  Recent remarkable advances in the experimental techniques have provided a
background for inferring neuronal couplings from point process data that
includes a great number of neurons. Here, we propose a systematic procedure for
pre- and post-processing generic point process data in an objective manner, to
handle data in the framework of a binary simple statistical model, the Ising or
generalized McCulloch--Pitts model. The procedure involves two steps: (1)
determining time-bin size for transforming the point-process data into
discrete-time binary data and (2) screening relevant couplings from the
estimated couplings. For the first step, we decide the optimal time-bin size by
introducing the null hypothesis that all neurons would fire independently, then
choosing a time-bin size so that the null hypothesis is rejected with the most
strict criterion. The likelihood associated with the null hypothesis is
analytically evaluated and used for the rejection process. For the second
post-processing step, after a certain estimator of coupling is obtained based
on the pre-processed dataset, the estimate is compared with many other
estimates derived from datasets obtained by randomizing the original dataset in
the time direction. We accept the original estimate as relevant only if its
absolute value is sufficiently larger than them of randomized datasets. These
manipulations suppress false positive couplings induced by statistical noise.
We apply this inference procedure to spiking data from synthetic and in vitro
neuronal networks. The results show that the proposed procedure identifies the
presence/absence of synaptic couplings fairly well including their signs, for
the synthetic and experimental data. In particular, the results support that we
can infer the physical connections of underlying systems in favorable
situations, even when using the simple statistical model.
