scholarly journals On Determining the Order of Markov Dependence of an Observed Process Governed by a Hidden Markov Model

2002 ◽  
Vol 10 (3) ◽  
pp. 241-251 ◽  
Author(s):  
R.J. Boys ◽  
D.A. Henderson
Keyword(s):  
Markov Chain ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Real Data ◽  
Information Criteria ◽  
Monte Carlo Algorithm ◽  
Model Parameters ◽  
Markov Dependence ◽  
Finite State

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.

scholarly journals On the rate of convergence for the length of the longest common subsequences in hidden Markov models

2019 ◽  
Vol 56 (2) ◽  
pp. 558-573
Author(s):  
C. Houdré ◽  
G. Kerchev
Keyword(s):  
Markov Chain ◽  
Rate Of Convergence ◽  
Hidden Markov Models ◽  
Markov Models ◽  
Hidden Markov ◽  
Convergence Result ◽  
Output Process ◽  
Longest Common Subsequences ◽  
Finite State ◽  
Irreducible Markov Chain

AbstractLet (X, Y) = (Xn, Yn)n≥1 be the output process generated by a hidden chain Z = (Zn)n≥1, where Z is a finite-state, aperiodic, time homogeneous, and irreducible Markov chain. Let LCn be the length of the longest common subsequences of X1,..., Xn and Y1,..., Yn. Under a mixing hypothesis, a rate of convergence result is obtained for E[LCn]/n.

An MEWMA-based segmental multivariate hidden Markov model for degradation assessment and prediction

2021 ◽  
pp. 1748006X2199052
Author(s):  
Yaping Li ◽  
Enrico Zio ◽  
Ershun Pan
Keyword(s):  
Markov Models ◽  
Hidden Markov ◽  
Average Run Length ◽  
Moving Average ◽  
Model Parameters ◽  
Current Time ◽  
Multivariate Processes ◽  
Industrial Systems ◽  
Hidden States ◽  
Multivariate Signals

Degradation is an unavoidable phenomenon in industrial systems. Hidden Markov models (HMMs) have been used for degradation modeling. In particular, segmental HMMs have been developed to model the explicit relationship between degradation signals and hidden states. However, existing segmental HMMs deal only with univariate cases, whereas in real systems, signals from various sensors are collected simultaneously, which makes it necessary to adapt the segmental HMMs to deal with multivariate processes. Also, to make full use of the information from the sensors, it is important to differentiate stable signals from deteriorating ones, but there is no good way for this, especially in multivariate processes. In this paper, the multivariate exponentially weighted moving average (MEWMA) control chart is employed to identify deteriorating multivariate signals. Specifically, the MEWMA statistic is used as a comprehensive indicator for differentiating multivariate observations. Likelihood Maximization is used to estimate the model parameters. To avoid underflow, the forward and backward probabilities are normalized. In order to assess degradation, joint probabilities are defined and derived. Further, the occurrence probability of each degradation state at the current time, as well as in the future, is derived. The Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset of NASA is employed for comparative analysis. In terms of degradation assessment and prediction, the proposed model performs very well in general. By sensitivity analysis, we show that in order to improve further the performance of the method, the weight of the chart should be set relatively small, whereas the method is not sensitive to the change of the in-control average run length (ARL).

scholarly journals Bayesian selection of Hidden Markov models for multi-dimensional ion channel data

2020 ◽  
Author(s):  
Jan Münch ◽  
Fabian Paul ◽  
Ralf Schmauder ◽  
Klaus Benndorf
Keyword(s):  
Hidden Markov Models ◽  
Cross Validation ◽  
Markov Models ◽  
Hidden Markov ◽  
Conformational Dynamics ◽  
Kinetic Scheme ◽  
Rate Equations ◽  
Model Parameters ◽  
Limited Information ◽  
Daunting Task

AbstractInferring the complex conformational dynamics of ion channels from ensemble currents is a daunting task due to limited information in the data leading to poorly determined model inference and selection. We address this problem with a parallelized Kalman filter for specifying Hidden Markov Models for current and fluorescence data. We demonstrate the flexibility of this Bayesian network by including different noises distributions. The accuracy of the parameter estimation is increased by tenfold compared to fitting Rate Equations. Furthermore, adding orthogonal fluorescence data increases the accuracy of the model parameters by up to two orders of magnitude. Additional prior information alleviates parameter unidenfiability for weakly informative data. We show that with Rate Equations a reliable detection of the true kinetic scheme requires cross validation. In contrast, our algorithm avoids overfitting by automatically switching of rates (continuous model expansion), by cross-validation, by applying the ‘widely applicable information criterion’ or variance-based model selection.

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

Extending hidden Markov models to allow conditioning on previous observations

2018 ◽  
Vol 16 (05) ◽  
pp. 1850019 ◽  
Author(s):  
Ioannis A. Tamposis ◽  
Margarita C. Theodoropoulou ◽  
Konstantinos D. Tsirigos ◽  
Pantelis G. Bagos
Keyword(s):  
Hidden Markov Models ◽  
Probabilistic Models ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Simple Extension ◽  
Computational Molecular Biology ◽  
Current State ◽  
Observation Sequence ◽  
Hidden States

Hidden Markov Models (HMMs) are probabilistic models widely used in computational molecular biology. However, the Markovian assumption regarding transition probabilities which dictates that the observed symbol depends only on the current state may not be sufficient for some biological problems. In order to overcome the limitations of the first order HMM, a number of extensions have been proposed in the literature to incorporate past information in HMMs conditioning either on the hidden states, or on the observations, or both. Here, we implement a simple extension of the standard HMM in which the current observed symbol (amino acid residue) depends both on the current state and on a series of observed previous symbols. The major advantage of the method is the simplicity in the implementation, which is achieved by properly transforming the observation sequence, using an extended alphabet. Thus, it can utilize all the available algorithms for the training and decoding of HMMs. We investigated the use of several encoding schemes and performed tests in a number of important biological problems previously studied by our team (prediction of transmembrane proteins and prediction of signal peptides). The evaluation shows that, when enough data are available, the performance increased by 1.8%–8.2% and the existing prediction methods may improve using this approach. The methods, for which the improvement was significant (PRED-TMBB2, PRED-TAT and HMM-TM), are available as web-servers freely accessible to academic users at www.compgen.org/tools/ .

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