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Zeitschriftenartikel zum Thema „Hidden Markov modelling“

Autor: Grafiati

Veröffentlicht am 26. Juni 2021

Zuletzt aktualisiert am 6. Februar 2022

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1

Rasku, J., M. Juhola, T. Tossavainen, I. Pyykkö und E. Toppila. „Modelling stabilograms with hidden Markov models“. Journal of Medical Engineering & Technology 32, Nr. 4 (Januar 2008): 273–83. http://dx.doi.org/10.1080/03091900600968908.

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2

Rama, J. „Fuzzy Methods for Soft Hidden Markov Modelling“. International Journal for Research in Applied Science and Engineering Technology 6, Nr. 1 (31.01.2018): 23–31. http://dx.doi.org/10.22214/ijraset.2018.1005.

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3

Nkemnole, Edesiri Bridget, und Ekene Nwaokoro. „Modelling Customer Relationships as Hidden Markov Chains“. Path of Science 6, Nr. 11 (30.11.2020): 5011–19. http://dx.doi.org/10.22178/pos.64-9.

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Models in behavioural relationship marketing suggest that relations between the customer and the company change over time as a result of the continuous encounter. Some theoretical models have been put forward concerning relationship marketing, both from the standpoints of consumer behaviour and empirical modelling. In addition to these, this study proposes the hidden Markov model (HMM) as a potential tool for assessing customer relationships. Specifically, the HMM is submitted via the framework of a Markov chain model to classify customers relationship dynamics of a telecommunication service company by using an experimental data set. We develop and estimate an HMM to relate the unobservable relationship states to the observed buying behaviour of the customers giving an appropriate classification of the customers into the relationship states. By merely accounting for the functional and unobserved heterogeneity with a two-state hidden Markov model and taking estimation into account via an optimal estimation method, the empirical results not only demonstrate the value of the proposed model in assessing the dynamics of a customer relationship over time but also gives the optimal marketing-mixed strategies in different customer state.

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4

Koski, Antti. „Modelling ECG signals with hidden Markov models“. Artificial Intelligence in Medicine 8, Nr. 5 (Oktober 1996): 453–71. http://dx.doi.org/10.1016/s0933-3657(96)00352-1.

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5

Baran, Robert H. „A software package for hidden Markov modelling“. Mathematical and Computer Modelling 11 (1988): 476–80. http://dx.doi.org/10.1016/0895-7177(88)90538-9.

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6

Vaseghi, S. V. „State duration modelling in hidden Markov models“. Signal Processing 41, Nr. 1 (Januar 1995): 31–41. http://dx.doi.org/10.1016/0165-1684(94)00088-h.

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7

Whiting, J. P., M. F. Lambert und A. V. Metcalfe. „Modelling persistence in annual Australia point rainfall“. Hydrology and Earth System Sciences 7, Nr. 2 (30.04.2003): 197–211. http://dx.doi.org/10.5194/hess-7-197-2003.

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Abstract. Annual rainfall time series for Sydney from 1859 to 1999 is analysed. Clear evidence of nonstationarity is presented, but substantial evidence for persistence or hidden states is more elusive. A test of the hypothesis that a hidden state Markov model reduces to a mixture distribution is presented. There is strong evidence of a correlation between the annual rainfall and climate indices. Strong evidence of persistence of one of these indices, the Pacific Decadal Oscillation (PDO), is presented together with a demonstration that this is better modelled by fractional differencing than by a hidden state Markov model. It is shown that conditioning the logarithm of rainfall on PDO, the Southern Oscillation index (SOI), and their interaction provides realistic simulation of rainfall that matches observed statistics. Similar simulation models are presented for Brisbane, Melbourne and Perth. Keywords: Hydrological persistence,hidden state Markov models, fractional differencing, PDO, SOI, Australian rainfall

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8

Chordia, Parag, Avinash Sastry und Sertan Şentürk. „Predictive Tabla Modelling Using Variable-length Markov and Hidden Markov Models“. Journal of New Music Research 40, Nr. 2 (Juni 2011): 105–18. http://dx.doi.org/10.1080/09298215.2011.576318.

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9

Segura, J. C., A. J. Rubio, A. M. Peinado, P. García und R. Román. „Multiple VQ hidden Markov modelling for speech recognition“. Speech Communication 14, Nr. 2 (April 1994): 163–70. http://dx.doi.org/10.1016/0167-6393(94)90006-x.

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10

Resnick, Sidney, und Ajay Subramanian. „Heavy tailed hidden semi-markov models“. Communications in Statistics. Stochastic Models 14, Nr. 1-2 (Januar 1998): 319–34. http://dx.doi.org/10.1080/15326349808807474.

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11

Nagaraja, Haikady N. „Inference in Hidden Markov Models“. Technometrics 48, Nr. 4 (November 2006): 574–75. http://dx.doi.org/10.1198/tech.2006.s440.

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12

George, Sebastian, und Ambily Jose. „Generalized Poisson Hidden Markov Model for Overdispersed or Underdispersed Count Data“. Revista Colombiana de Estadística 43, Nr. 1 (01.01.2020): 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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13

Durand, Jean-Baptiste, und Olivier Gaudoin. „Software reliability modelling and prediction with hidden Markov chains“. Statistical Modelling: An International Journal 5, Nr. 1 (April 2005): 75–93. http://dx.doi.org/10.1191/1471082x05st087oa.

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14

Banachewicz, Konrad, André Lucas und Aad van der Vaart. „Modelling Portfolio Defaults Using Hidden Markov Models with Covariates“. Econometrics Journal 11, Nr. 1 (März 2008): 155–71. http://dx.doi.org/10.1111/j.1368-423x.2008.00232.x.

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15

Qiu, Qinfu, und Xiong Chen. „Behaviour-driven dynamic pricing modelling via hidden Markov model“. International Journal of Bio-Inspired Computation 11, Nr. 1 (2018): 27. http://dx.doi.org/10.1504/ijbic.2018.090071.

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16

Stanislavsky, A., W. Nitka, M. Małek, K. Burnecki und J. Janczura. „Prediction performance of Hidden Markov modelling for solar flares“. Journal of Atmospheric and Solar-Terrestrial Physics 208 (Oktober 2020): 105407. http://dx.doi.org/10.1016/j.jastp.2020.105407.

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17

Ge, Yuan, Yan Zhang, Wengen Gao, Fanyong Cheng, Nuo Yu und Jincenzi Wu. „Modelling and Prediction of Random Delays in NCSs Using Double-Chain HMMs“. Discrete Dynamics in Nature and Society 2020 (29.10.2020): 1–16. http://dx.doi.org/10.1155/2020/6848420.

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This paper is concerned with the modelling and prediction of random delays in networked control systems. The stochastic distribution of the random delay in the current sampling period is assumed to be affected by the network state in the current sampling period as well as the random delay in the previous sampling period. Based on this assumption, the double-chain hidden Markov model (DCHMM) is proposed in this paper to model the delays. There are two Markov chains in this model. One is the hidden Markov chain which consists of the network states and the other is the observable Markov chain which consists of the delays. Moreover, the delays are also affected by the hidden network states, which constructs the DCHMM-based delay model. The initialization and optimization problems of the model parameters are solved by using the segmental K-mean clustering algorithm and the expectation maximization algorithm, respectively. Based on the model, the prediction of the controller-to-actuator (CA) delay in the current sampling period is obtained. The prediction can be used to design a controller to compensate the CA delay in the future research. Some comparative experiments are carried out to demonstrate the effectiveness and superiority of the proposed method.

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18

Du, Shi Ping, Jian Wang und Yu Ming Wei. „The Training Algorithm of Fuzzy Coupled Hidden Markov Models“. Applied Mechanics and Materials 568-570 (Juni 2014): 254–59. http://dx.doi.org/10.4028/www.scientific.net/amm.568-570.254.

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A variety of coupled hidden Markov models (CHMMs) have recently been proposed as extensions of HMM to better characterize multiple interdependent sequences. The resulting models have multiple state variables that are temporally coupled via matrices of conditional probabilities. A generalised fuzzy approach to statistical modelling techniques is proposed in this paper. Fuzzy C-means (FCM) and fuzzy entropy (FE) techniques are combined into a generalised fuzzy technique and applied to coupled hidden Markov models. The CHMM based on the fuzzy c-means (FCM) and fuzzy entropy (FE) is referred to as FCM-FE-CHMM in this paper. By building up a generalised fuzzy objective function, several new formulae solving Training algorithms are theoretically derived for FCM-FE-CHMM. The fuzzy modelling techniques are very flexible since the degree of fuzziness, the degree of fuzzy entropy.

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19

Ossadtchi, A., J. C. Mosher, W. W. Sutherling, R. E. Greenblatt und R. M. Leahy. „Hidden Markov modelling of spike propagation from interictal MEG data“. Physics in Medicine and Biology 50, Nr. 14 (06.07.2005): 3447–69. http://dx.doi.org/10.1088/0031-9155/50/14/017.

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20

Jacobsen, C. R., und M. Nielsen. „Stylometry of paintings using hidden Markov modelling of contourlet transforms“. Signal Processing 93, Nr. 3 (März 2013): 579–91. http://dx.doi.org/10.1016/j.sigpro.2012.09.019.

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21

Sánchez, Veralia Gabriela, Ola Marius Lysaker und Nils-Olav Skeie. „Human behaviour modelling for welfare technology using hidden Markov models“. Pattern Recognition Letters 137 (September 2020): 71–79. http://dx.doi.org/10.1016/j.patrec.2019.09.022.

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22

Megali, G., S. Sinigaglia, O. Tonet und P. Dario. „Modelling and Evaluation of Surgical Performance Using Hidden Markov Models“. IEEE Transactions on Biomedical Engineering 53, Nr. 10 (Oktober 2006): 1911–19. http://dx.doi.org/10.1109/tbme.2006.881784.

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23

Anisimov, Vladimir V., Hugo J. Maas, Meindert Danhof und Oscar Della Pasqua. „Analysis of responses in migraine modelling using hidden Markov models“. Statistics in Medicine 26, Nr. 22 (2007): 4163–78. http://dx.doi.org/10.1002/sim.2852.

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24

Lethanh, Nam, und Bryan T. Adey. „Use of exponential hidden Markov models for modelling pavement deterioration“. International Journal of Pavement Engineering 14, Nr. 7 (Oktober 2013): 645–54. http://dx.doi.org/10.1080/10298436.2012.715647.

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25

Huang, X. D., und M. A. Jack. „Hidden Markov modelling of speech based on a semicontinuous model“. Electronics Letters 24, Nr. 1 (07.01.1988): 6–7. http://dx.doi.org/10.1049/el:19880004.

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26

Fisher, Aiden, David Green und Andrew Metcalfe. „Modelling of hydrological persistence for hidden state Markov decision processes“. Annals of Operations Research 199, Nr. 1 (05.10.2011): 215–24. http://dx.doi.org/10.1007/s10479-011-0992-2.

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27

Ghiringhelli, C., F. Bartolucci, A. Mira und G. Arbia. „Modelling Nonstationary Spatial Lag Models with Hidden Markov Random Fields“. Spatial Statistics 44 (August 2021): 100522. http://dx.doi.org/10.1016/j.spasta.2021.100522.

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28

Sebastian, Tunny, Visalakshi Jeyaseelan, Lakshmanan Jeyaseelan, Shalini Anandan, Sebastian George und 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, Nr. 5 (04.04.2018): 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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29

MUKHERJEE, SHIBAJI, und SUSHMITA MITRA. „HIDDEN MARKOV MODELS, GRAMMARS, AND BIOLOGY: A TUTORIAL“. Journal of Bioinformatics and Computational Biology 03, Nr. 02 (April 2005): 491–526. http://dx.doi.org/10.1142/s0219720005001077.

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Biological sequences and structures have been modelled using various machine learning techniques and abstract mathematical concepts. This article surveys methods using Hidden Markov Model and functional grammars for this purpose. We provide a formal introduction to Hidden Markov Model and grammars, stressing on a comprehensive mathematical description of the methods and their natural continuity. The basic algorithms and their application to analyzing biological sequences and modelling structures of bio-molecules like proteins and nucleic acids are discussed. A comparison of the different approaches is discussed, and possible areas of work and problems are highlighted. Related databases and softwares, available on the internet, are also mentioned.

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DUVAL, LAURENT, und CAROLINE CHAUX. „LAPPED TRANSFORMS AND HIDDEN MARKOV MODELS FOR SEISMIC DATA FILTERING“. International Journal of Wavelets, Multiresolution and Information Processing 02, Nr. 04 (Dezember 2004): 455–76. http://dx.doi.org/10.1142/s0219691304000676.

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Seismic exploration provides information about the ground substructures. Seismic images are generally corrupted by several noise sources. Hence, efficient denoising procedures are required to improve the detection of essential geological information. Wavelet bases provide sparse representation for a wide class of signals and images. This property makes them good candidates for efficient filtering tools, allowing the separation of signal and noise coefficients. Recent works have improved their performance by modelling the intra- and inter-scale coefficient dependencies using hidden Markov models, since image features tend to cluster and persist in the wavelet domain. This work focuses on the use of lapped transforms associated with hidden Markov modelling. Lapped transforms are traditionally viewed as block-transforms, composed of M pass-band filters. Seismic data present oscillatory patterns and lapped transforms oscillatory bases have demonstrated good performances for seismic data compression. A dyadic like representation of lapped transform coefficient is possible, allowing a wavelet-like modelling of coefficients dependencies. We show that the proposed filtering algorithm often outperforms the wavelet performance both objectively (in terms of SNR) and subjectively: lapped transform better preserve the oscillatory features present in seismic data at low to moderate noise levels.

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31

BALDI, PIERRE. „Substitution Matrices and Hidden Markov Models“. Journal of Computational Biology 2, Nr. 3 (Januar 1995): 487–91. http://dx.doi.org/10.1089/cmb.1995.2.487.

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32

Genon-Catalot, Valentine, und Catherine Laredo. „Leroux's method for general hidden Markov models“. Stochastic Processes and their Applications 116, Nr. 2 (Februar 2006): 222–43. http://dx.doi.org/10.1016/j.spa.2005.10.005.

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33

GALIANO, I., E. SANCHIS, F. CASACUBERTA und I. TORRES. „ACOUSTIC-PHONETIC DECODING OF SPANISH CONTINUOUS SPEECH“. International Journal of Pattern Recognition and Artificial Intelligence 08, Nr. 01 (Februar 1994): 155–80. http://dx.doi.org/10.1142/s0218001494000073.

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The design of current acoustic-phonetic decoders for a specific language involves the selection of an adequate set of sublexical units, and a choice of the mathematical framework for modelling the corresponding units. In this work, the baseline chosen for continuous Spanish speech consists of 23 sublexical units that roughly correspond to the 24 Spanish phonemes. The process of selection of such a baseline was based on language phonetic criteria and some experiments with an available speech corpora. On the other hand, two types of models were chosen for this work, conventional Hidden Markov Models and Inferred Stochastic Regular Grammars. With these two choices we could compare classical Hidden Markov modelling where the structure of a unit-model is deductively supplied, with Grammatical Inference modelling where the baseforms of model-units are automatically generated from training samples. The best speaker-independent phone recognition rate was 64% for the first type of modelling, and 66% for the second type.

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34

Vaičiūnas, Airenas, Gailius Raškinis und Asta Kazlauskienė. „Corpus-Based Hidden Markov Modelling of the Fundamental Frequency of Lithuanian“. Informatica 27, Nr. 3 (01.01.2016): 673–88. http://dx.doi.org/10.15388/informatica.2016.105.

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35

Zhou, GuoDong. „Direct modelling of output context dependence in discriminative hidden Markov model“. Pattern Recognition Letters 26, Nr. 5 (April 2005): 545–53. http://dx.doi.org/10.1016/j.patrec.2004.09.009.

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36

Harrison, P. G., S. K. Harrison, N. M. Patel und S. Zertal. „Storage workload modelling by hidden Markov models: Application to Flash memory“. Performance Evaluation 69, Nr. 1 (Januar 2012): 17–40. http://dx.doi.org/10.1016/j.peva.2011.07.022.

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37

Lin, H. P., F. S. Tsai und M. J. Tseng. „Satellite propagation channel modelling using photogrammetry and hidden Markov model approach“. IEE Proceedings - Microwaves, Antennas and Propagation 148, Nr. 6 (2001): 375. http://dx.doi.org/10.1049/ip-map:20010728.

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38

Stjernqvist, Susann, Tobias Rydén, Martin Sköld und Johan Staaf. „Continuous-index hidden Markov modelling of array CGH copy number data“. Bioinformatics 23, Nr. 8 (19.02.2007): 1006–14. http://dx.doi.org/10.1093/bioinformatics/btm059.

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39

Wei-ho Chung und Kung Yao. „Modified hidden semi-markov model for modelling the flat fading channel“. IEEE Transactions on Communications 57, Nr. 6 (Juni 2009): 1806–14. http://dx.doi.org/10.1109/tcomm.2009.06.070417.

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40

Mastrantonio, Gianluca, Antonello Maruotti und Giovanna Jona-Lasinio. „Bayesian hidden Markov modelling using circular-linear general projected normal distribution“. Environmetrics 26, Nr. 2 (09.01.2015): 145–58. http://dx.doi.org/10.1002/env.2326.

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41

Vaseghi, S. V., P. N. Conner und B. P. Milner. „Speech modelling using cepstral-time feature matrices in hidden Markov models“. IEE Proceedings I Communications, Speech and Vision 140, Nr. 5 (1993): 317. http://dx.doi.org/10.1049/ip-i-2.1993.0046.

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42

Ariki, Y., und M. A. Jack. „Enhanced time duration constraints in hidden Markov modelling for phoneme recognition“. Electronics Letters 25, Nr. 13 (1989): 824. http://dx.doi.org/10.1049/el:19890555.

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43

Mitra, Sovan, und Tong Ji. „Optimisation of stochastic programming by hidden Markov modelling based scenario generation“. International Journal of Mathematics in Operational Research 2, Nr. 4 (2010): 436. http://dx.doi.org/10.1504/ijmor.2010.033439.

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44

Luck, Alexander, Pascal Giehr, Karl Nordstrom, Jorn Walter und Verena Wolf. „Hidden Markov Modelling Reveals Neighborhood Dependence of Dnmt3a and 3b Activity“. IEEE/ACM Transactions on Computational Biology and Bioinformatics 16, Nr. 5 (01.09.2019): 1598–609. http://dx.doi.org/10.1109/tcbb.2019.2910814.

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45

Le Ngo, Anh Cat, Kenneth Li-Minn Ang, Jasmine Kah-Phooi Seng und Guoping Qiu. „Multi-scale discriminant saliency with wavelet-based Hidden Markov Tree modelling“. Computers & Electrical Engineering 40, Nr. 4 (Mai 2014): 1376–89. http://dx.doi.org/10.1016/j.compeleceng.2014.01.012.

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46

Wu, Hao, und Frank Noé. „Probability Distance Based Compression of Hidden Markov Models“. Multiscale Modeling & Simulation 8, Nr. 5 (Januar 2010): 1838–61. http://dx.doi.org/10.1137/090774161.

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47

Aggoun, Lakhdar. „Recursive smoothers for hidden discrete-time Markov chains“. Journal of Applied Mathematics and Stochastic Analysis 2005, Nr. 3 (01.01.2005): 345–51. http://dx.doi.org/10.1155/jamsa.2005.345.

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We consider a discrete-time Markov chain observed through another Markov chain. The proposed model extends models discussed by Elliott et al. (1995). We propose improved recursive formulae to update smoothed estimates of processes related to the model. These recursive estimates are used to update the parameter of the model via the expectation maximization (EM) algorithm.

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48

Damian, Camilla, Zehra Eksi und Rüdiger Frey. „EM algorithm for Markov chains observed via Gaussian noise and point process information: Theory and case studies“. Statistics & Risk Modeling 35, Nr. 1-2 (01.01.2018): 51–72. http://dx.doi.org/10.1515/strm-2017-0021.

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AbstractIn this paper we study parameter estimation via the Expectation Maximization (EM) algorithm for a continuous-time hidden Markov model with diffusion and point process observation. Inference problems of this type arise for instance in credit risk modelling. A key step in the application of the EM algorithm is the derivation of finite-dimensional filters for the quantities that are needed in the E-Step of the algorithm. In this context we obtain exact, unnormalized and robust filters, and we discuss their numerical implementation. Moreover, we propose several goodness-of-fit tests for hidden Markov models with Gaussian noise and point process observation. We run an extensive simulation study to test speed and accuracy of our methodology. The paper closes with an application to credit risk: we estimate the parameters of a hidden Markov model for credit quality where the observations consist of rating transitions and credit spreads for US corporations.

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Goodall, Victoria L., Sam M. Ferreira, Paul J. Funston und Nkabeng Maruping-Mzileni. „Uncovering hidden states in African lion movement data using hidden Markov models“. Wildlife Research 46, Nr. 4 (2019): 296. http://dx.doi.org/10.1071/wr18004.

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Context Direct observations of animals are the most reliable way to define their behavioural characteristics; however, to obtain these observations is costly and often logistically challenging. GPS tracking allows finer-scale interpretation of animal responses by measuring movement patterns; however, the true behaviour of the animal during the period of observation is seldom known. Aims The aim of our research was to draw behavioural inferences for a lioness with a hidden Markov model and to validate the predicted latent-state sequence with field observations of the lion pride. Methods We used hidden Markov models to model the movement of a lioness in the Kruger National Park, South Africa. A three-state log-normal model was selected as the most suitable model. The model outputs are related to collected data by using an observational model, such as, for example, a distribution for the average movement rate and/or direction of movement that depends on the underlying model states that are taken to represent behavioural states of the animal. These inferred behavioural states are validated against direct observation of the pride’s behaviour. Key results Average movement rate provided a useful alternative for the application of hidden Markov models to irregularly spaced GPS locations. The movement model predicted resting as the dominant activity throughout the day, with a peak in the afternoon. The local-movement state occurred consistently throughout the day, with a decreased proportion during the afternoon, when more resting takes place, and an increase towards the early evening. The relocating state had three peaks, namely, during mid-morning, early evening and about midnight. Because of the differences in timing of the direct observations and the GPS locations, we had to compare point observations of the true behaviour with an interval prediction of the modelled behavioural state. In 75% of the cases, the model-predicted behaviour and the field-observed behaviour overlapped. Conclusions Our data suggest that the hidden Markov modelling approach is successful at predicting a realistic behaviour of lions on the basis of the GPS location coordinates and the average movement rate between locations. The present study provided a unique opportunity to uncover the hidden states and compare the true behaviour with the inferred behaviour from the predicted state sequence. Implications Our results illustrated the potential of using hidden Markov models with movement rate as an input to understand carnivore behavioural patterns that could inform conservation management practices.

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Huang, Huilin. „Strong Law of Large Numbers for Hidden Markov Chains Indexed by an Infinite Tree with Uniformly Bounded Degrees“. International Journal of Stochastic Analysis 2014 (09.12.2014): 1–6. http://dx.doi.org/10.1155/2014/628321.

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We study strong limit theorems for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees. We mainly establish the strong law of large numbers for hidden Markov chains fields indexed by an infinite tree with uniformly bounded degrees and give the strong limit law of the conditional sample entropy rate.

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