  Emerging technologies are revealing the spiking activity in ever larger
neural ensembles. Frequently, this spiking is far from independent, with
correlations in the spike times of different cells. Understanding how such
correlations impact the dynamics and function of neural ensembles remains an
important open problem. Here we describe a new, generative model for correlated
spike trains that can exhibit many of the features observed in data. Extending
prior work in mathematical finance, this generalized thinning and shift (GTaS)
model creates marginally Poisson spike trains with diverse temporal correlation
structures. We give several examples which highlight the model's flexibility
and utility. For instance, we use it to examine how a neural network responds
to highly structured patterns of inputs. We then show that the GTaS model is
analytically tractable, and derive cumulant densities of all orders in terms of
model parameters. The GTaS framework can therefore be an important tool in the
experimental and theoretical exploration of neural dynamics.
