Bayesian statistical procedures use probabilistic models and probability distributions to summarize data, estimate unknown quantities of interest, and predict future observations. The procedures borrow strength from other observations in the dataset by using prior distributions and/or hierarchical model specifications. The unique posterior sampling techniques can handle different issues, e.g., missing data, imputation, and extraction of parameters (and their functional forms) that would otherwise be difficult to address using conventional methods. In this dissertation, we propose Bayesian modeling strategies to address various challenges arising in the fields of neuroscience and medicine. Specifically, we propose a sparse Bayesian hierarchical Vector Autoregressive (VAR) model to map human brain connectivity using multi-subject multi-session functional magnetic resonance image (fMRI) data. We use the same model on patient diary databases, focusing on patient-level prediction of medical conditions using posterior predictive samples. We also propose a Bayesian model with an augmented Markov Chain Monte Carlo (MCMC) algorithm on repeat Electrical Stimulation Mappings (ESM) to evaluate the variability of localization in brain sites responsible for language function. We close by using Bayesian disproportionality analyses on spontaneous reporting system (SRS) databases for post-market drug safety surveillance, illustrating the caution required in real-world analysis and decision making.