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State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data
Figure 8
Analysis of stationary spike correlations of 
simulated neurons using Bayes factor.
(A) Sketch of different time periods and the underlying models used for the generation of parallel spike sequences: (I) Model of independent spiking (
, 
, 
for 
and 
); (II) Model of simultaneously positive pairwise interactions, without a triple-wise interaction (
, 
, 
for 
); (III) Model of triple-wise interaction, with negative pair interactions (
, 
, 
for 
). (B) Raster display of three parallel spike sequences, 
, within one example trial. Each spike is colored according to the spike pattern in which it appears: Spikes occurring in triplets are shown in red, spikes within doublets (all types) are marked in blue, and spikes not involved in any synchrony pattern are shown in black. (C) The bar plots demonstrate the Bayes factors (BFs), Eq. 48, for each of the time periods I–III in bit units. The upper panel shows the average BF when testing simultaneously positive pairwise interactions (Test 1), averaged across 200 realizations (
). A positive value for the log of the BF supports the model for the presence of simultaneously positive pairwise interactions, 
, while a negative value supports the absence of such an assembly, 
. The BFs per sample and time period are computed by applying a pairwise state-space log-linear model (
) independently to the three periods. We use a state model with 
. The lower panel shows the BF for the positive triple-wise spike interaction (Test 2), 
, as opposed to a zero or negative triple-wise spike interaction, 
, in each of the three periods. The BFs are computed from a full state-space log-linear model (
). (D) Bar plot of the bin-by-bin BFs (Eq. 52) sorted by the different spike patterns in the three periods (from top to bottom). The contributions to the BFs (shown in C) from the different spike patterns are sorted and displayed using the indicated spike patterns (000, 100, 110 and 111) as representative examples. The gray bars indicate the average BFs of simultaneously positive pairwise interactions, with the average computed for the spike patterns observed in 200 realizations in the respective periods, while the dark gray bars indicate the average BFs for the triple-wise spike correlation.
doi: https://doi.org/10.1371/journal.pcbi.1002385.g008