Geração e análise de dados sintéticos via Redes Bayesianas: uma abordagem robusta para quantificação de incerteza via paradigma Bayesiano

Abstract

The disclosure of confidential data represents an area of great interest, and among the various existing methodologies, the synthetic data approach stands out for its ability to generate information discreetly. This methodology is highly flexible, aiming to disclose data with distributions very similar to those of the original data, thus also preserving the security of sensitive information. The Bayesian network model, in turn, is designed to efficiently estimate the joint distribution of relevant data. This method is an intriguing choice for generating synthetic data as it provides a flexible and robust approach to describing relationships between variables present in the original database. By adopting the Bayesian paradigm, we can create a robust model not only to estimate the network and simulated data but also to quantify the intrinsic uncertainty in the process of generating this new data. This thesis proposes a study that utilizes a state-of-the-art Markov chain Monte Carlo (MCMC) model for generating synthetic data. Additionally, we introduce an innovative approach to disseminating relevant information to the end user, aiming to reduce the uncertainty associated with the estimation process. The main contributions of this work include a comprehensive analysis using the Bayesian paradigm to generate synthetic data through Bayesian networks, incorporating a robust study on quantifying uncertainty in the process of generating this new data. We also introduce a general class of penalizing priors for the network. The thesis comprises three simulation studies as well as an application to real data that illustrates the analysis of the proposed model.