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 Sensitivity of hidden Markov models

2005 ◽  
Vol 42 (03) ◽  
pp. 632-642 ◽  
Author(s):  
Alexander Yu. Mitrophanov ◽  
Alexandre Lomsadze ◽  
Mark Borodovsky
Keyword(s):  
Markov Chain ◽  
Hidden Markov Models ◽  
Stochastic Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Initial Distribution ◽  
Transition Probability Matrix ◽  
Perturbation Bound ◽  
Semi Markov Processes

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.

scholarly journals Sensitivity of hidden Markov models

2005 ◽  
Vol 42 (3) ◽  
pp. 632-642 ◽  
Author(s):  
Alexander Yu. Mitrophanov ◽  
Alexandre Lomsadze ◽  
Mark Borodovsky
Keyword(s):  
Markov Chain ◽  
Hidden Markov Models ◽  
Stochastic Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Transition Probability ◽  
Initial Distribution ◽  
Transition Probability Matrix ◽  
Perturbation Bound ◽  
Semi Markov Processes

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.

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

scholarly journals Handling underlying discrete variables with bivariate mixed hidden Markov models in NONMEM

2019 ◽  
Vol 46 (6) ◽  
pp. 591-604 ◽  
Author(s):  
A. Brekkan ◽  
S. Jönsson ◽  
M. O. Karlsson ◽  
E. L. Plan
Keyword(s):  
Hidden Markov Models ◽  
Transition Rate ◽  
Markov Models ◽  
Drug Effect ◽  
Hidden Markov ◽  
Transition Probability ◽  
Hidden Variables ◽  
Model Parameters ◽  
Patient Reported ◽  
Parameter Precision

Abstract Non-linear mixed effects models typically deal with stochasticity in observed processes but models accounting for only observed processes may not be the most appropriate for all data. Hidden Markov models (HMMs) characterize the relationship between observed and hidden variables where the hidden variables can represent an underlying and unmeasurable disease status for example. Adding stochasticity to HMMs results in mixed HMMs (MHMMs) which potentially allow for the characterization of variability in unobservable processes. Further, HMMs can be extended to include more than one observation source and are then multivariate HMMs. In this work MHMMs were developed and applied in a chronic obstructive pulmonary disease example. The two hidden states included in the model were remission and exacerbation and two observation sources were considered, patient reported outcomes (PROs) and forced expiratory volume (FEV1). Estimation properties in the software NONMEM of model parameters were investigated with and without random and covariate effect parameters. The influence of including random and covariate effects of varying magnitudes on the parameters in the model was quantified and a power analysis was performed to compare the power of a single bivariate MHMM with two separate univariate MHMMs. A bivariate MHMM was developed for simulating and analysing hypothetical COPD data consisting of PRO and FEV1 measurements collected every week for 60 weeks. Parameter precision was high for all parameters with the exception of the variance of the transition rate dictating the transition from remission to exacerbation (relative root mean squared error [RRMSE] > 150%). Parameter precision was better with higher magnitudes of the transition probability parameters. A drug effect was included on the transition rate probability and the precision of the drug effect parameter improved with increasing magnitude of the parameter. The power to detect the drug effect was improved by utilizing a bivariate MHMM model over the univariate MHMM models where the number of subject required for 80% power was 25 with the bivariate MHMM model versus 63 in the univariate MHMM FEV1 model and > 100 in the univariate MHMM PRO model. The results advocates for the use of bivariate MHMM models when implementation is possible.

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