  We present two Bayesian procedures to infer the interactions and external
currents in an assembly of stochastic integrate-and-fire neurons from the
recording of their spiking activity. The first procedure is based on the exact
calculation of the most likely time courses of the neuron membrane potentials
conditioned by the recorded spikes, and is exact for a vanishing noise variance
and for an instantaneous synaptic integration. The second procedure takes into
account the presence of fluctuations around the most likely time courses of the
potentials, and can deal with moderate noise levels. The running time of both
procedures is proportional to the number S of spikes multiplied by the squared
number N of neurons. The algorithms are validated on synthetic data generated
by networks with known couplings and currents. We also reanalyze previously
published recordings of the activity of the salamander retina (including from
32 to 40 neurons, and from 65,000 to 170,000 spikes). We study the dependence
of the inferred interactions on the membrane leaking time; the differences and
similarities with the classical cross-correlation analysis are discussed.
