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Granger causality for sets of time series: development of methodologies to model selection and extensions in the frequency domain with applications to molecular biology and neuroscience

Abstract

Wiener (1956) and Granger (1969) have introduced an intuitive concept of causality (Granger causality) between two variables, which is based on the idea that an effect never occurs before its cause. Although Granger causality is not "effective causality" in the Aristothelic sense, this concept is useful to infer directionality and information flow in data sets. Later, Geweke (1984) generalized the bivariate Granger causality to a multivariate fashion in order to identify conditional Granger causality, i.e., when m time series Granger-cause another time series, while Fujita et al. (2010) generalized the concept to be used between sets of time series, i.e., when m time series Granger-cause n other time series. Although the proposed technique used to identify Granger causality between sets of time series is useful to explain several natural events, there are still some limitations to be overcome. For example, in order to identify Granger causality in actual data, it is necessary to define, objectively, which variables belong to which groups when no a priori information is provided. In addition, little (or nothing) is known about the Granger causality for sets of time series in the frequency domain. Therefore, in this project, we propose to develop (1) a model selection criterion in order to objectively define which time series belong to which data set and (2) a concept and methodology to identify Granger causality in the frequency domain. Moreover, we will apply these new approaches on actual gene expression data sets derived from cancer research and functional Magnetic Resonance Imaging (fMRI) in order to better comprehend intricate cancer-related gene networks and also the functional connectivity of the brain under different stimuli. (AU)

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Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
TAKAHASHI, DANIEL YASUMASA; SATO, JOAO RICARDO; FERREIRA, CARLOS EDUARDO; FUJITA, ANDRE. Discriminating Different Classes of Biological Networks by Analyzing the Graphs Spectra Distribution. PLoS One, v. 7, n. 12, . (11/07762-8, 10/01394-4)
AZEVEDO, HATYLAS; FUJITA, ANDRE; BANDO, SILVIA YUMI; IAMASHITA, PRISCILA; MOREIRA-FILHO, CARLOS ALBERTO. Transcriptional Network Analysis Reveals that AT1 and AT2 Angiotensin II Receptors Are Both Involved in the Regulation of Genes Essential for Glioma Progression. PLoS One, v. 9, n. 11, . (05/56446-0, 11/07762-8, 11/50761-2, 09/53443-1)
SANTOS, SUZANA DE SIQUEIRA; TAKAHASHI, DANIEL YASUMASA; NAKATA, ASUKA; FUJITA, ANDRE. A comparative study of statistical methods used to identify dependencies between gene expression signals. BRIEFINGS IN BIOINFORMATICS, v. 15, n. 6, p. 906-918, . (13/03447-6, 12/25417-9, 11/07762-8, 11/50761-2)
FUJITA, ANDRE; TAKAHASHI, DANIEL Y.; PATRIOTA, ALEXANDRE G.. A non-parametric method to estimate the number of clusters. COMPUTATIONAL STATISTICS & DATA ANALYSIS, v. 73, p. 27-39, . (11/07762-8)

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