Functional magnetic resonance imaging (FMRI) allows to non-invasively measure human brain activity at the millimeter scale. As such, it is widely used in computational neuroimaging studies that aim to build models to predict stimulus-induced neural responses in visual cortex. A popular method is population receptive field (PRF) mapping, which is able to characterize responses to a large range of stimuli. For each voxel, the PRF method estimates the best fitting receptive field properties (such as location and size in the visual field) using a coarse-to-fine approach which minimizes, but not eliminates, the risk of returning a local minimum. Here, we provide a Bayesian approach to the PRF method based on the slice sampler. Using this approach, we provide estimates of receptive field properties while at the same time being able to quantify their uncertainty. We test the performance of conventional and Bayesian approaches on simulated and empirical data.