Avaliação de critérios de convergência aplicados ao método MCMC

• Autor(a) principal: Albuquerque, Douglas de Souza de
• Data de Publicação: 2023
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/370
• topic: Convergência; Markov, Processos de; Método Monte Carlo; Distância de Hellinger; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE

The Markov Chain Monte Carlo Method (MCMC) is a widely used statistical method in Bayesian Inference. However, it is computationally expensive because it requires running many simulations of the model and does not have a clear convergence criterion. In this paper, we present some convergence tests for MCMC. To perform the tests, we created a synthetic data set for a Convection-Diffusion problem and an epidemiology problem, represented by a compartmental SIRS-type Model. After evaluating the behavior of the diagnostics, we adopted Hellinger’s criterion because it is the most robust. The use of convergence diagnostics is extremely important for the analysis of the solution indicated by the MCMC. However, MCMC does not have a stopping criterion, so we incorporated a strategy into the Hellinger Diagnostic that allows us to choose the level of accuracy and obtain it with the least number of iterations possible. Furthermore, we take advantage of the structure of this diagnostic to determine the amount of knowledge acquired by the parameters in the Bayesian Inference process.