidity based on a Markov chain. The non-linear model was tested using Genetic Algorithms with twenty five Brazilian stocks from 2007 to 2009. The results suggest that this is an innovative development methodology and useful for developing an efficient and realistic financial portfolio, as it considers many attributes such as risk, return and liquidity.
On approximation of Markov binomial distributions
Xia, Aihua; 10.3150/09-BEJ194
2010-01-01
For a Markov chain $\\mathbf{X}=\\{X_i,i=1,2,...,n\\}$ with the state space $\\{0,1\\}$, the random variable $S:=\\sum_{i=1}^nX_i$ is said to follow a Markov binomial distribution. The exact distribution of $S$, denoted $\\mathcal{L}S$, is very computationally intensive for large $n$ (see Gabriel [Biometrika 46 (1959) 454--460] and Bhat and Lal [Adv. in Appl. Probab. 20 (1988) 677--680]) and this paper concerns suitable approximate distributions for $\\mathcal{L}S$ when $\\mathbf{X}$ is stationary. We conclude that the negative binomial and binomial distributions are appropriate approximations for $\\mathcal{L}S$ when $\\operatorname {Var}S$ is greater than and less than $\\mathbb{E}S$, respectively. Also, due to the unique structure of the distribution, we are able to derive explicit error estimates for these approximations.
Markov Processes: Linguistics and Zipf's Law
Kanter, I.; Kessler, D. A.
1995-05-01
It is shown that a 2-parameter random Markov process constructed with N states and biased random transitions gives rise to a stationary distribution where the probabilities of occurrence of the states, P\\(k\\), k = 1,...,N, exhibit the following three universal behaviors which characterize biological sequences and texts in natural languages: (a) the rank-ordered frequencies of occurrence of words are given by Zipf's law P\\(k\\)~1/kρ, where ρ\\(k\\) is slowly increasing for small k; (b) the frequencies of occurrence of letters are given by P\\(k\\) = A-Dln\\(k\\); and (c) long-range correlations are observed over long but finite intervals, as a result of the quasiergodicity of the Markov process.
On Markov properties in evidence theory
Czech Academy of Sciences Publication Activity Database
Vejnarová, Jiřina
Ostrava : Universitatis Ostraviensis, 2009 - (Novák, V.; Pavliska, V.; Štěpnička, M.), s. 131-142 [Czech-Japan Seminar on Data Analysis and Decision-Making under Uncertainty /12./. Litomyšl (CZ), 24.09.2009-27.09.2009] R&D Projects: GA AV ČR IAA100750603; GA ČR GA201/08/0539 Grant ostatní: GA MŠk(CZ) 2C06019 Institutional research plan: CEZ:AV0Z10750506 Keywords : Evidence theory * Markov properties * conditional independence Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2009/MTR/vejnarova-on markov properties in evidence theory .pdf
Boundary value problems and Markov processes
Taira, Kazuaki
2009-01-01
This volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called a Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel' boundary condition, on the boundary of the domain. Probabilistically, a Markovian particle moves both by jumps and continuously in the state space and it obeys the Ventcel' boundary condition, which consists of six terms corresponding to the diffusion along the boundary, the absorption phenomenon, the reflection phenomenon, the sticking (or viscosity) phenomenon, the jump phenomenon on the boundary, and the inward jump phenomenon from the boundary. In particular, second-order elliptic differential operators are called diffusion operators and describe analytically strong Markov pr...
Semigroups, boundary value problems and Markov processes
Taira, Kazuaki
2014-01-01
A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes ...
Sistem Bonus Malus sebagai Model Rantai Markov
Directory of Open Access Journals (Sweden)
- Supandi
2010-06-01
Full Text Available Sistem bonus-malus (BMS yang dibangun mempunyaiÂ tujuan untuk membuat premi yang dibayarkan oleh tertanggung sedekat mungkin dengan harapan terjadinya klaim setiap tahunnya. Bila kita ingin meneliti bagaimana efisiensi suatu BMS, kita harus melihat bagaimana premi itu bergantungÂ pada frekuensi klaim. Efisiensi sistem bonus-malus dicari melalui model Markovnya,Â yaitu dengan mencari distribusi stasioner dari rantai markov BMS-nya. Dalam paper ini BMS yang digunakan adalah BMS Brasil dan modifkasinya pada nilai preminya untuk keadaan bawah. Dari modifikasi ini akan dibahas pengaruh perubahan premi terhadapÂ efisiensi BMS tersebut. Kata kunci : BMS, rantai markov, stationer,Â efisiensi
Large deviations for Markov processes with resetting.
Meylahn, Janusz M; Sabhapandit, Sanjib; Touchette, Hugo
2015-12-01
Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of time-additive functions or observables of Markov processes with resetting. By deriving a renewal formula linking generating functions with and without resetting, we are able to obtain the rate function of such observables, characterizing the likelihood of their fluctuations in the long-time limit. We consider as an illustration the large deviations of the area of the Ornstein-Uhlenbeck process with resetting. Other applications involving diffusions, random walks, and jump processes with resetting or catastrophes are discussed. PMID:26764673
Shape-Driven Nested Markov Tessellations
Schreiber, Tomasz
2011-01-01
A new and rather broad class of stationary (i.e. stochastically translation invariant) random tessellations of the $d$-dimensional Euclidean space is introduced, which are called shape-driven nested Markov tessellations. Locally, these tessellations are constructed by means of a spatio-temporal random recursive split dynamics governed by a family of Markovian split kernel, generalizing thereby the -- by now classical -- construction of iteration stable random tessellations. By providing an explicit global construction of the tessellations, it is shown that under suitable assumptions on the split kernels (shape-driven), there exists a unique time-consistent whole-space tessellation-valued Markov process of stationary random tessellations compatible with the given split kernels. Beside the existence and uniqueness result, the typical cell and some aspects of the first-order geometry of these tessellations are in the focus of our discussion.
Nuclear security assessment with Markov model approach
International Nuclear Information System (INIS)
Nuclear security risk assessment with the Markov model based on random event is performed to explore evaluation methodology for physical protection in nuclear facilities. Because the security incidences are initiated by malicious and intentional acts, expert judgment and Bayes updating are used to estimate scenario and initiation likelihood, and it is assumed that the Markov model derived from stochastic process can be applied to incidence sequence. Both an unauthorized intrusion as Design Based Threat (DBT) and a stand-off attack as beyond-DBT are assumed to hypothetical facilities, and performance of physical protection and mitigation and minimization of consequence are investigated to develop the assessment methodology in a semi-quantitative manner. It is shown that cooperation between facility operator and security authority is important to respond to the beyond-DBT incidence. (author)
A Markov decision model for determining optimal outpatient scheduling.
Patrick, Jonathan
2012-06-01
Managing an efficient outpatient clinic can often be complicated by significant no-show rates and escalating appointment lead times. One method that has been proposed for avoiding the wasted capacity due to no-shows is called open or advanced access. The essence of open access is "do today's demand today". We develop a Markov Decision Process (MDP) model that demonstrates that a short booking window does significantly better than open access. We analyze a number of scenarios that explore the trade-off between patient-related measures (lead times) and physician- or system-related measures (revenue, overtime and idle time). Through simulation, we demonstrate that, over a wide variety of potential scenarios and clinics, the MDP policy does as well or better than open access in terms of minimizing costs (or maximizing profits) as well as providing more consistent throughput. PMID:22089944
HYDRA: a Java library for Markov Chain Monte Carlo
Directory of Open Access Journals (Sweden)
Gregory R. Warnes
2002-03-01
Full Text Available Hydra is an open-source, platform-neutral library for performing Markov Chain Monte Carlo. It implements the logic of standard MCMC samplers within a framework designed to be easy to use, extend, and integrate with other software tools. In this paper, we describe the problem that motivated our work, outline our goals for the Hydra pro ject, and describe the current features of the Hydra library. We then provide a step-by-step example of using Hydra to simulate from a mixture model drawn from cancer genetics, first using a variable-at-a-time Metropolis sampler and then a Normal Kernel Coupler. We conclude with a discussion of future directions for Hydra.
Rate-Distortion via Markov Chain Monte Carlo
Jalali, Shirin
2008-01-01
We propose an approach to lossy source coding, utilizing ideas from Gibbs sampling, simulated annealing, and Markov Chain Monte Carlo (MCMC). The idea is to sample a reconstruction sequence from a Boltzmann distribution associated with an energy function that incorporates the distortion between the source and reconstruction, the compressibility of the reconstruction, and the point sought on the rate-distortion curve. To sample from this distribution, we use a 'heat bath algorithm': Starting from an initial candidate reconstruction (say the original source sequence), at every iteration, an index i is chosen and the i-th sequence component is replaced by drawing from the conditional probability distribution for that component given all the rest. At the end of this process, the encoder conveys the reconstruction to the decoder using universal lossless compression. The complexity of each iteration is independent of the sequence length and only linearly dependent on a certain context parameter (which grows sub-log...
Distribution estimation of hyperparameters in Markov random field models
International Nuclear Information System (INIS)
We developed a method of distribution estimation of hyperparameters in Markov random field (MRF) models. This study was motivated by the growing quantity of image data in natural sciences owing to recent advances in measurement techniques. MRF models are used to restore images in information science, and the hyperparameters of these models can be adjusted to improve restoration performance. The parameters appearing in data analysis represent physical quantities such as diffusion coefficients. Indeed, many frameworks of hyperparameter estimation have been proposed, but most are point estimation that is susceptible to stochastic fluctuations. Distribution estimation can be used to evaluate the confidence one has in point estimates of hyperparameters, in a similar way to physicists using error bars when they evaluate important physical quantities. We use a solvable MRF model to investigate the performance of distribution estimation in simulations. (paper)
Anatomy Ontology Matching Using Markov Logic Networks
Li, Chunhua; Zhao, Pengpeng; Wu, Jian; Cui, Zhiming
2016-01-01
The anatomy of model species is described in ontologies, which are used to standardize the annotations of experimental data, such as gene expression patterns. To compare such data between species, we need to establish relationships between ontologies describing different species. Ontology matching is a kind of solutions to find semantic correspondences between entities of different ontologies. Markov logic networks which unify probabilistic graphical model and first-order logic provide an exc...
Kajian Peluang Steady State Pada Rantai Markov
Novalina, Mariantan
2011-01-01
Markov chain says that the conditional probability of any future event given any past even and the present state is independent of the past event and depend only upon the present state. = is the transition probability from state i to state j The transition probability of well-balanced situation level is the transition probability which has reached balance so that will not change to change of time that happened or change that phase that happened. Formally, the transition probabi...
Dynamic risk management with Markov decision processes
Mundt, André Philipp
2008-01-01
An important tool in risk management is the implementation of risk measures. We study dynamic models where risk measures and dynamic risk measures can be applied. In particular, we solve various portfolio optimization problems and introduce a class of dynamic risk measures via the notion of Markov decision processes. Using Bayesian control theory we furthermore derive an extension of the latter setting when we face model uncertainty.
Handbook of Markov chain Monte Carlo
Brooks, Steve
2011-01-01
""Handbook of Markov Chain Monte Carlo"" brings together the major advances that have occurred in recent years while incorporating enough introductory material for new users of MCMC. Along with thorough coverage of the theoretical foundations and algorithmic and computational methodology, this comprehensive handbook includes substantial realistic case studies from a variety of disciplines. These case studies demonstrate the application of MCMC methods and serve as a series of templates for the construction, implementation, and choice of MCMC methodology.
Topologies of Stochastic Markov Models: Computational Aspects
Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim G.; Mardare, Radu
2014-01-01
In this paper we propose two behavioral distances that support approximate reasoning on Stochastic Markov Models (SMMs), that are continuous-time stochastic transition systems where the residence time on each state is described by a generic probability measure on the positive real line. In particular, we study the problem of measuring the behavioral dissimilarity of two SMMs against linear real-time specifications expressed as Metric Temporal Logic (MTL) formulas or Deterministic Timed-Automa...
Numerical methods in Markov chain modeling
Philippe, Bernard; Saad, Youcef; Stewart, William J.
1989-01-01
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
Analysis of a quantum Markov chain
International Nuclear Information System (INIS)
A quantum chain is analogous to a classical stationary Markov chain except that the probability measure is replaced by a complex amplitude measure and the transition probability matrix is replaced by a transition amplitude matrix. After considering the general situation, we study a particular example of a quantum chain whose transition amplitude matrix has the form of a Dirichlet matrix. Such matrices generate a discrete analog of the usual continuum Feynman amplitude. We then compute the probability distribution for these quantum chains
Constrained Risk-Sensitive Markov Decision Chains
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
Berlin : Springer, 2009 - (Fleischmann, B.; Borgwardt, K.; Klein, R.; Tuma, A.), s. 363-368 ISBN 978-3-642-00141-3. [Operations Research 2008. Augsburg (DE), 03.09.2008-05.09.2008] R&D Projects: GA ČR(CZ) GA402/08/0107; GA ČR GA402/07/1113 Institutional research plan: CEZ:AV0Z10750506 Keywords : Markov decision chain s * exponential utility functions * constraints Subject RIV: BB - Applied Statistics, Operational Research
Piecewise deterministic Markov processes: an analytic approach
Alkurdi, Taleb Salameh Odeh
2013-01-01
The subject of this thesis, piecewise deterministic Markov processes, an analytic approach, is on the border between analysis and probability theory. Such processes can either be viewed as random perturbations of deterministic dynamical systems in an impulsive fashion, or as a particular kind of stochastic process in continuous time in which parts of the sample trajectories are deterministic. Accordingly, questions concerning theses processes may be approached starting from either side. The a...
Mean variance optimality in Markov decision chains
Czech Academy of Sciences Publication Activity Database
Sladký, Karel; Sitař, Milan
Hradec Králové : Gadeamus, 2005 - (Skalská, H.), s. 350-357 ISBN 978-80-7041-535-1. [Mathematical Methods in Economics 2005 /23./. Hradec Králové (CZ), 14.09.2005-16.09.2005] R&D Projects: GA ČR GA402/05/0115 Institutional research plan: CEZ:AV0Z10750506 Keywords : Markov reward processes * expectation and variance of cumulative rewards Subject RIV: BB - Applied Statistics, Operational Research
On adaptive Markov chain Monte Carlo algorithms
Atchadé, Yves F.; Rosenthal, Jeffrey S.
2005-01-01
We look at adaptive Markov chain Monte Carlo algorithms that generate stochastic processes based on sequences of transition kernels, where each transition kernel is allowed to depend on the history of the process. We show under certain conditions that the stochastic process generated is ergodic, with appropriate stationary distribution. We use this result to analyse an adaptive version of the random walk Metropolis algorithm where the scale parameter σ is sequentially adapted using a Robbins-...