  A fundamental problem in neuroscience is to characterize the dynamics of
spiking from the neurons in a circuit that is involved in learning about a
stimulus or a contingency. A key limitation of current methods to analyze
neural spiking data is the need to collapse neural activity over time or
trials, which may cause the loss of information pertinent to understanding the
function of a neuron or circuit. We introduce a new method that can determine
not only the trial-to-trial dynamics that accompany the learning of a
contingency by a neuron, but also the latency of this learning with respect to
the onset of a conditioned stimulus. The backbone of the method is a separable
two-dimensional (2D) random field (RF) model of neural spike rasters, in which
the joint conditional intensity function of a neuron over time and trials
depends on two latent Markovian state sequences that evolve separately but in
parallel. Classical tools to estimate state-space models cannot be applied
readily to our 2D separable RF model. We develop efficient statistical and
computational tools to estimate the parameters of the separable 2D RF model. We
apply these to data collected from neurons in the pre-frontal cortex (PFC) in
an experiment designed to characterize the neural underpinnings of the
associative learning of fear in mice. Overall, the separable 2D RF model
provides a detailed, interpretable, characterization of the dynamics of neural
spiking that accompany the learning of a contingency.
