Posterior Concentration

Posterior concentration, a key concept in Bayesian statistics, focuses on how tightly a posterior distribution clusters around the true underlying model parameters as more data becomes available. Current research investigates posterior concentration rates in various models, including Bayesian neural networks (with a focus on Gaussian priors and improved approximation theories), and within the context of algorithms like Thompson sampling and Langevin Monte Carlo for enhanced efficiency in high-dimensional settings. Understanding and improving posterior concentration is crucial for ensuring reliable inference and prediction in diverse applications, from machine learning (e.g., graph neural networks for link prediction) to statistical modeling (e.g., sparse factor models). This research aims to establish theoretical guarantees for efficient and accurate Bayesian inference in complex scenarios.