Métodos de estimação e medidas de informação e aplicações em Neurociências.

Abstract

Many modern system projects depend on their components, which may relate to each other by dependency or causality relations. What is meant by systems in this work are those whose components may be evaluated or measured. For example: financial systems, whose components may be stock markets; medical/biological systems, whose components may be respiration, blood pressure, and heart rate; neurophysiological system, whose components may be electroencephalogram or functional magnetic resonance imaging from different parts of the brain; among many other systems that allow mathematical treatment. Information theory has been presented as an efficient mean to quantify the relations in these systems, bringing useful concepts and evaluating measures such as mutual information, directed information, and transfer entropy. A fundamental question when dealing with real systems concerns the difficulty to model the true underlying probability densities of the involved variables. The definitions of mutual information, directed information, and transfer entropy rely on these densities. In this context, the present work evolves to investigate and contribute with estimation methods to measure the relations among variables when studying systems. This work gives a special attention to neuronal systems.