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Master's Dissertation
DOI
10.11606/D.95.2010.tde-12052013-133201
Document
Author
Full name
Carlos Stein Naves de Brito
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2010
Supervisor
Committee
Sameshima, Koichi (President)
Amaro Júnior, Edson
Vencio, Ricardo Zorzetto Nicoliello
Title in Portuguese
Medidas de dependência entre séries temporais: estudo comparativo, análise estatística e aplicações em neurociências
Keywords in Portuguese
Conectividade funcional
Eletrofisiologia
Inferencia estatistica
Medidas de dependencia
Neurociencia computacional
Series temporais
Abstract in Portuguese
Medidas de dependência entre séries temporais são estudadas com a perspectiva de evidenciar como diferentes regiões do cérebro interagem, por meio da aplicação a sinais eletrofisiológicos. Baseado na representação auto-regressiva e espectral de séries temporais, diferentes medidas são comparadas entre si, incluindo coerência espectral e a coerência parcial direcionada, e introduz-se uma nova medida, denominada transferência parcial direcionada. As medidas são analisadas pelas propriedades de parcialização, relações diretas ou indiretas e direcionalidade temporal, e são mostradas suas relações com a correlação quadrática. Conclui-se que, entre as medidas analisadas, a coerência parcial direcionada e a transferência parcial direcionada possuem o maior número de características desejáveis, fundamentadas no conceito de causalidade de Granger. A estatística assintótica é desenvolvida para todas as medidas, incluindo intervalo de confiança e teste de hipótese nula, assim como sua implementação computacional. A aplicação a séries simuladas e a análise de dados eletrofisiológicos reais ilustram o estudo comparativo e a aplicabilidade das novas estatísticas apresentadas.
Title in English
Measures of dependence between time series: Comparative study, statistical analysis and applications in neuroscience
Keywords in English
Computational neuroscience
Electrophysiology
Functional connectivity
Measure of dependence
Statistical inference
Time series
Abstract in English
Measures of dependence between temporal series are studied in the context of revealing how different brain regions interact, through their application to electrophysiology. Based on the spectral and autoregressive model of time series, different measures are compared, including coherence and partial directed coherence, and a new measure is introduced, named partial directed transfer. The measures are analyzed through the properties of partialization, direct or indirect relations and temporal directionality, and their relation to quadratic correlation is shown. It results that among the presented measures, partial directed coherence and partial directed transfer reveal the highest number of desirable properties, being grounded on the concept of Granger causality. The asymptotic statistics for all measures are developed, including confidence intervals and null hypothesis testing, as well as their computational implementation. The application to simulated series and the analysis of electrophysiological data illustrate the comparative study and the applicability of the newly presented statistics.
 
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Publishing Date
2013-09-05
 
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