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Modelling and Analysis of Some Random Process Data from Neurophysiology
"... Models, graphs and networks are particularly useful for examining statistical dependencies amongst quantities via conditioning. In this article the nodal random variables are point processes. Basic to the study of statistical networks is some measure of the strength of (possibly directed) connection ..."
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Models, graphs and networks are particularly useful for examining statistical dependencies amongst quantities via conditioning. In this article the nodal random variables are point processes. Basic to the study of statistical networks is some measure of the strength of (possibly directed) connections between the nodes. The coe#cients of determination and of mutual information are considered in a study for inference concerning statistical graphical models. The focus of this article is simple networks. Both secondorder moment and threshold modelbased analyses are presented. The article includes examples from neurophysiology.
Testing for directed influences among neural signals using partial directed coherence
, 2005
"... One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity. When applying multivariate time series analysis techniques to neural signals, detection of directed relationships, which can be described in terms of Grangercausality, is of parti ..."
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One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity. When applying multivariate time series analysis techniques to neural signals, detection of directed relationships, which can be described in terms of Grangercausality, is of particular interest. Partial directed coherence has been introduced for a frequency domain analysis of linear Grangercausality based on modeling the underlying dynamics by vector autoregressive processes. We discuss the statistical properties of estimates for partial directed coherence and propose a significance level for testing for nonzero partial directed coherence at a given frequency. The performance of this test is illustrated by means of linear and nonlinear model systems and in an application to electroencephalography and electromyography data recorded from a patient suffering from essential tremor. © 2005 Elsevier B.V. All rights reserved.
Combining Graphical Models and PCA for Statistical Process Control
, 2002
"... Principal component analysis (PCA) is frequently used for de tection of common structures in multivariate data, e.g. in statistical process control. Critical issues are the choice of the number of principal components and their interpretation. These tasks become even more difficult when dy namic P ..."
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Principal component analysis (PCA) is frequently used for de tection of common structures in multivariate data, e.g. in statistical process control. Critical issues are the choice of the number of principal components and their interpretation. These tasks become even more difficult when dy namic PCA (Brillinger, 1981) is applied to incorporate dependencies within time series data. We use the information obtained from graphical models to improve pattern detection based on PCA.
Inference About Functional Connectivity From Multiple Neural Spike Trains
, 2011
"... In neuroscience study, it is desirable to understand how the neuronal activities are associated and how the association changes with time based on multiple spike train recordings from multielectrode array. The term functional connectivity is used to describe the association between neurons and the c ..."
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In neuroscience study, it is desirable to understand how the neuronal activities are associated and how the association changes with time based on multiple spike train recordings from multielectrode array. The term functional connectivity is used to describe the association between neurons and the change of association with task purpose. In this proposed thesis, I will study the statistical details of functional connectivity inference. First, the preliminary results show the effect of sample size, connection strength and basis set on functional connectivity inference, I would like to explore further for large networks so that I can estimate the sample size needed for functional connectivity inference; secondly, I will explore the models and algorithms being used for inference, and the current plan is to combine two families of methods, i.e. point processgeneralized linear model based methods and graph theory based methods, to develop procedure that can be used to infer functional connectivity network given limited amount of data; finally, I will explore the possible information we can obtain when the sample size is too small to infer functional connectivity reliably. 1
1 ARMA Identification of Graphical Models
"... vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nodes signifies conditional independence. Thi ..."
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vector process with the property that designated pairs of components are conditionally independent given the rest of the components. Such processes can be represented on a graph where the components are nodes and the lack of a connecting link between two nodes signifies conditional independence. This leads to a sparsity pattern in the inverse of the matrixvalued spectral density. Such graphical models find applications in speech, bioinformatics, image processing, econometrics and many other fields, where the problem to fit an autoregressive (AR) model to such a process has been considered. In this paper we take this problem one step further, namely to fit an autoregressive movingaverage (ARMA) model to the same data. We develop a theoretical framework and an optimization procedure which also spreads further light on previous approaches and results. This procedure is then applied to the identification problem of estimating the ARMA parameters as well as the topology of the graph from statistical data. I.
Intervention and causality in a dynamic Bayesian network
, 2008
"... The use of intervention for time series modelling is a well established technique for online forecasting and decisionmaking in the context of Bayesian dynamic linear models. Intervention has also been recently used in (nondynamic) Bayesian networks to investigate causal relationships between vari ..."
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The use of intervention for time series modelling is a well established technique for online forecasting and decisionmaking in the context of Bayesian dynamic linear models. Intervention has also been recently used in (nondynamic) Bayesian networks to investigate causal relationships between variables, and in dynamic Bayesian networks to investigate lagged causal relationships between time series. The Multiregression Dynamic Model (MDM) is a Bayesian dynamic model and an example of a dynamic Bayesian network. The focus of this paper is the use of intervention in the MDM. It will be demonstrated that not only is intervention in the MDM a powerful tool for forecasting, but intervention can also aid in the identification of contemporaneous causal relationships between time series, thus going beyond the identification of lagged causal relationships previously addressed in dynamic Bayesian networks.
pp:1210ðcol:fig::NILÞ ARTICLE IN PRESS ED:MangalaGowri PAGN:Raj SCAN:v4soft
, 2003
"... Latent variable analysis and partial correlation graphs for multivariate time series ..."
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Latent variable analysis and partial correlation graphs for multivariate time series