We propose a scalable semiparametric Bayesian model to capture dependencies
among multiple neurons by detecting their co-firing (possibly with some lag
time) patterns over time. After discretizing time so there is at most one spike
at each interval, the resulting sequence of 1's (spike) and 0's (silence) for
each neuron is modeled using the logistic function of a continuous latent
variable with a Gaussian process prior. For multiple neurons, the corresponding
marginal distributions are coupled to their joint probability distribution
using a parametric copula model. The advantages of our approach are as follows:
the nonparametric component (i.e., the Gaussian process model) provides a
flexible framework for modeling the underlying firing rates; the parametric
component (i.e., the copula model) allows us to make inference regarding both
contemporaneous and lagged relationships among neurons; using the copula model,
we construct multivariate probabilistic models by separating the modeling of
univariate marginal distributions from the modeling of dependence structure
among variables; our method is easy to implement using a computationally
efficient sampling algorithm that can be easily extended to high dimensional
problems. Using simulated data, we show that our approach could correctly
capture temporal dependencies in firing rates and identify synchronous neurons.
We also apply our model to spike train data obtained from prefrontal cortical
areas in rat's brain
