Functional magnetic resonance imaging (fMRI) is a non-invasive, widely available tool to study the function, organization and connectivity of the brain. Given its high dimensionality and complex spatiotemporal structure, fMRI data is often analyzed using computationally convenient but statistically suboptimal methods. These are typically insufficient to overcome its high noise levels, leading to a lack of accuracy and power in individual-level analysis. As a result, fMRI has mostly been used to make discoveries about average population trends. While these have greatly advanced our understanding of the human brain, they have not lead to biomarker discovery or clinical utility.  Bayesian methods that can pool information shared across observations (e.g., brain locations, subjects) have long been recognized as a way to increase statistical efficiency and power in subject-level fMRI analysis. Yet they have historically not received widespread adoption, in part due to their computational burden. In this talk, I will discuss my work to develop computationally efficient, targeted Bayesian methods for fMRI analysis for precise functional brain mapping in individuals. These include the use of surface-based spatial priors designed to leverage dependencies along the cortical surface of the brain and the use of empirical population priors to leverage information from the population. A key aspect of this work is the use of “gray-ordinates” fMRI data, a technological advance that isolates the gray matter structures of the brain and improves inter-subject alignment. I will discuss the software my group has developed to facilitate statistical method development for grayordinate neuroimaging data and to encourage its adoption in the neuroimaging and statistics communities. Finally, I will present findings from recent studies of psilocybin therapy and neurodegenerative disease.