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| Author(s): |
Gustavo Pinto Vilela
Total Authors: 1
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| Document type: | Doctoral Thesis |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) |
| Defense date: | 2017-02-14 |
| Advisor: | André Fujita |
| Abstract | |
Several natural systems such as protein-protein interactions, genetic regulation, functi- onal connectivity of the brain, and social relationships can be modeled as graphs where its vertices represent the entities under study and the edges represent which pair of entities are associated. It is known that much of these systems are modular, i.e., they can be clustered into sub-systems, which interact and influence each other. However, from a computatio- nal statistical viewpoint, little is known about statistical methods to analyze graphs. For example, how can one identify whether a graph 'causes' another graph? In this context, we propose a method to identify Granger causality among time series of graphs in the frequency domain. This method is based on the idea of spectral analysis of random graphs and also on the Partial Directed Coherence. We present the model, a method to estimate the parameters of the model, and a statistical test. We demonstrate the usefulness of the method in intensive Monte Carlo simulations. Results show that the method effectively controls the type I error and also present high statistical power to identify Granger causality in five different random graph models. Finally, we illustrate an application of the method in an electrocorticography data collected from a macaque under anesthesia. (AU) | |
| FAPESP's process: | 12/12320-7 - Granger causality for sets of time series in the frequency domain, with applications in neuroscience |
| Grantee: | Gustavo Pinto Vilela |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |