We investigate the two-way connection between rare-event simulation and Bayesian computation. Rare-event techniques (such as importance sampling, splitting, and cross entropy) offer powerful tools for exploring low-probability regions that often dominate complex posteriors in high-dimensional, multimodal, or heavy-tailed Bayesian models. At the same time, Bayesian updating provides a principled mechanism to adapt biasing distributions and quantify uncertainty when estimating small probabilities from limited or extreme data. The project aims to design Bayesian-guided rare-event schemes, study their efficiency, and integrate them into MCMC and particle filtering to improve sampling of unlikely but influential states. Applications include reliability, extreme-value modeling, and tail-risk inference. The goal is a unified methodology where rare-event methods enhance Bayesian algorithms and Bayesian structure informs rare-event estimation.