  Data analysed here derive from experiments conducted to study neurons'
activity in the visual cortex of behaving monkeys. We consider a
spatio-temporal adaptive penalized spline (P-spline) approach for modelling the
firing rate of visual neurons. To the best of our knowledge, this is the first
attempt in the statistical literature for locally adaptive smoothing in three
dimensions. Estimation is based on the Separation of Overlapping Penalties
(SOP) algorithm, which provides the stability and speed we look for.
