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Journal articles on the topic 'Mixture Markov Model'

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Author: Grafiati

Published: 9 March 2023

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1

Ming-Fang Yen, Amy, and Tony Hsiu-Hsi Chen. "Mixture Multi-state Markov Regression Model." Journal of Applied Statistics 34, no. 1 (January 2007): 11–21. http://dx.doi.org/10.1080/02664760600994711.

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2

Jang, Yoonsun, and Allan S. Cohen. "The Impact of Markov Chain Convergence on Estimation of Mixture IRT Model Parameters." Educational and Psychological Measurement 80, no. 5 (January 9, 2020): 975–94. http://dx.doi.org/10.1177/0013164419898228.

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A nonconverged Markov chain can potentially lead to invalid inferences about model parameters. The purpose of this study was to assess the effect of a nonconverged Markov chain on the estimation of parameters for mixture item response theory models using a Markov chain Monte Carlo algorithm. A simulation study was conducted to investigate the accuracy of model parameters estimated with different degree of convergence. Results indicated the accuracy of the estimated model parameters for the mixture item response theory models decreased as the number of iterations of the Markov chain decreased. In particular, increasing the number of burn-in iterations resulted in more accurate estimation of mixture IRT model parameters. In addition, the different methods for monitoring convergence of a Markov chain resulted in different degrees of convergence despite almost identical accuracy of estimation.

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3

Danaher, Peter J. "A Markov Mixture Model for Magazine Exposure." Journal of the American Statistical Association 84, no. 408 (December 1989): 922–26. http://dx.doi.org/10.1080/01621459.1989.10478856.

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4

Labeeuw, Wouter, and Geert Deconinck. "Residential Electrical Load Model Based on Mixture Model Clustering and Markov Models." IEEE Transactions on Industrial Informatics 9, no. 3 (August 2013): 1561–69. http://dx.doi.org/10.1109/tii.2013.2240309.

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5

Berthelsen, Kasper K., Laird A. Breyer, and Gareth O. Roberts. "Perfect posterior simulation for mixture and hidden Markov models." LMS Journal of Computation and Mathematics 13 (August 10, 2010): 246–59. http://dx.doi.org/10.1112/s1461157007000022.

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AbstractIn this paper we present an application of the read-once coupling from the past algorithm to problems in Bayesian inference for latent statistical models. We describe a method for perfect simulation from the posterior distribution of the unknown mixture weights in a mixture model. Our method is extended to a more general mixture problem, where unknown parameters exist for the mixture components, and to a hidden Markov model.

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6

Zaki, Ahmad, Wahidah Sanusi, and Saiful Bahri. "Model Rantai Markov dan Model ARIMA serta Kombinasinya dalam Memprediksi Curah Hujan di Kota Makassar." Journal of Mathematics, Computations, and Statistics 1, no. 1 (May 17, 2019): 8. http://dx.doi.org/10.35580/jmathcos.v1i1.9169.

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Abstrak. Curah hujan merupakan suatu data deret waktu yang bersifat kontinu, namun juga dapat diformulasikan sebagai peubah diskrit yaitu dengan menggolongkan suatu hari menjadi hujan dan tidak hujan. Curah hujan yang dicatat oleh pos hujan dapat digunakan untuk memprediksi curah hujan pada waktu yang akan datang melalui pemodelan deret waktu ARIMA musiman, Rantai Markov atau dengan campuran keduanya. Proses Markov merupakan suatu sistem stokastik di mana kejadian di masa yang akan datang bergantung pada kejadian sesaat sebelumnya Deret waktu merupakan serangkaian data yang disusun menurut urutan waktu Tujuan penelitian ini adalah untuk memodelkan dan memprediksi curah hujan dengan campuran Rantai Markov dan model deret waktu. Data yang digunakan dalam penelitian ini adalah curah hujan bulanan kota Makassar tahun 2007 sampai 2017. Campuran model deret waktu lebih sesuai digunakan untuk memprediksi curah hujan bulanan dibandingkan dengan pemodelan deret waktu saja hal ini dapat dilihat dai nilai MSE.Kata Kunci: Rantai Markov, Deret Waktu, ARIMA MusimanAbstract. Rainfall is a time series data that is continuous, but can also be formulated as a discrete variable that is by classifying one day as rainy and not rainy. Rainfall recorded by rain posts can be used to predict rainfall in the future through seasonal ARIMA time series modeling, Markov Chain or with a mixture of both. The Markov process is a stochastic system in which future events depend on the events of the previous moment. The time series is a series of data arranged in time sequence. The purpose of this study is to model and predict rainfall with a mixture of Markov Chains and time series models. The data used in this study is the monthly rainfall of Makassar city in 2007 to 2017. A mixture of time series models is more suitable to be used to predict monthly rainfall compared to modeling time series. This can be seen from the MSE value.Keywords: Markov chain, Time Series, seasonal ARIMA.

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Yuan, Shenfang, Jinjin Zhang, Jian Chen, Lei Qiu, and Weibo Yang. "A uniform initialization Gaussian mixture model–based guided wave–hidden Markov model with stable damage evaluation performance." Structural Health Monitoring 18, no. 3 (June 29, 2018): 853–68. http://dx.doi.org/10.1177/1475921718783652.

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During practical applications, the time-varying service conditions usually lead to difficulties in properly interpreting structural health monitoring signals. The guided wave–hidden Markov model–based damage evaluation method is a promising approach to address the uncertainties caused by the time-varying service condition. However, researches that have been performed to date are not comprehensive. Most of these research studies did not introduce serious time-varying factors, such as those that exist in reality, and hidden Markov model was applied directly without deep consideration of the performance improvement of hidden Markov model itself. In this article, the training stability problem when constructing the guided wave–hidden Markov model initialized by usually adopted k-means clustering method and its influence to damage evaluation were researched first by applying it to fatigue crack propagation evaluation of an attachment lug. After illustrating the problem of stability induced by k-means clustering, a novel uniform initialization Gaussian mixture model–based guided wave–hidden Markov model was proposed that provides steady and reliable construction of the guided wave–hidden Markov model. The advantage of the proposed method is demonstrated by lug fatigue crack propagation evaluation experiments.

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8

Tran, Dat, Wanli Ma, and Dharmendra Sharma. "Fuzzy Observable Markov Models for Pattern Recognition." Journal of Advanced Computational Intelligence and Intelligent Informatics 11, no. 6 (July 20, 2007): 662–67. http://dx.doi.org/10.20965/jaciii.2007.p0662.

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This paper presents a mathematical framework for fuzzy discrete and continuous observable Markov models (OMMs) and their applications to written language, spam email and typist recognition. Experimental results show that the proposed OMMs are more effective than models such as vector quantization, Gaussian mixture model and hidden Markov model.

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Chen, Zhongsheng, Yongmin Yang, Zheng Hu, and Qinghu Zeng. "Fault prognosis of complex mechanical systems based on multi-sensor mixtured hidden semi-Markov models." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 8 (November 21, 2012): 1853–63. http://dx.doi.org/10.1177/0954406212467260.

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Accurate fault prognosis is of vital importance for condition-based maintenance. As to complex mechanical systems, multiple sensors are often used to collect condition signals and the observation process may rather be non-Gaussian and non-stationary. Traditional hidden semi-Markov models cannot provide adequate representation for multivariate non-Gaussian and non-stationary time series. The innovation of this article is to extend classical hidden semi-Markov models by modeling the observation as a linear mixture of non-Gaussian multi-sensor signals. The proposed model is called as a multi-sensor mixtured hidden semi-Markov model. Under this new framework, modified parameter re-estimation algorithms are derived in detail based on the complete-data expectation maximization algorithm. In the end the proposed prognostic methodology is validated on a practical bearing application. The experimental results show that the proposed method is indeed promising to obtain better prognostic performance than classical hidden semi-Markov models.

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10

Berchtold, André. "Confidence Intervals for the Mixture Transition Distribution (MTD) Model and Other Markovian Models." Symmetry 12, no. 3 (March 1, 2020): 351. http://dx.doi.org/10.3390/sym12030351.

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The Mixture Transition Distribution (MTD) model used for the approximation of high-order Markov chains does not allow a simple calculation of confidence intervals, and computationnally intensive methods based on bootstrap are generally used. We show here how standard methods can be extended to the MTD model as well as other models such as the Hidden Markov Model. Starting from existing methods used for multinomial distributions, we describe how the quantities required for their application can be obtained directly from the data or from one run of the E-step of an EM algorithm. Simulation results indicate that when the MTD model is estimated reliably, the resulting confidence intervals are comparable to those obtained from more demanding methods.

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Sebastian, Tunny, Visalakshi Jeyaseelan, Lakshmanan Jeyaseelan, Shalini Anandan, Sebastian George, and Shrikant I. Bangdiwala. "Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models." Statistical Methods in Medical Research 28, no. 5 (April 4, 2018): 1552–63. http://dx.doi.org/10.1177/0962280218766964.

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Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as ‘Low’, ‘Moderate’ and ‘High’ with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

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Berchtold, André, Ogier Maitre, and Kevin Emery. "Optimization of the Mixture Transition Distribution Model Using the March Package for R." Symmetry 12, no. 12 (December 8, 2020): 2031. http://dx.doi.org/10.3390/sym12122031.

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Optimization of mixture models such as the mixture transition distribution (MTD) model is notoriously difficult because of the high complexity of their solution space. The best approach comprises combining features of two types of algorithms: an algorithm that can explore as completely as possible the whole solution space (e.g., an evolutionary algorithm), and another that can quickly identify an optimum starting from a set of initial conditions (for instance, an EM algorithm). The march package for the R environment is a library dedicated to the computation of Markovian models for categorical variables. It includes different algorithms that can manage the complexity of the MTD model, including an ad hoc hill-climbing procedure. In this article, we first discuss the problems related to the optimization of the MTD model, and then we show how march can be used to solve these problems; further, we provide different syntaxes for the computation of other models, including homogeneous Markov chains, hidden Markov models, and double chain Markov models.

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13

Mitrophanov, Alexander Yu, Alexandre Lomsadze, and Mark Borodovsky. "Sensitivity of hidden Markov models." Journal of Applied Probability 42, no. 3 (September 2005): 632–42. http://dx.doi.org/10.1239/jap/1127322017.

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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 processes.

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Mitrophanov, Alexander Yu, Alexandre Lomsadze, and Mark Borodovsky. "Sensitivity of hidden Markov models." Journal of Applied Probability 42, no. 03 (September 2005): 632–42. http://dx.doi.org/10.1017/s002190020000067x.

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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 processes.

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Berchtold, André. "Special Issue: “The Mixture Transition Distribution Model and Other Models for High-Order Dependencies”." Symmetry 14, no. 2 (January 21, 2022): 206. http://dx.doi.org/10.3390/sym14020206.

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Bacci, Silvia, and Bruno Bertaccini. "A Mixture Hidden Markov Model to Mine Students’ University Curricula." Data 7, no. 2 (February 21, 2022): 25. http://dx.doi.org/10.3390/data7020025.

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In the context of higher education, the wide availability of data gathered by universities for administrative purposes or for recording the evolution of students’ learning processes makes novel data mining techniques particularly useful to tackle critical issues. In Italy, current academic regulations allow students to customize the chronological sequence of courses they have to attend to obtain the final degree. This leads to a variety of sequences of exams, with an average time taken to obtain the degree that may significantly differ from the time established by law. In this contribution, we propose a mixture hidden Markov model to classify students into groups that are homogenous in terms of university paths, with the aim of detecting bottlenecks in the academic career and improving students’ performance.

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17

Shiping Du, Houhui Huang, and Yuming Wei. "The Baum-Welch Algorithm of Mixture Coupled Hidden Markov Model." Journal of Convergence Information Technology 8, no. 1 (January 15, 2013): 620–27. http://dx.doi.org/10.4156/jcit.vol8.issue1.76.

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18

Jian Zhou and Xiao-Ping Zhang. "An ICA Mixture Hidden Markov Model for Video Content Analysis." IEEE Transactions on Circuits and Systems for Video Technology 18, no. 11 (November 2008): 1576–86. http://dx.doi.org/10.1109/tcsvt.2008.2005614.

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19

Kappe, Eelco, Ashley Stadler Blank, and Wayne S. DeSarbo. "A random coefficients mixture hidden Markov model for marketing research." International Journal of Research in Marketing 35, no. 3 (September 2018): 415–31. http://dx.doi.org/10.1016/j.ijresmar.2018.07.002.

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20

Wang, Xiaofeng, and Xiao-Ping Zhang. "Ice hockey shooting event modeling with mixture hidden Markov model." Multimedia Tools and Applications 57, no. 1 (January 11, 2011): 131–44. http://dx.doi.org/10.1007/s11042-010-0722-9.

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21

Xu, Jiawei, and Qian Luo. "Human action recognition based on mixed gaussian hidden markov model." MATEC Web of Conferences 336 (2021): 06004. http://dx.doi.org/10.1051/matecconf/202133606004.

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Human action recognition is a challenging field in recent years. Many traditional signal processing and machine learning methods are gradually trying to be applied in this field. This paper uses a hidden Markov model based on mixed Gaussian to solve the problem of human action recognition. The model treats the observed human actions as samples which conform to the Gaussian mixture model, and each Gaussian mixture model is determined by a state variable. The training of the model is the process that obtain the model parameters through the expectation maximization algorithm. The simulation results show that the Hidden Markov Model based on the mixed Gaussian distribution can perform well in human action recognition.

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22

Sansom, John, and Peter Thomson. "Fitting hidden semi-Markov models to breakpoint rainfall data." Journal of Applied Probability 38, A (2001): 142–57. http://dx.doi.org/10.1239/jap/1085496598.

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The paper proposes a hidden semi-Markov model for breakpoint rainfall data that consist of both the times at which rain-rate changes and the steady rates between such changes. The model builds on and extends the seminal work of Ferguson (1980) on variable duration models for speech. For the rainfall data the observations are modelled as mixtures of log-normal distributions within unobserved states where the states evolve in time according to a semi-Markov process. For the latter, parametric forms need to be specified for the state transition probabilities and dwell-time distributions.Recursions for constructing the likelihood are developed and the EM algorithm used to fit the parameters of the model. The choice of dwell-time distribution is discussed with a mixture of distributions over disjoint domains providing a flexible alternative. The methods are also extended to deal with censored data. An application of the model to a large-scale bivariate dataset of breakpoint rainfall measurements at Wellington, New Zealand, is discussed.

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Sansom, John, and Peter Thomson. "Fitting hidden semi-Markov models to breakpoint rainfall data." Journal of Applied Probability 38, A (2001): 142–57. http://dx.doi.org/10.1017/s0021900200112744.

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The paper proposes a hidden semi-Markov model for breakpoint rainfall data that consist of both the times at which rain-rate changes and the steady rates between such changes. The model builds on and extends the seminal work of Ferguson (1980) on variable duration models for speech. For the rainfall data the observations are modelled as mixtures of log-normal distributions within unobserved states where the states evolve in time according to a semi-Markov process. For the latter, parametric forms need to be specified for the state transition probabilities and dwell-time distributions. Recursions for constructing the likelihood are developed and the EM algorithm used to fit the parameters of the model. The choice of dwell-time distribution is discussed with a mixture of distributions over disjoint domains providing a flexible alternative. The methods are also extended to deal with censored data. An application of the model to a large-scale bivariate dataset of breakpoint rainfall measurements at Wellington, New Zealand, is discussed.

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Baena-Mirabete, S., Anna Espinal, and Pedro Puig. "Exploring the randomness of mentally generated head–tail sequences." Statistical Modelling 20, no. 3 (January 16, 2019): 225–48. http://dx.doi.org/10.1177/1471082x18816410.

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It is well known that people deviate from randomness as they attempt to mentally generate head–tail sequences as randomly as possible. This deviation from randomness is quantified by an excess of repetitions or alternations between successive responses more than would be expected by chance. We conducted an experiment in which a sample of students was asked to mentally simulate a sequence as if it is produced by a fair coin. We propose several models based on Markov chains for analysing the dynamic of head–tail outcomes in these sequences. First, we explore observed Markov chains and suggest some practical solutions to reduce the number of parameters. However, there is a need for more sophisticated models, and in this case, we propose latent Markov models and mixture of Markov chains to analyse these head–tail sequences. A generalization of the so-called mixture transition distribution (MTD) model is also considered.

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Tian, Fukui, Qingyi Zhou, and Chuanchuan Yang. "Gaussian mixture model-hidden Markov model based nonlinear equalizer for optical fiber transmission." Optics Express 28, no. 7 (March 20, 2020): 9728. http://dx.doi.org/10.1364/oe.386476.

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26

Solikhah, Arifatus, Heri Kuswanto, Nur Iriawan, and Kartika Fithriasari. "Fisher’s z Distribution-Based Mixture Autoregressive Model." Econometrics 9, no. 3 (June 29, 2021): 27. http://dx.doi.org/10.3390/econometrics9030027.

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We generalize the Gaussian Mixture Autoregressive (GMAR) model to the Fisher’s z Mixture Autoregressive (ZMAR) model for modeling nonlinear time series. The model consists of a mixture of K-component Fisher’s z autoregressive models with the mixing proportions changing over time. This model can capture time series with both heteroskedasticity and multimodal conditional distribution, using Fisher’s z distribution as an innovation in the MAR model. The ZMAR model is classified as nonlinearity in the level (or mode) model because the mode of the Fisher’s z distribution is stable in its location parameter, whether symmetric or asymmetric. Using the Markov Chain Monte Carlo (MCMC) algorithm, e.g., the No-U-Turn Sampler (NUTS), we conducted a simulation study to investigate the model performance compared to the GMAR model and Student t Mixture Autoregressive (TMAR) model. The models are applied to the daily IBM stock prices and the monthly Brent crude oil prices. The results show that the proposed model outperforms the existing ones, as indicated by the Pareto-Smoothed Important Sampling Leave-One-Out cross-validation (PSIS-LOO) minimum criterion.

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Bolano, Danilo. "Handling Covariates in Markovian Models with a Mixture Transition Distribution Based Approach." Symmetry 12, no. 4 (April 4, 2020): 558. http://dx.doi.org/10.3390/sym12040558.

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This paper presents and discusses the use of a Mixture Transition Distribution-like model (MTD) to account for covariates in Markovian models. The MTD was introduced in 1985 by Raftery as an approximation of higher order Markov chains. In the MTD, each lag is estimated separately using an additive model, which introduces a kind of symmetrical relationship between the past and the present. Here, using an MTD-based approach, we consider each covariate separately, and we combine the effects of the lags and of the covariates by means of a mixture model. This approach has three main advantages. First, no modification of the estimation procedure is needed. Second, it is parsimonious in terms of freely estimated parameters. Third, the weight parameters of the mixture can be used as an indication of the relevance of the covariate in explaining the time dependence between states. An illustrative example taken from life course studies using a 3-state hidden Markov model and a covariate with three levels shows how to interpret the results of such models.

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Ding, Lusa, Ting Zhu, Yanli Wang, and Yajie Zou. "Finite Mixture of the Hidden Markov Model for Driving Style Analysis." Journal of Advanced Transportation 2022 (January 31, 2022): 1–8. http://dx.doi.org/10.1155/2022/4989947.

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Analyzing driving style is useful for developing intelligent vehicles. Previous studies usually consider the statistical features (e.g., the means and standard deviations of brake pressure) of the measured driving data or manually define the number of patterns divided by behavior semantics to characterize driving styles. In this paper, we propose a driving style analysis to describe the personalized driving styles from time-series driving data without specifying the levels in advance but by estimating them from the data. First, range, range rate, and acceleration are selected as three feature variables to describe car-following scenarios. Then, the car-following data are normalized to reduce the scale influence of different variables on the segmentation results. The hidden Markov model (HMM) and the finite mixture of the hidden Markov model (MHMM) are adopted to extract behavior semantics. Compared with the HMM, the MHMM can identify the heterogeneity of data and then provide more reasonable primitive driving patterns. Based on the results, this study uses the K-means clustering to label all the driving patterns semantically and identifies a total of 75 different driving patterns. We use the normalized frequency distributions to describe personalized driving behavior characteristics, and similarity evaluations of driving styles are applied using the Kolmogorov–Smirnov test. The proposed approach in this paper is useful for exploring the characteristics of driving habits.

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Yi, Junkai, Guanglin Gong, Zeyu Liu, and Yacong Zhang. "Classification of Markov Encrypted Traffic on Gaussian Mixture Model Constrained Clustering." Wireless Communications and Mobile Computing 2021 (October 7, 2021): 1–11. http://dx.doi.org/10.1155/2021/4935108.

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In order to solve the problem that traditional analysis approaches of encrypted traffic in encryption transmission of network application only consider the traffic classification in the complete communication process with ignoring traffic classification in the simplified communication process, and there are a lot of duplication problems in application fingerprints during state transition, a new classification approach of encrypted traffic is proposed. The article applies the Gaussian mixture model (GMM) to analyze the length of the message, and the model is established to solve the problem of application fingerprint duplication. The fingerprints with similar lengths of the same application are divided into as few clusters as possible by constrained clustering approach, which speeds up convergence speed and improves the clustering effect. The experimental results show that compared with the other encryption traffic classification approaches, the proposed approach has 11.7%, 19.8%, 6.86%, and 5.36% improvement in TPR, FPR, Precision, and Recall, respectively, and the classification effect of encrypted traffic is significantly improved.

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Jin Gyo Kim. "Dynamic Heterogeneous Choice Heuristics: A Bayesian Hidden Markov Mixture Model Approach." Seoul Journal of Business 19, no. 1 (June 2013): 106–35. http://dx.doi.org/10.35152/snusjb.2013.19.1.004.

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31

Ghanbari, Hamid, Saeid Homayouni, Abdolreza Safari, and Pedram Ghamisi. "Gaussian mixture model and Markov random fields for hyperspectral image classification." European Journal of Remote Sensing 51, no. 1 (January 1, 2018): 889–900. http://dx.doi.org/10.1080/22797254.2018.1503565.

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Cao, Guoxiang, Anlin Wang, and Donghuan Xu. "Wheel Loader Driving Intention Recognition with Gaussian Mixture - Hidden Markov Model." MATEC Web of Conferences 237 (2018): 03001. http://dx.doi.org/10.1051/matecconf/201823703001.

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Accurate recognition of driving intentions can delay upshifts under the intention of quick acceleration to maximize vehicle power performance; avoid frequent gear changes in automatic transmissions for rapid deceleration intention and make all power to flow to the bucket in the desire for fast motion of cylinders. However, due to the ambiguity of the human intentions and multiple meanings of depressing on the accelerator pedal in wheel loader, it is difficult to recognize driving intention. Nevertheless, the driver’s intentions are directly reflected in the accelerator pedal, brake pedal and hydraulic valve control handle. By detecting these observable signals such as the signals of acceleration pedal’s displacement and velocity, brake pedal’s displacement and velocity and valve status Gaussian Mixture – Hidden Markov Model(MGHMM) can recognize the unobservable driving intentions. The experiment is done in Simulink and the results show that MGHMM can recognize driving intentions as expected.

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Wang, Min, Sherif Abdelfattah, Nour Moustafa, and Jiankun Hu. "Deep Gaussian Mixture-Hidden Markov Model for Classification of EEG Signals." IEEE Transactions on Emerging Topics in Computational Intelligence 2, no. 4 (August 2018): 278–87. http://dx.doi.org/10.1109/tetci.2018.2829981.

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Mayrink, Vinícius Diniz, and Flávio Bambirra Gonçalves. "A Bayesian hidden Markov mixture model to detect overexpressed chromosome regions." Journal of the Royal Statistical Society: Series C (Applied Statistics) 66, no. 2 (September 17, 2016): 387–412. http://dx.doi.org/10.1111/rssc.12178.

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Bathaee, Najmeh, and Hamid Sheikhzadeh. "Non-parametric Bayesian inference for continuous density hidden Markov mixture model." Statistical Methodology 33 (December 2016): 256–75. http://dx.doi.org/10.1016/j.stamet.2016.10.003.

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Nagy, Ivan, and Evgenia Suzdaleva. "Mixture estimation with state-space components and Markov model of switching." Applied Mathematical Modelling 37, no. 24 (December 2013): 9970–84. http://dx.doi.org/10.1016/j.apm.2013.05.038.

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Liang, Yulan, and Arpad Kelemen. "Bayesian Finite Markov Mixture Model for Temporal Multi-Tissue Polygenic Patterns." Biometrical Journal 51, no. 1 (February 2009): 56–69. http://dx.doi.org/10.1002/bimj.200710489.

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Gao, Xin, Yurong R. Cao, Nicholas Ogden, Louise Aubin, and Huaiping P. Zhu. "Mixture Markov regression model with application to mosquito surveillance data analysis." Biometrical Journal 59, no. 3 (March 6, 2017): 462–77. http://dx.doi.org/10.1002/bimj.201600137.

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ODEN, J. TINSLEY, ERNESTO E. PRUDENCIO, and ANDREA HAWKINS-DAARUD. "SELECTION AND ASSESSMENT OF PHENOMENOLOGICAL MODELS OF TUMOR GROWTH." Mathematical Models and Methods in Applied Sciences 23, no. 07 (April 2, 2013): 1309–38. http://dx.doi.org/10.1142/s0218202513500103.

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We address general approaches to the rational selection and validation of mathematical and computational models of tumor growth using methods of Bayesian inference. The model classes are derived from a general diffuse-interface, continuum mixture theory and focus on mass conservation of mixtures with up to four species. Synthetic data are generated using higher-order base models. We discuss general approaches to model calibration, validation, plausibility, and selection based on Bayesian-based methods, information theory, and maximum information entropy. We also address computational issues and provide numerical experiments based on Markov chain Monte Carlo algorithms and high performance computing implementations.

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Zhang, Mingchi, Xuemin Chen, and Wei Li. "A Hybrid Hidden Markov Model for Pipeline Leakage Detection." Applied Sciences 11, no. 7 (April 1, 2021): 3138. http://dx.doi.org/10.3390/app11073138.

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In this paper, a deep neural network hidden Markov model (DNN-HMM) is proposed to detect pipeline leakage location. A long pipeline is divided into several sections and the leakage occurs in different section that is defined as different state of hidden Markov model (HMM). The hybrid HMM, i.e., DNN-HMM, consists of a deep neural network (DNN) with multiple layers to exploit the non-linear data. The DNN is initialized by using a deep belief network (DBN). The DBN is a pre-trained model built by stacking top-down restricted Boltzmann machines (RBM) that compute the emission probabilities for the HMM instead of Gaussian mixture model (GMM). Two comparative studies based on different numbers of states using Gaussian mixture model-hidden Markov model (GMM-HMM) and DNN-HMM are performed. The accuracy of the testing performance between detected state sequence and actual state sequence is measured by micro F1 score. The micro F1 score approaches 0.94 for GMM-HMM method and it is close to 0.95 for DNN-HMM method when the pipeline is divided into three sections. In the experiment that divides the pipeline as five sections, the micro F1 score for GMM-HMM is 0.69, while it approaches 0.96 with DNN-HMM method. The results demonstrate that the DNN-HMM can learn a better model of non-linear data and achieve better performance compared to GMM-HMM method.

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George, Sebastian, and Ambily Jose. "Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data." Revista Colombiana de Estadística 43, no. 1 (January 1, 2020): 71–82. http://dx.doi.org/10.15446/rce.v43n1.77542.

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The most suitable statistical method for explaining serial dependency in time series count data is that based on Hidden Markov Models (HMMs). These models assume that the observations are generated from a finite mixture of distributions governed by the principle of Markov chain (MC). Poisson-Hidden Markov Model (P-HMM) may be the most widely used method for modelling the above said situations. However, in real life scenario, this model cannot be considered as the best choice. Taking this fact into account, we, in this paper, go for Generalised Poisson Distribution (GPD) for modelling count data. This method can rectify the overdispersion and underdispersion in the Poisson model. Here, we develop Generalised Poisson Hidden Markov model (GP-HMM) by combining GPD with HMM for modelling such data. The results of the study on simulated data and an application of real data, monthly cases of Leptospirosis in the state of Kerala in South India, show good convergence properties, proving that the GP-HMM is a better method compared to P-HMM.

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Toivonen, Jarkko, Pratyush K. Das, Jussi Taipale, and Esko Ukkonen. "MODER2: first-order Markov modeling and discovery of monomeric and dimeric binding motifs." Bioinformatics 36, no. 9 (January 30, 2020): 2690–96. http://dx.doi.org/10.1093/bioinformatics/btaa045.

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Abstract Motivation Position-specific probability matrices (PPMs, also called position-specific weight matrices) have been the dominating model for transcription factor (TF)-binding motifs in DNA. There is, however, increasing recent evidence of better performance of higher order models such as Markov models of order one, also called adjacent dinucleotide matrices (ADMs). ADMs can model dependencies between adjacent nucleotides, unlike PPMs. A modeling technique and software tool that would estimate such models simultaneously both for monomers and their dimers have been missing. Results We present an ADM-based mixture model for monomeric and dimeric TF-binding motifs and an expectation maximization algorithm MODER2 for learning such models from training data and seeds. The model is a mixture that includes monomers and dimers, built from the monomers, with a description of the dimeric structure (spacing, orientation). The technique is modular, meaning that the co-operative effect of dimerization is made explicit by evaluating the difference between expected and observed models. The model is validated using HT-SELEX and generated datasets, and by comparing to some earlier PPM and ADM techniques. The ADM models explain data slightly better than PPM models for 314 tested TFs (or their DNA-binding domains) from four families (bHLH, bZIP, ETS and Homeodomain), the ADM mixture models by MODER2 being the best on average. Availability and implementation Software implementation is available from https://github.com/jttoivon/moder2. Supplementary information Supplementary data are available at Bioinformatics online.

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Brianzoni, Serena, Cristiana Mammana, Elisabetta Michetti, and Francesco Zirilli. "A Stochastic Cobweb Dynamical Model." Discrete Dynamics in Nature and Society 2008 (2008): 1–18. http://dx.doi.org/10.1155/2008/219653.

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We consider the dynamics of a stochastic cobweb model with linear demand and a backward-bending supply curve. In our model, forward-looking expectations and backward-looking ones are assumed, in fact we assume that the representative agent chooses the backward predictor with probability , and the forward predictor with probability , so that the expected price at time is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.

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de Figueiredo, Leandro Passos, Dario Grana, Mauro Roisenberg, and Bruno B. Rodrigues. "Gaussian mixture Markov chain Monte Carlo method for linear seismic inversion." GEOPHYSICS 84, no. 3 (May 1, 2019): R463—R476. http://dx.doi.org/10.1190/geo2018-0529.1.

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We have developed a Markov chain Monte Carlo (MCMC) method for joint inversion of seismic data for the prediction of facies and elastic properties. The solution of the inverse problem is defined by the Bayesian posterior distribution of the properties of interest. The prior distribution is a Gaussian mixture model, and each component is associated to a potential configuration of the facies sequence along the seismic trace. The low frequency is incorporated by using facies-dependent depositional trend models for the prior means of the elastic properties in each facies. The posterior distribution is also a Gaussian mixture, for which the Gaussian component can be analytically computed. However, due to the high number of components of the mixture, i.e., the large number of facies configurations, the computation of the full posterior distribution is impractical. Our Gaussian mixture MCMC method allows for the calculation of the full posterior distribution by sampling the facies configurations according to the acceptance/rejection probability. The novelty of the method is the use of an MCMC framework with multimodal distributions for the description of the model properties and the facies along the entire seismic trace. Our method is tested on synthetic seismic data, applied to real seismic data, and validated using a well test.

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Crayen, Claudia, Michael Eid, Tanja Lischetzke, and Jeroen K. Vermunt. "A Continuous-Time Mixture Latent-State-Trait Markov Model for Experience Sampling Data." European Journal of Psychological Assessment 33, no. 4 (July 2017): 296–311. http://dx.doi.org/10.1027/1015-5759/a000418.

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Abstract. In psychological research, statistical models of latent state-trait (LST) theory are popular for the analysis of longitudinal data. We identify several limitations of available models when applied to intensive longitudinal data with categorical observed and latent variables and inter- and intraindividually varying time intervals. As an extension of available LST models for categorical data, we describe a general mixed continuous-time LST model that is suitable for intensive longitudinal data with unobserved heterogeneity and individually varying time intervals. This model is illustrated by an application to momentary mood data that were collected in an experience sampling study (N = 164). In addition, the results of a simulation study are reported that was conducted to find out (a) the minimal data requirements with respect to sample size and number of occasions, and (b) how strong the bias is if the continuous-time structure is ignored. The empirical application revealed two classes for which the transition pattern and effects of time-varying covariates differ. In the simulation study, only small differences between the continuous-time model and its discrete-time counterpart emerged. Sample sizes N = 100 and larger in combination with six or more occasions of measurement tended to produce reliable estimation results. Implications of the models for future research are discussed.

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Désir, Antoine, Vineet Goyal, and Jiawei Zhang. "Technical Note—Capacitated Assortment Optimization: Hardness and Approximation." Operations Research 70, no. 2 (March 2022): 893–904. http://dx.doi.org/10.1287/opre.2021.2142.

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Assortment optimization is an important problem arising in various applications. In many practical settings, the assortment is subject to a capacity constraint. In “Capacitated Assortment Optimization: Hardness and Approximation,” Désir, Goyal, and Zhang study the capacitated assortment optimization problem. The authors first show that adding a general capacity constraint makes the problem NP-hard even for the simple multinomial logit model. They also show that under the mixture of multinomial logit model, even the unconstrained problem is hard to approximate within any reasonable factor when the number of mixtures is not constant. In view of these hardness results, the authors present near-optimal algorithms for a large class of parametric choice models including the mixture of multinomial logit, Markov chain, nested logit, and d-level nested logit choice models. In fact, their approach extends to a large class of objective functions that depend only on a small number of linear functions.

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Geliazkova, Maya. "A Bayesian Spatial Mixture Model for FMRI Analysis." Serdica Journal of Computing 4, no. 4 (January 20, 2011): 417–34. http://dx.doi.org/10.55630/sjc.2010.4.417-434.

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We develop, implement and study a new Bayesian spatial mixture model (BSMM). The proposed BSMM allows for spatial structure in the binary activation indicators through a latent thresholded Gaussian Markov random field. We develop a Gibbs (MCMC) sampler to perform posterior inference on the model parameters, which then allows us to assess the posterior probabilities of activation for each voxel. One purpose of this article is to compare the HJ model and the BSMM in terms of receiver operating characteristics (ROC) curves. Also we consider the accuracy of the spatial mixture model and the BSMM for estimation of the size of the activation region in terms of bias, variance and mean squared error. We perform a simulation study to examine the aforementioned characteristics under a variety of configurations of spatial mixture model and BSMM both as the size of the region changes and as the magnitude of activation changes.

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Sun, Jianjun, Yan Zhao, Shigang Wang, and Jian Wei. "Image compression based on Gaussian mixture model constrained using Markov random field." Signal Processing 183 (June 2021): 107990. http://dx.doi.org/10.1016/j.sigpro.2021.107990.

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Cho, Sun-Joo, Allan S. Cohen, and Seock-Ho Kim. "Markov chain Monte Carlo estimation of a mixture item response theory model." Journal of Statistical Computation and Simulation 83, no. 2 (February 2013): 278–306. http://dx.doi.org/10.1080/00949655.2011.603090.

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Choi, Seunghyun, Myungsik Do, Daeseok Han, Hyeonjeong Sim, and Chandle Chae. "Estimation of Road Pavements Life Expectancy via Bayesian Markov Mixture Hazard Model." International Journal of Highway Engineering 21, no. 6 (December 30, 2019): 57–67. http://dx.doi.org/10.7855/ijhe.2019.21.6.057.

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