  A common analytical problem in neuroscience is the interpretation of neural
activity with respect to sensory input or behavioral output. This is typically
achieved by regressing measured neural activity against known stimuli or
behavioral variables to produce a "tuning function" for each neuron.
Unfortunately, because this approach handles neurons individually, it cannot
take advantage of simultaneous measurements from spatially adjacent neurons
that often have similar tuning properties. On the other hand, sharing
information between adjacent neurons can errantly degrade estimates of tuning
functions across space if there are sharp discontinuities in tuning between
nearby neurons. In this paper, we develop a computationally efficient block
Gibbs sampler that effectively pools information between neurons to de-noise
tuning function estimates while simultaneously preserving sharp discontinuities
that might exist in the organization of tuning across space. This method is
fully Bayesian and its computational cost per iteration scales
sub-quadratically with total parameter dimensionality. We demonstrate the
robustness and scalability of this approach by applying it to both real and
synthetic datasets. In particular, an application to data from the spinal cord
illustrates that the proposed methods can dramatically decrease the
experimental time required to accurately estimate tuning functions.
