Precipitation exceedance probabilities play a critical role in engineering design, risk assessment, and floodplain management. While climate variability and change impact the frequency and intensity of heavy rainfall, the assumption that extreme precipitation is stationary in time, as implemented in official guidance like Atlas 14, can underestimate present and future hazards. Previous studies show that conditioning the statistical distribution parameters on time-varying climate covariates can improve estimates of nonstationary precipitation frequencies. However, this approach increases the number of parameters to be estimated, exacerbating parametric uncertainty. To address this, we propose a nonstationary and spatially varying model for process-informed precipitation frequency analyses. Specifically, we assume that the robust effects of climate covariates on the probability distribution of extreme rainfall are heterogeneous in space. We employ a hierarchical Bayesian model, leveraging Gaussian processes and extreme value theory, and apply this model to infer nonstationary rainfall exceedance probabilities for the Western Gulf Coast. The proposed approach is highly flexible, naturally allows the use of stations with incomplete observational records, identifies robust temporal trends along with smooth return level estimates, and quantifies parametric uncertainty. This framework can be used to improve adaptation guidance (such as IDF curves) in other regions.