## Efficient Markov chain Monte Carlo methods for
decoding neural spike trains

In press, Neural Computation

Stimulus reconstruction or decoding methods provide an important tool
for understanding how sensory and motor information is represented in
neural activity. We discuss Bayesian decoding methods based on an
encoding generalized linear model (GLM) that accurately describes how
stimuli are transformed into the spike trains of a group of
neurons. The form of the GLM likelihood ensures that the posterior
distribution over the stimuli that caused an observed set of spike
trains is log-concave so long as the prior is. This allows the maximum
a posteriori (MAP) stimulus estimate to be obtained using efficient
optimization algorithms. Unfortunately, the MAP estimate can have a
relatively large average error when the posterior is highly
non-Gaussian. Here we compare several Markov chain Monte Carlo (MCMC)
algorithms that allow for the calculation of general Bayesian
estimators involving posterior expectations (conditional on model
parameters). An efficient version of the hybrid Monte Carlo (HMC)
algorithm was significantly superior to other MCMC methods for
Gaussian priors. When the prior distribution has sharp edges and
corners, on the other hand, the "hit-and-run" algorithm performed
better than other MCMC methods. Using these algorithms we show that
for this latter class of priors the posterior mean estimate can have a
considerably lower average error than MAP, whereas for Gaussian priors
the two estimators have roughly equal efficiency. We also address the
application of MCMC methods for extracting non-marginal properties of
the posterior distribution. For example, by using MCMC to calculate
the mutual information between the stimulus and response, we verify
the validity of a computationally efficient Laplace approximation to
this quantity for Gaussian priors in a wide range of model parameters;
this makes direct model-based computation of the mutual information
tractable even in the case of large observed neural populations, where
methods based on binning the spike train fail. Finally, we consider
the effect of uncertainty in the GLM parameters on the posterior
estimators.

Reprint | Liam Paninski's research page