  One of the main current issues in Neurobiology concerns the understanding of
interrelated spiking activity among multineuronal ensembles and differences
between stimulus-driven and spontaneous activity in neurophysiological
experiments. Multi electrode array recordings that are now commonly used
monitor neuronal activity in the form of spike trains from many well identified
neurons. A basic question when analyzing such data is the identification of the
directed graph describing "synaptic coupling" between neurons. In this article
we deal with this matter working with a high quality multielectrode array
recording dataset (Pouzat et al., 2015) from the first olfactory relay of the
locust, $Schistocerca$ $americana$. From a mathematical point of view this
paper presents two novelties. First we propose a procedure allowing to deal
with the small sample sizes met in actual datasets. Moreover we address the
sensitive case of partially observed networks. Our starting point is the
procedure introduced in Duarte et al. (2016). We evaluate the performance of
both original and improved procedures through simulation studies, which are
also used for parameter tuning and for exploring the effect of recording only a
small subset of the neurons of a network.
