Markov Chain Models and Hidden Markov Models

Data Mining ◽  
2013 ◽  
pp. 287-305
Author(s):  
Nong Ye
Keyword(s):  
Markov Chain ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Markov Chain Models

Markov chain existence and Hidden Markov models in spectrum sensing

2009 ◽  
Author(s):  
Chittabrata Ghosh ◽  
Carlos Cordeiro ◽  
Dharma P. Agrawal ◽  
M. Bhaskara Rao
Keyword(s):  
Markov Chain ◽  
Hidden Markov Models ◽  
Spectrum Sensing ◽  
Markov Models ◽  
Hidden Markov

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models

2018 ◽  
Vol 28 (5) ◽  
pp. 1552-1563 ◽  
Author(s):  
Tunny Sebastian ◽  
Visalakshi Jeyaseelan ◽  
Lakshmanan Jeyaseelan ◽  
Shalini Anandan ◽  
Sebastian George ◽  
...  
Keyword(s):  
Logistic Regression ◽  
Markov Chain ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Passage Time ◽  
Transition Probability Matrix ◽  
Ordinal Logistic Regression ◽  
The Mean

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.

scholarly journals Time series segmentation with shifting means hidden markov models

2006 ◽  
Vol 13 (3) ◽  
pp. 339-352 ◽  
Author(s):  
Ath. Kehagias ◽  
V. Fortin
Keyword(s):  
Time Series ◽  
Markov Chain ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Computing Time ◽  
Estimation Method ◽  
Discrete State ◽  
New Family ◽  
Starting Point

Abstract. We present a new family of hidden Markov models and apply these to the segmentation of hydrological and environmental time series. The proposed hidden Markov models have a discrete state space and their structure is inspired from the shifting means models introduced by Chernoff and Zacks and by Salas and Boes. An estimation method inspired from the EM algorithm is proposed, and we show that it can accurately identify multiple change-points in a time series. We also show that the solution obtained using this algorithm can serve as a starting point for a Monte-Carlo Markov chain Bayesian estimation method, thus reducing the computing time needed for the Markov chain to converge to a stationary distribution.

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