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State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data
Figure 4
Estimation of triple-wise interaction from simulated parallel spike sequences of 3 neurons.
(A) Dot displays of the simulated spike sequences, 
, which are sampled repeatedly for 
trials from a time-dependent log-linear model containing time varying pairwise and triple-wise interactions (duration: 
bins; see the dashed lines in C for the model parameters). Each of the 3 panels shows the spike events for each of the 3 variables, 
(
and 
), as black dots. Synchronous spike events across the 3 neurons as detected in individual trials are marked by blue circles. (B) Observed rates of joint spike events, 
(
). (Top) Observed rates of the synchronous spike events between all possible pair constellations as specified by index 
(
). (Bottom) Observed rate of the synchronous spikes across all 3 neurons, 
. (C) Smoothed estimates of the time-varying log-linear parameters, 
. The three panels depict the smoothed estimates (solid lines) of the log-linear parameters, 
, of the different orders (
), as obtained from the data shown in A and B (top and middle: the first and second order log-linear parameters; bottom: triple-wise spike interaction, 
). The gray bands indicate the 99% credible interval of the marginal posterior densities of the log-linear parameters. The dashed lines indicate the underlying time-dependent parameters used for the generation of the spike sequences.
doi: https://doi.org/10.1371/journal.pcbi.1002385.g004