Revealing ensemble state transition patterns in multi-electrode neuronal recordings using hidden Markov models

In order to harness the computational capacity of dissociated cultured neuronal networks, it is necessary to understand neuronal dynamics and connectivity on a mesoscopic scale. To this end, this paper uncovers dynamic spatiotemporal patterns emerging from electrically stimulated neuronal cultures using hidden Markov models (HMMs) to characterize multi-channel spike trains as a progression of patterns of underlying states of neuronal activity. However, experimentation aimed at optimal choice of parameters for such models is essential and results are reported in detail. Results derived from ensemble neuronal data revealed highly repeatable patterns of state transitions in the order of milliseconds in response to probing stimuli

Handling Covariates in Markovian Models with a Mixture Transition Distribution Based Approach

This paper presents and discusses the use of a Mixture Transition Distribution-like model (MTD) to account for covariates in Markovian models. The MTD was introduced in 1985 by Raftery as an approximation of higher order Markov chains. In the MTD, each lag is estimated separately using an additive model, which introduces a kind of symmetrical relationship between the past and the present. Here, using an MTD-based approach, we consider each covariate separately, and we combine the effects of the lags and of the covariates by means of a mixture model. This approach has three main advantages. First, no modification of the estimation procedure is needed. Second, it is parsimonious in terms of freely estimated parameters. Third, the weight parameters of the mixture can be used as an indication of the relevance of the covariate in explaining the time dependence between states. An illustrative example taken from life course studies using a 3-state hidden Markov model and a covariate with three levels shows how to interpret the results of such models

Linked Markov sources: Modeling outcome-dependent social processes

Many social processes are adaptive in the sense that the process changes as a result of previous outcomes. Data on such processes may come in the form of categorical time series. First, the authors propose a class of Markov Source models that embody such adaptation. Second, the authors discuss new methods to evaluate the fit of such models. Third, the authors apply these models and methods to data on a social process that is a preeminent example of an adaptive process: (encoded) conversation as arises in structured interviews. © 2007 Sage Publications

Estimation of Particulate Matter Contributions from Desert Outbreaks in Mediterranean Countries (2015-2018) Using the Time Series Clustering Method

North African dust intrusions can contribute to exceedances of the European PM10 and PM2.5 limit values and World Health Organisation standards, diminishing air quality, and increased mortality and morbidity at higher concentrations. In this study, the contribution of North African dust in Mediterranean countries was estimated using the time series clustering method. This method combines the non-parametric approach of Hidden Markov Models for studying time series, and the definition of different air pollution profiles (regimes of concentration). Using this approach, PM10 and PM2.5 time series obtained at background monitoring stations from seven countries were analysed from 2015 to 2018. The average characteristic contributions to PM10 were estimated as 11.6 +/- 10.3 mu g.m(-3) (Bosnia and Herzegovina), 8.8 +/- 7.5 mu g.m(-3) (Spain), 7.0 +/- 6.2 mu g.m(-3) (France), 8.1 +/- 5.9 mu g.m(-3) (Croatia), 7.5 +/- 5.5 mu g.m(-3) (Italy), 8.1 +/- 7.0 mu g.m(-3) (Portugal), and 17.0 +/- 9.8 mu g.m(-3) (Turkey). For PM2.5, estimated contributions were 4.1 +/- 3.5 mu g.m(-3) (Spain), 6.0 +/- 4.8 mu g.m(-3) (France), 9.1 +/- 6.4 mu g.m(-3) (Croatia), 5.2 +/- 3.8 mu g.m(-3) (Italy), 6.0 +/- 4.4 mu g.m(-3) (Portugal), and 9.0 +/- 5.6 mu g.m(-3) (Turkey). The observed PM2.5/PM10 ratios were between 0.36 and 0.69, and their seasonal variation was characterised, presenting higher values in colder months. Principal component analysis enabled the association of background sites based on their estimated PM10 and PM2.5 pollution profiles

Estimation of Particulate Matter Contributions from Desert Outbreaks in Mediterranean Countries (2015–2018) Using the Time Series Clustering Method

North African dust intrusions can contribute to exceedances of the European PM10 and PM2.5 limit values and World Health Organisation standards, diminishing air quality, and increased mortality and morbidity at higher concentrations. In this study, the contribution of North African dust in Mediterranean countries was estimated using the time series clustering method. This method combines the non-parametric approach of Hidden Markov Models for studying time series, and the definition of different air pollution profiles (regimes of concentration). Using this approach, PM10 and PM2.5 time series obtained at background monitoring stations from seven countries were analysed from 2015 to 2018. The average characteristic contributions to PM10 were estimated as 11.6 ± 10.3 µg·m−3 (Bosnia and Herzegovina), 8.8 ± 7.5 µg·m−3 (Spain), 7.0 ± 6.2 µg·m−3 (France), 8.1 ± 5.9 µg·m−3 (Croatia), 7.5 ± 5.5 µg·m−3 (Italy), 8.1 ± 7.0 µg·m−3 (Portugal), and 17.0 ± 9.8 µg·m−3 (Turkey). For PM2.5, estimated contributions were 4.1 ± 3.5 µg·m−3 (Spain), 6.0 ± 4.8 µg·m−3 (France), 9.1 ± 6.4 µg·m−3 (Croatia), 5.2 ± 3.8 µg·m−3 (Italy), 6.0 ± 4.4 µg·m−3 (Portugal), and 9.0 ± 5.6 µg·m−3 (Turkey). The observed PM2.5/PM10 ratios were between 0.36 and 0.69, and their seasonal variation was characterised, presenting higher values in colder months. Principal component analysis enabled the association of background sites based on their estimated PM10 and PM2.5 pollution profiles

The Expanded Evidence-Centered Design (e-ECD) for Learning and Assessment Systems: A Framework for Incorporating Learning Goals and Processes Within Assessment Design

Evidence-centered design (ECD) is a framework for the design and development of assessments that ensures consideration and collection of validity evidence from the onset of the test design. Blending learning and assessment requires integrating aspects of learning at the same level of rigor as aspects of testing. In this paper, we describe an expansion to the ECD framework (termed e-ECD) such that it includes the specifications of the relevant aspects of learning at each of the three core models in the ECD, as well as making room for specifying the relationship between learning and assessment within the system. The framework proposed here does not assume a specific learning theory or particular learning goals, rather it allows for their inclusion within an assessment framework, such that they can be articulated by researchers or assessment developers that wish to focus on learning

ON MARKOV AND HIDDEN MARKOV MODELS WITH APPLICATIONS TO TRAJECTORIES

Markov and hidden Markov models (HMMs) provide a special angle to characterize trajectories using their state transition patterns. Distinct from Markov models, HMMs assume that an unobserved sequence governs the observed sequence and the Markovian property is imposed on the hidden chain rather than the observed one. In the first part of this dissertation, we develop a model for HMMs with exponential family distribution and extend it to incorporate covariates. We call it HMM-GLM, for which we propose a joint model selection method. The proposed selection criterion is tailored for HMM-GLM aiming at a more accurate approximation of the Kullback-Leibler divergence; we seek improvement of the widely-used Akaike information criterion. The second and the third parts of this dissertation are about clustering trajectories with HMMs and Markov mixture models. The research interests for HMM clustering are to develop a less computationally expensive and more interpretable algorithm for HMM sequence clustering problem, based on the emission and transition features of the chains. We propose an efficient clustering method using Bhattacharyya affinity to measure the pairwise similarity between sequences and apply a spectral clustering algorithm to obtain the cluster assignment. The computational efficiency benefits from the fact that our method avoids iterative computation for the affinity of a pair of sequences. Meanwhile, both simulation and empirical studies show that the proposed algorithm maintains good performance compared to other similar methods. In the third part of the dissertation, we address a study of the course of children and adolescents with bipolar disorder. Measuring and making sense of the fluctuations in different moods over time is challenging. We use a Markov mixture model with different transition matrices to find homogeneous clusters and capture different longitudinal mood change patterns. We also conduct a simulation study to investigate the performance of the model when there are violations of model assumptions. The results show that this model is fairly robust in the tested situations. We find that the clusters separate out those who tend to stay in a mood state from those who fluctuate between mood states more frequently