  We introduce a probabilistic (Bayesian) framework and associated software
toolbox for mapping population receptive fields (pRFs) based on fMRI data. This
generic approach is intended to work with stimuli of any dimension and is
demonstrated and validated in the context of 2D retinotopic mapping. The
framework enables the experimenter to specify generative (encoding) models of
fMRI timeseries, in which experimental manipulations enter a pRF model of
neural activity, which in turns drives a nonlinear model of neurovascular
coupling and Blood Oxygenation Level Dependent (BOLD) response. The neuronal
and haemodynamic parameters are estimated together on a voxel-by-voxel or
region-of-interest basis using a Bayesian estimation algorithm (variational
Laplace). This offers several novel contributions to receptive field modelling.
The variance / covariance of parameters are estimated, enabling receptive
fields to be plotted while properly representing uncertainty about pRF size and
location. Variability in the haemodynamic response across the brain is
accounted for. Furthermore, the framework introduces formal hypothesis testing
to pRF analysis, enabling competing models to be evaluated based on their model
evidence (approximated by the variational free energy), which represents the
optimal tradeoff between accuracy and complexity. Using simulations and
empirical data, we found that parameters typically used to represent pRF size
and neuronal scaling are strongly correlated, which should be taken into
account when making inferences. We used the framework to compare the evidence
for six variants of pRF model using 7T functional MRI data and we found a
circular Difference of Gaussians (DoG) model to be the best explanation for our
data overall. We hope this framework will prove useful for mapping stimulus
spaces with any number of dimensions onto the anatomy of the brain.
