Qualificação de doutorado do discente Roger Ngassi, dia 27/08, às 15:00.

Qualificação de doutorado do discente Roger Corneille Ndjeumou Ngassi, dia 27/08, às 15:00.

Título: Improving Bayesian Inference Through Sequential Monte Carlo

Abstract: Markov Chain Monte Carlo (MCMC) methods are fundamental to Bayesian inference, particularly when posterior distributions cannot be obtained analytically. However, reliable Bayesian inference depends on determining whether the generated chains have adequately converged to their target stationary distributions. This qualification reviews convergence assessment methods for MCMC samplers in univariate and multivariate settings, focusing on classical single-chain and multiple-chain diagnostics and their limitations. Methods such as the Geweke, Heidelberger-Welch, Raftery-Lewis, Gelman-Rubin, and Effective Sample Size diagnostics are examined, highlighting their predominantly retrospective nature, reliance on pre-specified simulation lengths or burn-in periods, and limited ability to formally signal convergence. Sequential Monte Carlo methods are then discussed as an alternative framework for adaptive inference with controlled statistical error, leading to the Exact Non-Parametric Sequential Convergence Test (SeqTest) proposed by \citet{Silva-2026-SeqTest}. The SeqTest formulates convergence assessment as a sequential hypothesis-testing problem and employs an alpha-spending strategy to provide formal error control while enabling convergence to be assessed during sampling. Its practical application is investigated in Bayesian Additive Regression Trees (BART) through its integration with the Metropolis-within-Gibbs sampler implemented in the \texttt{bartMachine} package, using the sequential stabilization of Hastings acceptance ratios as the basis for convergence assessment. Simulation results demonstrate consistent convergence detection and substantial computational savings. Future research will primarily investigate the application of SeqTest to multi-objective stochastic optimization, followed by simulation studies, real-world applications, and methodological extensions.

Banca Avaliadora: Prof. Dr. Ivair Ramos Silva; Prof. Dr. Gladston Juliano Prates Moreira; Prof. Dr. Jadston Castro Gertrudes; Prof. Dr. Clécio da Silva Ferreira