The spontaneous firing activity of the place cells reflects the position of
an experimental animal in its arena. The firing rate is high inside a part
of the arena, called the firing field, and low outside. It is generally ac
cepted concept that this is the way in which the hippocampus stores a map o
f the environment. This well known fact was recently reinvestigated [Fenton
, A.A., Muller, R.U., 1998. Proc. Natl. Acad. Sci. USA 95, 3182-3187] and i
t was found that while the activity was highly reliable in position, it did
not retain the same reliability in time. The number of action potentials f
ired during different passes through the firing field were substantially di
fferent (overdispersion). We present a mathematical model based on a doubly
stochastic Poisson process which is able to reproduce the experimental fin
dings. Further, it enables us to propose specific statistical inference on
the experiments in aim to verify data and model compatibility. The model pe
rmits to speculate about the neural mechanisms leading to the overdispersio
n in the activity of the hippocampal place cells. Namely, the statistical v
ariation of the intensity of firing can be achieved, for example, by introd
ucing a hierarchical structure into the local neural network. (C) 2000 Else
vier Science Ireland Ltd. All rights reserved.