  By varying the noise intensity, we study stochastic spiking coherence (i.e.,
collective coherence between noise-induced neural spikings) in an inhibitory
population of subthreshold neurons (which cannot fire spontaneously without
noise). This stochastic spiking coherence may be well visualized in the raster
plot of neural spikes. For a coherent case, partially-occupied "stripes"
(composed of spikes and indicating collective coherence) are formed in the
raster plot. This partial occupation occurs due to "stochastic spike skipping"
which is well shown in the multi-peaked interspike interval histogram. The main
purpose of our work is to quantitatively measure the degree of stochastic
spiking coherence seen in the raster plot. We introduce a new spike-based
coherence measure $M_s$ by considering the occupation pattern and the pacing
pattern of spikes in the stripes. In particular, the pacing degree between
spikes is determined in a statistical-mechanical way by quantifying the average
contribution of (microscopic) individual spikes to the (macroscopic)
ensemble-averaged global potential. This "statistical-mechanical" measure $M_s$
is in contrast to the conventional measures such as the "thermodynamic" order
parameter (which concerns the time-averaged fluctuations of the macroscopic
global potential), the "microscopic" correlation-based measure (based on the
cross-correlation between the microscopic individual potentials), and the
measures of precise spike timing (based on the peri-stimulus time histogram).
In terms of $M_s$, we quantitatively characterize the stochastic spiking
coherence, and find that $M_s$ reflects the degree of collective spiking
coherence seen in the raster plot very well. Hence, the
"statistical-mechanical" spike-based measure $M_s$ may be used usefully to
quantify the degree of stochastic spiking coherence in a statistical-mechanical
way.
