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Grangercausality graphs for multivariate time series
"... In this paper, we discuss the properties of mixed graphs which visualize causal relationships between the components of multivariate time series. In these Grangercausality graphs, the vertices, representing the components of the time series, are connected by arrows according to the Grangercausalit ..."
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In this paper, we discuss the properties of mixed graphs which visualize causal relationships between the components of multivariate time series. In these Grangercausality graphs, the vertices, representing the components of the time series, are connected by arrows according to the Grangercausality relations between the variables whereas lines correspond to contemporaneous conditional association. We show that the concept of Grangercausality graphs provides a framework for the derivation of general noncausality relations relative to reduced information sets by performing sequences of simple operations on the graphs. We briefly discuss the implications for the identification of causal relationships. Finally we provide an extension of the linear concept to strong Grangercausality. JEL classification: C320 Keywords: Grangercausality, graphical models, spurious causality, multivariate
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.
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
ARMA Identification of Graphical Models
"... Consider a Gaussian stationary stochastic 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 nod ..."
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Consider a Gaussian stationary stochastic 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.
Abstract Journal of Neuroscience Methods xxx (2005) xxx–xxx 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.
Fitting Graphical Interaction Models to Multivariate Time Series
"... Graphical interaction models have become an important tool for analysing multivariate time series. In these models, the interrelationships among the components of a time series are described by undirected graphs in which the vertices depict the components while the edges indictate possible dependenc ..."
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Graphical interaction models have become an important tool for analysing multivariate time series. In these models, the interrelationships among the components of a time series are described by undirected graphs in which the vertices depict the components while the edges indictate possible dependencies between the components. Current methods for the identification of the graphical structure are based on nonparametric spectral estimation, which prevents application of common model selection strategies. In this paper, we present a parametric approach for graphical interaction modelling of multivariate stationary time series. The proposed models generalize covariance selection models to the time series setting and are formulated in terms of inverse covariances. We show that these models correspond to vector autoregressive models under conditional independence constraints encoded by undirected graphs. Furthermore, we discuss maximum likelihood estimation based on Whittle’s approximation to the loglikelihood function and propose an iterative method for solving the resulting likelihood equations. The concepts are illustrated by an example. 1
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.
in Encyclopedia of Environmetrics (ISBN 0471 899976) Edited by
, 1900
"... Point processes, temporal A temporal point process is a random process whose realizations consist of the times f jg, j 2 �, j D 0, š1, š2,... of isolated events scattered in time. A point process is also known as a counting process or a random scatter. The times may correspond to events of several t ..."
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Point processes, temporal A temporal point process is a random process whose realizations consist of the times f jg, j 2 �, j D 0, š1, š2,... of isolated events scattered in time. A point process is also known as a counting process or a random scatter. The times may correspond to events of several types. Figure 1 presents an example of temporal point process data. The figure actually provides three different ways of representing the timing of floods on the Amazon River near Manaus, Brazil, during the period 1892–1992 (see Hydrological extremes) [7]. The formal use of the concept of point process has a long history going back at least to the life tables of Graunt [14]. Physicists contributed many ideas in the first half of the twentieth century; see, for example, [23]. The book by Daley and VereJones [11]