The purpose of this post-doctoral project is to propose different estimation methods that can be applied in complex networks. Firstly, we will consider Bayesian methods to determine the minimum size of networks so that real network properties are observed as well as the distribution of the number of connections. This study will solve a fundamental problem in networks which are related to the construction of a taxonomy of complex networks. In this case, we will able to determine the main similarities and differences between classes of networks such as social and biological. Another important problem in complex systems is related to the use of power law distributions. The parameter estimators of such distributions have been discussed earlier under the maximum likelihood estimators. However, different estimation procedures, as well as, Bayesian methods may return better estimates, especially for small samples. Therefore, we will develop new tools to obtain the parameter estimates of power law distributions. In this project, we will also explore regression methods to quantify the relationship between the dynamic structure of complex networks. The aim is to quantify how local properties of the vertices can be used to predict dynamic properties, such as the oscillator synchronization level. In this case, the challenge lies in the fact that the observations are not independent and, therefore, sophisticated Bayesian methods need be considered, for instance, models using a regression structure with coupling functions. Finally, we will introduce a new estimation procedure based on a modification of the maximum likelihood estimators that allow us to obtain closed-form estimators. For this new method, sufficient and necessary conditions will be studied to obtain its asymptotic properties. (AU)
News published in Agência FAPESP Newsletter about the scholarship:
FERREIRA, PAULO H.;
RAMOS, PEDRO L.;
GONZALES, JHON F. B.;
TOMAZELLA, VERA L. D.;
EHLERS, RICARDO S.;
SILVA, EVELINY B.;
Objective Bayesian analysis for the Lomax distribution.
Statistics & Probability Letters,
Web of Science Citations: 0.