Hidden Markov models with duration-dependent state transition probabilities

1991 ◽  
Vol 27 (8) ◽  
pp. 625 ◽  
Author(s):  
S.V. Vaseghi
Keyword(s):  
Hidden Markov Models ◽  
State Transition ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Dependent State

scholarly journals Worth the effort? A practical examination of random effects in hidden Markov models for animal telemetry data

2020 ◽  
Author(s):  
Brett T. McClintock
Keyword(s):  
Hidden Markov Models ◽  
Random Effects ◽  
State Transition ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Random Effect ◽  
Costs And Benefits ◽  
State Process ◽  
Random Effect Models

AbstractHidden Markov models (HMMs) that include individual-level random effects have recently been promoted for inferring animal movement behaviour from biotelemetry data. These “mixed HMMs” come at significant cost in terms of implementation and computation, and discrete random effects have been advocated as a practical alternative to more computationally-intensive continuous random effects. However, the performance of mixed HMMs has not yet been sufficiently explored to justify their widespread adoption, and there is currently little guidance for practitioners weighing the costs and benefits of mixed HMMs for a particular research objective.I performed an extensive simulation study comparing the performance of a suite of fixed and random effect models for individual heterogeneity in the hidden state process of a 2-state HMM. I focused on sampling scenarios more typical of telemetry studies, which often consist of relatively long time series (30 – 250 observations per animal) for relatively few individuals (5 – 100 animals).I generally found mixed HMMs did not improve state assignment relative to standard HMMs. Reliable estimation of random effects required larger sample sizes than are often feasible in telemetry studies. Continuous random effect models performed reasonably well with data generated under discrete random effects, but not vice versa. Random effects accounting for unexplained individual variation can improve estimation of state transition probabilities and measurable covariate effects, but discrete random effects can be a relatively poor (and potentially misleading) approximation for continuous variation.When weighing the costs and benefits of mixed HMMs, three important considerations are study objectives, sample size, and model complexity. HMM applications often focus on state assignment with little emphasis on heterogeneity in state transition probabilities, in which case random effects in the hidden state process simply may not be worth the additional effort. However, if explaining variation in state transition probabilities is a primary objective and sufficient explanatory covariates are not available, then random effects are worth pursuing as a more parsimonious alternative to individual fixed effects.To help put my findings in context and illustrate some potential challenges that practitioners may encounter when applying mixed HMMs, I revisit a previous analysis of long-finned pilot whale biotelemetry data.

Extracting State Transition Dynamics from Multiple Spike Trains Using Hidden Markov Models with Correlated Poisson Distribution

2010 ◽  
Vol 22 (9) ◽  
pp. 2369-2389 ◽  
Author(s):  
Kentaro Katahira ◽  
Jun Nishikawa ◽  
Kazuo Okanoya ◽  
Masato Okada
Keyword(s):  
Hidden Markov Models ◽  
Poisson Distribution ◽  
State Transition ◽  
Markov Models ◽  
Hidden Markov ◽  
Synthetic Data ◽  
Poisson Model ◽  
Spike Trains ◽  
Output Distribution ◽  
Multivariate Poisson Distribution

Neural activity is nonstationary and varies across time. Hidden Markov models (HMMs) have been used to track the state transition among quasi-stationary discrete neural states. Within this context, an independent Poisson model has been used for the output distribution of HMMs; hence, the model is incapable of tracking the change in correlation without modulating the firing rate. To achieve this, we applied a multivariate Poisson distribution with correlation terms for the output distribution of HMMs. We formulated a variational Bayes (VB) inference for the model. The VB could automatically determine the appropriate number of hidden states and correlation types while avoiding the overlearning problem. We developed an efficient algorithm for computing posteriors using the recursive relationship of a multivariate Poisson distribution. We demonstrated the performance of our method on synthetic data and real spike trains recorded from a songbird.

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/ .

Equivalence of Linear Boltzmann Chains and Hidden Markov Models

1996 ◽  
Vol 8 (1) ◽  
pp. 178-181 ◽  
Author(s):  
David J. C. MacKay
Keyword(s):  
Probability Distribution ◽  
Markov Model ◽  
Hidden Markov Models ◽  
State Transition ◽  
Markov Models ◽  
Hidden Markov ◽  
Simple Condition ◽  
Transition Energies ◽  
State Sequence ◽  
The Relationship

Several authors have studied the relationship between hidden Markov models and “Boltzmann chains” with a linear or “time-sliced” architecture. Boltzmann chains model sequences of states by defining state-state transition energies instead of probabilities. In this note I demonstrate that under the simple condition that the state sequence has a mandatory end state, the probability distribution assigned by a strictly linear Boltzmann chain is identical to that assigned by a hidden Markov model.

scholarly journals A non-parametric hidden Markov model for climate state identification

2003 ◽  
Vol 7 (5) ◽  
pp. 652-667 ◽  
Author(s):  
M. F. Lambert ◽  
J. P. Whiting ◽  
A. V. Metcalfe
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Probability Distributions ◽  
Parametric Model ◽  
The State ◽  
Conditional Distributions ◽  
Wet And Dry Cycles ◽  
Non Parametric

Abstract. Hidden Markov models (HMMs) can allow for the varying wet and dry cycles in the climate without the need to simulate supplementary climate variables. The fitting of a parametric HMM relies upon assumptions for the state conditional distributions. It is shown that inappropriate assumptions about state conditional distributions can lead to biased estimates of state transition probabilities. An alternative non-parametric model with a hidden state structure that overcomes this problem is described. It is shown that a two-state non-parametric model produces accurate estimates of both transition probabilities and the state conditional distributions. The non-parametric model can be used directly or as a technique for identifying appropriate state conditional distributions to apply when fitting a parametric HMM. The non-parametric model is fitted to data from ten rainfall stations and four streamflow gauging stations at varying distances inland from the Pacific coast of Australia. Evidence for hydrological persistence, though not mathematical persistence, was identified in both rainfall and streamflow records, with the latter showing hidden states with longer sojourn times. Persistence appears to increase with distance from the coast. Keywords: Hidden Markov models, non-parametric, two-state model, climate states, persistence, probability distributions

Metal Label Pressed Protuberant Characters Recognition Based on Hidden Markov Model

2011 ◽  
Vol 187 ◽  
pp. 667-671
Author(s):  
Wei Chen
Keyword(s):  
Neural Network ◽  
Markov Model ◽  
Hidden Markov Models ◽  
State Transition ◽  
Markov Models ◽  
Hidden Markov ◽  
Shape Index ◽  
Surface Curvature ◽  
Word Choice ◽  
Recognition Method

A recognition method of pressed protuberant characters based on Hidden Markov models and Neural Network is applied, which the surface curvature properties and the relation of metal label characters are analyzed in detail. The shape index of the characters is extracted. A neural network is used to estimate probabilities for the characters depended on the surface curvature properties, then deriving the best word choice from a sequence of state transition. It is shown in test that the proposed method can be used to recognize the pressed protuberant on metal label.

scholarly journals A Hidden Semi-Markov Model with Duration-Dependent State Transition Probabilities for Prognostics

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ning Wang ◽  
Shu-dong Sun ◽  
Zhi-qiang Cai ◽  
Shuai Zhang ◽  
Can Saygin
Keyword(s):  
Markov Model ◽  
State Transition ◽  
Markov Models ◽  
Transition Probabilities ◽  
Independence Assumption ◽  
Modeling And Analysis ◽  
Maintenance Systems ◽  
Dependent State ◽  
Real World Problems

Realistic prognostic tools are essential for effective condition-based maintenance systems. In this paper, a Duration-Dependent Hidden Semi-Markov Model (DD-HSMM) is proposed, which overcomes the shortcomings of traditional Hidden Markov Models (HMM), including the Hidden Semi-Markov Model (HSMM): (1) it allows explicit modeling of state transition probabilities between the states; (2) it relaxes observations’ independence assumption by accommodating a connection between consecutive observations; and (3) it does not follow the unrealistic Markov chain’s memoryless assumption and therefore it provides a more powerful modeling and analysis capability for real world problems. To facilitate the computation of the proposed DD-HSMM methodology, new forward-backward algorithm is developed. The demonstration and evaluation of the proposed methodology is carried out through a case study. The experimental results show that the DD-HSMM methodology is effective for equipment health monitoring and management.

scholarly journals Residence Time Analysis of RNA Polymerase Transcription Dynamics: A Bayesian Sticky HMM Approach

2020 ◽  
Author(s):  
Zeliha Kilic ◽  
Ioannis Sgouralis ◽  
Steve Pressé
Keyword(s):  
Rna Polymerase ◽  
Hidden Markov Models ◽  
Residence Time ◽  
Optical Trapping ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
Transcription Elongation ◽  
Residence Times ◽  
Average Residence Time

ABSTRACTThe time spent by a single RNA polymerase (RNAP) at specific locations along the DNA, termed “residence time”, reports on the initiation, elongation and termination stages of transcription. At the single molecule level, this information can be obtained from dual ultra-stable optical trapping experiments, revealing a transcriptional elongation of RNAP interspersed with residence times of variable duration. Successfully discriminating between long and short residence times was used by previous approaches to learn about RNAP’s transcription elongation dynamics. Here, we propose an approach based on the Bayesian sticky hidden Markov models that treats all residence times, for an E. Coli RNAP, on an equal footing without a priori discriminating between long and short residence times. In addition, our method has two additional advantages, we provide: full distributions around key point statistics; and directly treat the sequence-dependence of RNAP’s elongation rate.By applying our approach to experimental data, we find: no emergent separation between long and short residence times warranted by the data; force dependent average residence time transcription elongation dynamics; limited effects of GreB on average backtracking durations and counts; and a slight drop in the average residence time as a function of applied force in RNaseA’s presence.STATEMENT OF SIGNIFICANCEMuch of what we know about RNA Polymerase, and its associated transcription factors, relies on successfully discriminating between what are believed to be short and long residence times in the data. This is achieved by applying pause-detection algorithms to trace analysis. Here we propose a new method relying on Bayesian sticky hidden Markov models to interpret time traces provided by dual optical trapping experiments associated with transcription elongation of RNAP. Our method does not discriminate between short and long residence times from the offset in the analysis. It allows for DNA site-dependent transition probabilities of RNAP to neighboring sites (thereby accounting for chemical variability in site to site transitions) and does not demand any time trace pre-processing (such as denoising).

scholarly journals Revealing Ensemble State Transition Patterns in Multi-Electrode Neuronal Recordings Using Hidden Markov Models

2011 ◽  
Vol 19 (4) ◽  
pp. 345-355 ◽  
Author(s):  
D. Xydas ◽  
J. H. Downes ◽  
M. C. Spencer ◽  
M. W. Hammond ◽  
S. J. Nasuto ◽  
...  
Keyword(s):  
Hidden Markov Models ◽  
State Transition ◽  
Markov Models ◽  
Hidden Markov

Bayesian quantile nonhomogeneous hidden Markov models

2020 ◽  
pp. 096228022094280 ◽  
Author(s):  
Hefei Liu ◽  
Xinyuan Song ◽  
Yanlin Tang ◽  
Baoxue Zhang
Keyword(s):  
Hidden Markov Models ◽  
Markov Models ◽  
Transition Probabilities ◽  
Hidden Markov ◽  
State Transitions ◽  
Response Distribution ◽  
Cocaine Use ◽  
Longitudinal Response ◽  
Observation Process ◽  
Time Specific

Hidden Markov models are useful in simultaneously analyzing a longitudinal observation process and its dynamic transition. Existing hidden Markov models focus on mean regression for the longitudinal response. However, the tails of the response distribution are as important as the center in many substantive studies. We propose a quantile hidden Markov model to provide a systematic method to examine the entire conditional distribution of the response given the hidden state and potential covariates. Instead of considering homogeneous hidden Markov models, which assume that the probabilities of between-state transitions are independent of subject- and time-specific characteristics, we allow the transition probabilities to depend on exogenous covariates, thereby yielding nonhomogeneous Markov chains and making the proposed model more flexible than its homogeneous counterpart. We develop a Bayesian approach coupled with efficient Markov chain Monte Carlo methods for statistical inference. Simulations are conducted to assess the empirical performance of the proposed method. The proposed methodology is applied to a cocaine use study to provide new insights into the prevention of cocaine use.

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