Functional MRI (fMRI) used for neurosurgical planning delineates functionally eloquent brain areas by time-series analysis of task-induced BOLD signal changes. Commonly used frequentist statistics protect against false positive results based on a p-value threshold. In surgical planning, false negative results are equally if not more harmful, potentially masking true brain activity leading to erroneous resection of eloquent regions. Bayesian statistics provides an alternative framework, categorizing areas as activated, deactivated, non-activated or with low statistical confidence. This approach has not yet found wide clinical application partly due to the lack of a method to objectively define an effect size threshold. We implemented a Bayesian analysis framework for neurosurgical planning fMRI. It entails an automated effect-size threshold selection method for posterior probability maps accounting for inter-individual BOLD response differences, which was calibrated based on the frequentist results maps thresholded by two clinical experts. We compared Bayesian and frequentist analysis of passive-motor fMRI data from 10 healthy volunteers measured on a pre-operative 3T and an intra-operative 1.5T MRI scanner. As a clinical case study, we tested passive motor task activation in a brain tumor patient at 3T under clinical conditions. With our novel effect size threshold method, the Bayesian analysis revealed regions of all four categories in the 3T data. Activated region foci and extent were consistent with the frequentist analysis results. In the lower signal-to-noise ratio 1.5T intra-operative scanner data, Bayesian analysis provided improved brain-activation detection sensitivity compared with the frequentist analysis, albeit the spatial extents of the activations were smaller than at 3T. Bayesian analysis of fMRI data using operator-independent effect size threshold selection may improve the sensitivity and certainty of information available to guide neurosurgery.