Exact likelihood evaluation in a Markov mixture model for time series of seizure counts.

This paper provides an alternative to Albert's (1991), Biometrics 47, 1371-1381) approximation to the E-step when using the EM algorithm for parameter estimation in Markov mixture models. Use of a recursive algorithm of Baum et al. (1970, Annals of Mathematical Statistics 41, 164-171) results in exact evaluation of the likelihood, optimal parameter estimates, and very efficient computation. Applications to time series of seizure counts and fetal movements clearly show the advantages of this exact approach.     

A two-stage model for multiple time series data of counts

We propose a two-stage model for time series data of counts from multiple locations. This method fits first-stage model(s) using the technique of iteratively weighted filtered least squares (IWFLS) to obtain location-specific intercepts and slopes, with possible lagged effects via polynomial distributed lag modeling. These slopes and/or intercepts are then taken to a second-stage mixed-effects meta-regression model in order to stabilize results from various locations. The representation of the models from the stages into a combined mixed-effects model, issues of inference and choices of the parameters in modeling the lag structure are discussed. We illustrate this proposed model via detailed analysis on the effect of air pollution on school absenteeism based on data from the Southern California Children's Health Study.     

Proposing a two-level stochastic model for epileptic seizure genesis

By assuming the brain as a multi-stable system, different scenarios have been introduced for transition from normal to epileptic state. But, the path through which this transition occurs is under debate. In this paper a stochastic model for seizure genesis is presented that is consistent with all scenarios: a two-level spontaneous seizure generation model is proposed in which, in its first level the behavior of physiological parameters is modeled with a stochastic process. The focus is on some physiological parameters that are essential in simulating different activities of ElectroEncephaloGram (EEG), i.e., excitatory and inhibitory synaptic gains of neuronal populations. There are many depth-EEG models in which excitatory and inhibitory synaptic gains are the adjustable parameters. Using one of these models at the second level, our proposed seizure generator is complete. The suggested stochastic model of first level is a hidden Markov process whose transition matrices are obtained through analyzing the real parameter sequences of a seizure onset area. These real parameter sequences are estimated from real depth-EEG signals via applying a parameter identification algorithm. In this paper both short-term and long-term validations of the proposed model are done. The long-term synthetic depth-EEG signals simulated by this model can be taken as a suitable tool for comparing different seizure prediction algorithms.     

Statistical inference from single channel records: two-state Markov model with limited time resolution

Though stochastic models are widely used to describe single ion channel behaviour, statistical inference based on them has received little consideration. This paper describes techniques of statistical inference, in particular likelihood methods, suitable for Markov models incorporating limited time resolution by means of a discrete detection limit. To simplify the analysis, attention is restricted to two-state models, although the methods have more general applicability. Non-uniqueness of the mean open-time and mean closed-time estimators obtained by moment methods based on single exponential approximations to the apparent open-time and apparent closed-time distributions has been reported. The present study clarifies and extends this previous work by proving that, for such approximations, the likelihood equations as well as the moment equations (usually) have multiple solutions. Such non-uniqueness corresponds to non-identifiability of the statistical model for the apparent quantities. By contrast, higher-order approximations yield theoretically identifiable models. Likelihood-based estimation procedures are developed for both single exponential and bi-exponential approximations. The methods and results are illustrated by numerical examples based on literature and simulated data, with consideration given to empirical distributions and model control, likelihood plots, and point estimation and confidence regions.     

Markov regression models for time series: a quasi-likelihood approach

This paper discusses a quasi-likelihood (QL) approach to regression analysis with time series data. We consider a class of Markov models, referred to by Cox (1981, Scandinavian Journal of Statistics 8, 93-115) as "observation-driven" models in which the conditional means and variances given the past are explicit functions of past outcomes. The class includes autoregressive and Markov chain models for continuous and categorical observations as well as models for counts (e.g., Poisson) and continuous outcomes with constant coefficient of variation (e.g., gamma). We focus on Poisson and gamma data for illustration. Analogous to QL for independent observations, large-sample properties of the regression coefficients depend only on correct specification of the first conditional moment.     

A multi-context learning approach for EEG epileptic seizure detection

Background

Epilepsy is a neurological disease characterized by unprovoked seizures in the brain. The recent advances in sensor technologies allow researchers to analyze the collected biological records to improve the treatment of epilepsy. Electroencephalogram (EEG) is the most commonly used biological measurement to effectively capture the abnormalities of different brain areas during the EEG seizures. To avoid manual visual inspection from long-term EEG readings, automatic epileptic EEG seizure detection has become an important research issue in bioinformatics.

Results

We present a multi-context learning approach to automatically detect EEG seizures by incorporating a feature fusion strategy. We generate EEG scalogram sequences from the EEG records by utilizing waveform transform to describe the frequency content over time. We propose a multi-stage unsupervised model that integrates the features extracted from the global handcrafted engineering, channel-wise deep learning, and EEG embeddings, respectively. The learned multi-context features are subsequently merged to train a seizure detector.

Conclusions

To validate the effectiveness of the proposed approach, extensive experiments against several baseline methods are carried out on two benchmark biological datasets. The experimental results demonstrate that the representative context features from multiple perspectives can be learned by the proposed model, and further improve the performance for the task of EEG seizure detection.

     

Wavelet-based Gaussian-mixture hidden Markov model for the detection of multistage seizure dynamics: A proof-of-concept study

Background  

Epilepsy is a common neurological disorder characterized by recurrent electrophysiological activities, known as seizures. Without the appropriate detection strategies, these seizure episodes can dramatically affect the quality of life for those afflicted. The rationale of this study is to develop an unsupervised algorithm for the detection of seizure states so that it may be implemented along with potential intervention strategies.     

A two-state piezoelectric model for outer hair cell motility

Recent studies have revealed that voltage-dependent length changes of the outer hair cell are based on charge transfer across the membrane. Such a motility can be explained by an area motor model, which assumes two states in the motor and that conformational transitions involve transfer of motor charge across the membrane and mechanical displacements of the membrane. Here it is shown that the area motor is piezoelectric and that the hair cell that incorporates such a motor in its lateral membrane is also piezoelectric. Distinctive features of the outer hair cell are its exceptionally large piezoelectric coefficient, which exceeds the best known piezoelectric material by four orders of magnitude, and its prominent nonlinearity due to the discreteness of motor states.     

A two-state recurrent stochastic model with time-dependent transition rates.

The two-state recurrent stochastic model with time-independent transition rates is generalized to a model with time-dependent transition rates. The rates can be any general function of external time, that is, any general function of the calendar time in which the process unfolds. Formulas for the state transition probabilities, the proportion of individuals in a particular state at time t, the distribution function, and the expectation of the number of individuals in a particular state at time t are derived.     

A hidden-state Markov model for cell population deconvolution.

Microarrays measure gene expression typically from a mixture of cell populations during different stages of a biological process. However, the specific effects of the distinct or pure populations on measured gene expression are difficult or impossible to determine. The ability to deconvolve measured gene expression into the contributions from pure populations is critical to maximizing the potential of microarray analysis for investigating complex biological processes. In this paper, we describe a novel approach called the multinomial hidden Markov model (MHMM) that produces: (i) a maximum a posteriori estimate of the fraction represented by each pure population and (ii) gene expression values for each pure population. Our method uses an unsupervised, probabilistic approach for handling missing data points and clusters genes based on expression in pure populations. MHMM, used with several yeast datasets, identified statistically significant temporal dynamics. This method, unlike the linear decomposition models used previously for deconvolution, can extract information from different types of data, does not require a priori identification of pure gene expression, exploits the temporal nature of time series data, and is less affected by missing data.     

Pseudoconservative transition: a two-state model for the co-operative behavior of oligomeric proteins.

A plausible extension of the two-state concerted model is proposed. This extended two-state model involves at least one state with pairwise asymmetry and consequent heterogeneous binding properties. Such a pseudoconservative transition model accounts in a predictably restricted manner for either positive or negative co-operativity² and for a combination of both in the binding of a single ligand. State and saturation functions are derived. Variation of the Hill number with respect to the extent of binding provides a diagnostic test for the combination of both positive and negative co-operativities in ligand binding. Applications of the model to recent experimental data are discussed.     

A two-component model for counts of infectious diseases

We propose a stochastic model for the analysis of time series of disease counts as collected in typical surveillance systems on notifiable infectious diseases. The model is based on a Poisson or negative binomial observation model with two components: a parameter-driven component relates the disease incidence to latent parameters describing endemic seasonal patterns, which are typical for infectious disease surveillance data. An observation-driven or epidemic component is modeled with an autoregression on the number of cases at the previous time points. The autoregressive parameter is allowed to change over time according to a Bayesian changepoint model with unknown number of changepoints. Parameter estimates are obtained through the Bayesian model averaging using Markov chain Monte Carlo techniques. We illustrate our approach through analysis of simulated data and real notification data obtained from the German infectious disease surveillance system, administered by the Robert Koch Institute in Berlin. Software to fit the proposed model can be obtained from http://www.statistik.lmu.de/ approximately mhofmann/twins.