Non-homogeneous Markov Model Research Articles

Potential climate predictability of renewable energy supply and demand for Texas given the ENSO hidden state.

Climate variability influences renewable electricity supply and demand and hence system reliability. Using the hidden states of the sea surface temperature of tropical Pacific Ocean that reflect El Niño-Southern Oscillation (ENSO) dynamics that is objectively identified by a nonhomogeneous hidden Markov model, we provide a first example of the potential predictability of monthly wind and solar energy and heating and cooling energy demand for 1 to 6 months ahead for Texas, United States, a region that has a high penetration of renewable electricity and is susceptible to disruption by climate-driven supply-demand imbalances. We find a statistically significant potential for oversupply or undersupply of energy and anomalous heating/cooling demand depending on the ENSO state and the calendar month. Implications for financial securitization and the potential application of forecasts are discussed.

Nonhomogeneous hidden semi-Markov models for toroidal data

Abstract A nonhomogeneous hidden semi-Markov model is proposed to segment bivariate time series of wind and wave directions according to a finite number of latent regimes and, simultaneously, estimate the influence of time-varying covariates on the process’ survival under each regime. The model is a mixture of toroidal densities, whose parameters depend on the evolution of a semi-Markov chain, which is in turn modulated by time-varying covariates. It includes nonhomogeneous hidden Markov models and hidden semi-Markov models as special cases. Parameter estimates are obtained using an Expectation-Maximization algorithm that relies on an efficient augmentation of the latent process. Fitted on a time series of wind and wave directions recorded in the Adriatic Sea, the model offers a clear-cut description of sea state dynamics in terms of latent regimes and captures the influence of time-varying weather conditions on the duration of such regimes.

Role of Multistate Models to Predict Patency, Limb Salvage, and Survival: New Concepts to Analyse Data in Peripheral Arterial Disease

In peripheral arterial disease, patency, limb salvage, and survival rates are mostly reported using Kaplan-Meier analyses. When comparing different revascularisation techniques, these methods have limitations in analysing complex patient flows over time. This study aimed to present, illustrate, and discuss new concepts based on multistate models of analysing outcome parameters in peripheral arterial disease. Previously published data from a single centre, randomised controlled trial (RCT) with 218 cases that underwent either vein bypass surgery (bypass group, n = 109) or nitinol stent angioplasty (stent group, n = 109) of long femoropopliteal lesions were re-analysed using non-homogeneous Markov models. A step by step description of the concepts of states, state space, definitions, and illustration of transition probability curves as well as the benefits of multistate models is given. The RCT was registered at ISRCTN.com (ISRCTN18315574). Transition probability curves over time showed similar patterns in the bypass and stent groups. Significant differences in the transition probabilities were found for transitions from primary patency as well as secondary patency to end of patency. The transition probability for patients with preserved primary patency at 24 months who moved to end of patency at 48 months was 19.9% in the stent group vs. 6.4% in the bypass group (p < .001). The proposed method can answer important questions, such as: Did patients after femoropopliteal stenting with preserved primary patency at two years lose their patency more quickly within the following years compared with bypass surgery? and Did stent patients after a re-intervention to maintain patency at one year lose their patency more quickly compared with bypass surgery within the following years? Completely new research questions can now be raised and answered to optimise treatment and follow up strategies; this might lead to better identification of subgroups at higher risk of clinical deterioration following revascularisation procedures.

The analysis of asthma control using Markov models: MOSAR study (Multicenter Observational Study of Asthma in Rabat-Morocco)

Background This study aimed to analyze the probabilities of transitioning between controlled, uncontrolled, and partially controlled states of asthma patients and investigate the influence of age, smoking, dust allergy, and obesity on these probabilities. Methods This study aimed to analyze the probabilities of transitioning between controlled, uncontrolled, and partially controlled states of asthma patients and investigate the influence of age, smoking, dust allergy, and obesity on these probabilities. Results Results showed that controlled patients were more likely to remain in that state, with approximately 79 out of 100 patients expected to stay in optimal control in the long term. A discrete nonhomogeneous time Markov Model with the stationarity criterion was used to examine the factors affecting patient states and transitions. Patients seen during the spring and summer seasons were more likely to move into a controlled state compared with those seen in the fall and winter seasons. Patients with dust allergies and obesity significantly impacted asthma exacerbation, with overweight patients more likely to transition into a controlled state. The study estimated the transition intensities matrix under certain conditions, assuming the regularity of patients. In the long term, the probability of an asthmatic patient being in a controlled state was approximately 0.8. Conclusion This study provided insights into the probabilities and factors influencing asthma progression in Morocco. Dust allergy and obesity were identified as significant contributors to asthma exacerbation, emphasizing the need for effective management strategies.

A Reliability Assessment Method for Complex Systems Based on Non-Homogeneous Markov Processes.

The Markov method is a common reliability assessment method. It is often used to describe the dynamic characteristics of a system, such as its repairability, fault sequence and multiple degradation states. However, the "curse of dimensionality", which refers to the exponential growth of the system state space with the increase in system complexity, presents a challenge to reliability assessments for complex systems based on the Markov method. In response to this challenge, a novel reliability assessment method for complex systems based on non-homogeneous Markov processes is proposed. This method entails the decomposition of a complex system into multilevel subsystems, each with a relatively small state space, in accordance with the system function. The homogeneous Markov model or the non-homogeneous Markov model is established for each subsystem/system from bottom to top. In order to utilize the outcomes of the lower-level subsystem models as inputs to the upper-level subsystem model, an algorithm is proposed for converting the unavailability curve of a subsystem into its corresponding 2×2 dynamic state transition probability matrix (STPM). The STPM is then employed as an input to the upper-level system's non-homogeneous Markov model. A case study is presented using the reliability assessment of the Reactor Protection System (RPS) based on the proposed method, which is then compared with the models based on the other two contrast methods. This comparison verifies the effectiveness and accuracy of the proposed method.

Correction to “The predictability of daily rainfall during rainy season over East Asia by a Bayesian nonhomogeneous hidden Markov model”

Correction to “The predictability of daily rainfall during rainy season over East Asia by a Bayesian nonhomogeneous hidden Markov model”

A predictor-informed multi-subject bayesian approach for dynamic functional connectivity.

Dynamic functional connectivity investigates how the interactions among brain regions vary over the course of an fMRI experiment. Such transitions between different individual connectivity states can be modulated by changes in underlying physiological mechanisms that drive functional network dynamics, e.g., changes in attention or cognitive effort. In this paper, we develop a multi-subject Bayesian framework where the estimation of dynamic functional networks is informed by time-varying exogenous physiological covariates that are simultaneously recorded in each subject during the fMRI experiment. More specifically, we consider a dynamic Gaussian graphical model approach where a non-homogeneous hidden Markov model is employed to classify the fMRI time series into latent neurological states. We assume the state-transition probabilities to vary over time and across subjects as a function of the underlying covariates, allowing for the estimation of recurrent connectivity patterns and the sharing of networks among the subjects. We further assume sparsity in the network structures via shrinkage priors, and achieve edge selection in the estimated graph structures by introducing a multi-comparison procedure for shrinkage-based inferences with Bayesian false discovery rate control. We evaluate the performances of our method vs alternative approaches on synthetic data. We apply our modeling framework on a resting-state experiment where fMRI data have been collected concurrently with pupillometry measurements, as a proxy of cognitive processing, and assess the heterogeneity of the effects of changes in pupil dilation on the subjects' propensity to change connectivity states. The heterogeneity of state occupancy across subjects provides an understanding of the relationship between increased pupil dilation and transitions toward different cognitive states.

FinaleMe: Predicting DNA methylation by the fragmentation patterns of plasma cell-free DNA

Analysis of DNA methylation in cell-free DNA reveals clinically relevant biomarkers but requires specialized protocols such as whole-genome bisulfite sequencing. Meanwhile, millions of cell-free DNA samples are being profiled by whole-genome sequencing. Here, we develop FinaleMe, a non-homogeneous Hidden Markov Model, to predict DNA methylation of cell-free DNA and, therefore, tissues-of-origin, directly from plasma whole-genome sequencing. We validate the performance with 80 pairs of deep and shallow-coverage whole-genome sequencing and whole-genome bisulfite sequencing data.

Event-based asynchronous state estimation for Markov jump memristive neural networks

This study endeavors to address the problem of asynchronous state estimation for generalized Markov jump memristive neural networks in the presence of a piecewise homogeneous Markov process and a memory-based dynamic event-triggered protocol. To avoid the commonly made assumption of time-invariant transition probabilities, a piecewise-homogeneous Markov chain is presented, wherein the variations of transition probabilities are regulated by a higher-level Markov process. Additionally, a memory-based dynamic event-triggered protocol is proposed to leverage the useful information contained in historically launched packets and achieve better control performance. Moreover, a hidden nonhomogeneous Markov model strategy is utilized to identify the modes mismatch between the estimator and the Markov jump memristive neural networks. This greatly reduces the complexity of processing the mode information of the system. Eventually, to verify the effectiveness of the theoretical results, a simulation example is carried out.

An investigation into the abnormal dynamic connection mechanism of generalized anxiety disorders based on non-homogeneous Markov models

BackgroundThe dynamic and hierarchical nature of the functional brain network. The neural dynamical systems tend to converge to multiple attractors (stable fixed points or dynamical states) in long run. Little is known about how the changes in this brain dynamic “long-term” behavior of the connectivity flow of brain network in generalized anxiety disorder (GAD). MethodsThis study recruited 92 patients with GAD and 77 healthy controls (HC). We applied a reachable probability approach combining a Non-homogeneous Markov model with transition probability to quantify all possible connectivity flows and the hierarchical structure of brain functional systems at the dynamic level and the stationary probability vector (10-step transition probabilities) to describe the steady state of the system in the long run. A random forest algorithm was conducted to predict the severity of anxiety. ResultsThe dynamic functional patterns in distributed brain networks had larger possibility to converge in bilateral thalamus, posterior cingulate cortex (PCC), right superior occipital gyrus (SOG) and smaller possibility to converge in bilateral superior temporal gyrus (STG) and right parahippocampal gyrus (PHG) in patients with GAD compared to HC. The abnormal transition probability pattern could predict anxiety severity in patients with GAD. LimitationsSmall samples and subjects taking medications may have influenced our results. Future studies are expected to rule out the potential confounding effects. ConclusionOur results have revealed abnormal dynamic neural communication and integration in emotion regulation in patients with GAD, which give new insights to understand the dynamics of brain function of patients with GAD.

Proportional-Integral Observer-Based State Estimation for Singularly Perturbed Complex Networks With Cyberattacks.

This article investigates the asynchronous proportional-integral observer (PIO) design issue for singularly perturbed complex networks (SPCNs) subject to cyberattacks. The switching topology of SPCNs is regulated by a nonhomogeneous Markov switching process, whose time-varying transition probabilities are polytope structured. Besides, the multiple scalar Winner processes are applied to character the stochastic disturbances of the inner linking strengths. Two mutually independent Bernoulli stochastic variables are exploited to characterize the random occurrences of cyberattacks. In a practical viewpoint, by resorting to the hidden nonhomogeneous Markov model, an asynchronous PIO is formulated. Under such a framework, by applying the Lyapunov theory, sufficient conditions are established such that the augmented dynamic is mean-square exponentially ultimately bounded. Finally, the effectiveness of the theoretical results is verified by two numerical simulations.

The predictability of daily rainfall during rainy season over East Asia by a Bayesian nonhomogeneous hidden Markov model

AbstractPrecipitation plays a significant role in human society and the environment, and how large‐scale climatic features influence precipitation has obtained worldwide attention. The nonhomogeneous hidden Markov model (NHMM) is a typical method to downscale large‐scale climatic elements to the regional level for many hydrologic applications. The traditional NHMM using point estimates of parameters has the risk to have no solutions for parameter estimation, but the Bayesian‐NHMM provides a Bayesian method to estimate parameters and avoids the risk. In this study, the suitability of the Bayesian‐NHMM in East Asia is evaluated. Two typical regions (i.e., the Yangtze River basin and the Zhujiang River basin in China) dominated by different climates were chosen to check model performance. Results show that: (1) the model could divide rainy‐season precipitation into several hidden states, whose variation is correspondent to the variability of monsoon and flux moisture transportation; (2) the model captures seasonality and inter‐annual variation of precipitation amount and also wet days during rainy season well in both river basins. These results suggest that the model could improve the prediction of daily precipitation in East Asia, which in turn could help many regions with similar climatic conditions worldwide to supervise floods and droughts.

Similarity learning hidden semi-Markov model for adaptive prognostics of composite structures

Data-driven methodologies have found increasing usage in the last decade for remaining useful life (RUL) prognostics of composite materials utilizing structural health monitoring (SHM) data. Of particular interest is the reliable RUL prediction in cases where the end-of-life is not in between the extreme values within the testing dataset. For example, when unexpected phenomena that severely compromise the structural integrity occur during the service life. Such cases are often referred as outliers and the RUL prognosis based on a data-driven model that learns from past data is often erroneous. This study addresses this challenge by proposing a new stochastic model; the Similarity Learning Hidden Semi Markov Model (SLHSMM), an extension of the Non-Homogenous Hidden Semi Markov Model (NHHSMM). Through the utilization of a nonparametric discrete distribution, which characterizes the similarity between the testing structure and the training structures, a dynamic re-estimation process is employed. This process assigns higher importance to the training structures that display greater similarity to the testing one. As a result, the estimated parameters effectively capture the specific characteristics of the testing structure. The training and testing SHM data sets consist of strain measurements collected from a case study where carbon–epoxy single-stringered panels, are subjected to constant, variable, and random amplitude fatigue loading until failure. RUL estimations from the SLHSMM, the NHHSMM, and the Gaussian Process Regression (GPR) are compared. The SLHSMM clearly outperforms its classical counterpart and GPR providing more accurate outlier and inlier prognostics, demonstrating its capability to adapt to unexpected phenomena and integrate unforeseen data into a prognostic platform.

Adaptive Prognostics: A reliable RUL approach

Prognostic methodologies have found increasing use the last decade and provide a platform for remaining useful life (RUL) predictions of engineering systems utilizing condition monitoring data. Of particular interest is the reliable RUL prediction of engineering assets that either underperform or outperform due to unexpected phenomena that might occur during the operational life. These assets are often referred as outliers and the prediction of their RUL is a challenging task. The challenge is to accurately predict the RUL of an outlier without taking into account outlier’s condition monitoring data in the training process but just in the testing process. As a result, the lifetime of the testing asset is shorter (left outlier) or longer (right outlier) than the training process’ lifetimes.&#x0D; This study addresses this challenge by proposing a new adaptive model; the Similarity Learning Hidden Semi Markov Model (SLHSMM), which is an extension of the Non-Homogenous Hidden Semi Markov Model (NHHSMM). The SLHSMM uses a similarity function, such as Minkowski distances, in order firstly to quantify the similarity between the testing asset and each training asset and secondly to adapt the trained parameters of the NHHSMM. To demonstrate the effectiveness of the proposed adaptive methodology, composite structures have been used as a validation engineering asset. In particular, the training data set consists of strain data collected from open-hole carbon–epoxy specimens, which were subjected to fatigue loading only, while the testing data set consists of strain data collected from specimens that were subjected to fatigue and in-situ impact loading, which can be considered as an unexpected phenomenon and unseen event regarding the training process. &#x0D; Utilizing the aforementioned strain data the SLHSMM RUL predictions and the NHHSMM RUL predictions were compared, so as to verify that the SLHSMM provides better prognostics than the NHHSMM. SLHSMM provides better predictions in comparison to the NHHSMM for all the test cases, demonstrating its capability to adapt to unexpected phenomena and integrate unforeseen data to the prognostics course.

Modeling three-dimensional T-cell motility using clustering and hidden Markov models.

Recent advances in imaging technologies now allow for real-time tracking of fast-moving immune cells as they search for targets such as pathogens and tumor cells through complex three-dimensional tissues. Cytotoxic T cells are specialized immune cells that continually scan tissues for such targets to engage and kill, and have emerged as the principle mediators of breakthrough immunotherapies against cancers. Modeling the way these T cells move is of great value in furthering our understanding of their collective search efficiency. T-cell motility is characterized by heterogeneity at two levels: (a) Individual cells display different distributions of translational speeds and turning angles, and (b) each cell can during a given track, its motility, switch between local search and directional motion. Despite a likely considerable influence on a motile population's search performance, statistical models that accurately capture both such heterogeneities in a distinguishing manner are lacking. Here, we model three-dimensional T-cell trajectories through a spherical representation of their incremental steps and compare model outputs to real-world motility data from primary T cells navigating physiological environments. T cells in a population are clustered based on their directional persistence and characteristic "step lengths" therein capturing between-cell heterogeneity. The motility dynamics of cells within each cluster are individually modeled through hidden Markov model to capture within-cell transitions between local and more extensive search patterns. We explore the importance of explicitly capturing altered motility patterns when cells lie in close proximity to one another, through a non-homogenous hidden Markov model.

Variational Bayesian analysis of nonhomogeneous hidden Markov models with long and ultralong sequences

Variational Bayesian analysis of nonhomogeneous hidden Markov models with long and ultralong sequences

Evaluation of the natural history of disease by combining incident and prevalent cohorts: application to the Nun Study.

The Nun study is a well-known longitudinal epidemiology study of aging and dementia that recruited elderly nuns who were not yet diagnosed with dementia (i.e., incident cohort) and who had dementia prior to entry (i.e., prevalent cohort). In such a natural history of disease study, multistate modeling of the combined data from both incident and prevalent cohorts is desirable to improve the efficiency of inference. While important, the multistate modeling approaches for the combined data have been scarcely used in practice because prevalent samples do not provide the exact date of disease onset and do not represent the target population due to left-truncation. In this paper, we demonstrate how to adequately combine both incident and prevalent cohorts to examine risk factors for every possible transition in studying the natural history of dementia. We adapt a four-state nonhomogeneous Markov model to characterize all transitions between different clinical stages, including plausible reversible transitions. The estimating procedure using the combined data leads to efficiency gains for every transition compared to those from the incident cohort data only.

Adaptive Fuzzy Asynchronous Control for Nonhomogeneous Markov Jump Power Systems Under Hybrid Attacks

This article investigates the adaptive fuzzy asynchronous control problem for discrete-time nonhomogeneous Markov jump power systems under hybrid attacks. A nonhomogeneous Markov process is used to describe the phenomenon of transient failures occurring in power lines and subsequent switching of associated circuit breakers. The corresponding nonhomogeneous hidden Markov model is utilized to detect the jump modes of power systems. Both deception attack and denial-of-service attack are analyzed simultaneously owing to the vulnerability of power systems. With detected modes and fuzzy logic systems, an adaptive fuzzy asynchronous control strategy is proposed. Using the mode-dependent Lyapunov function, the existence conditions of the desired controller law are obtained such that the closed-loop power systems are bounded stable in the mean-square sense. Finally, the usefulness of the developed control strategy is demonstrated by a numerical example.

BAYESIAN NON-HOMOGENEOUS HIDDEN MARKOV MODEL WITH VARIABLE SELECTION FOR INVESTIGATING DRIVERS OF SEIZURE RISK CYCLING.

A major issue in the clinical management of epilepsy is the unpredictability of seizures. Yet, traditional approaches to seizure forecasting and risk assessment in epilepsy rely heavily on raw seizure frequencies, which are a stochastic measurement of seizure risk. We consider a Bayesian non-homogeneous hidden Markov model for unsupervised clustering of zero-inflated seizure count data. The proposed model allows for a probabilistic estimate of the sequence of seizure risk states at the individual level. It also offers significant improvement over prior approaches by incorporating a variable selection prior for the identification of clinical covariates that drive seizure risk changes and accommodating highly granular data. For inference, we implement an efficient sampler that employs stochastic search and data augmentation techniques. We evaluate model performance on simulated seizure count data. We then demonstrate the clinical utility of the proposed model by analyzing daily seizure count data from 133 patients with Dravet syndrome collected through the Seizure Tracker™ system, a patient-reported electronic seizure diary. We report on the dynamics of seizure risk cycling, including validation of several known pharmacologic relationships. We also uncover novel findings characterizing the presence and volatility of risk states in Dravet syndrome, which may directly inform counseling to reduce the unpredictability of seizures for patients with this devastating cause of epilepsy.

Analyzing the Rainfall Pattern in Honduras Through Non-Homogeneous Hidden Markov Models

One of the major climatic interests of the last decades has been to understand and describe the rainfall patterns of specific areas of the world as functions of other climate covariates. We do it for the historical climate monitoring data from Tegucigalpa, Honduras, using non-homogeneous hidden Markov models (NHMMs), which are dynamic models usually used to identify and predict heterogeneous regimes. For estimating the NHMM in an efficient and scalable way, we propose the stochastic Expectation-Maximization (EM) algorithm and a Bayesian method, and compare their performance in synthetic data. Although these methodologies have already been used for estimating several other statistical models, it is not the case of NHMMs which are still widely fitted by the traditional EM algorithm. We observe that, under tested conditions, the performance of the Bayesian and stochastic EM algorithms is similar and discuss their slight differences. Analyzing the Honduras rainfall data set, we identify three heterogeneous rainfall periods and select temperature and humidity as relevant covariates for explaining the dynamic relation among these periods.