  Synapses change on multiple timescales, ranging from milliseconds to minutes,
due to a combination of both short- and long-term plasticity. Here we develop
an extension of the common Generalized Linear Model to infer both short- and
long-term changes in the coupling between a pre- and post-synaptic neuron based
on observed spiking activity. We model short-term synaptic plasticity using
additive effects that depend on the presynaptic spike timing, and we model
long-term changes in both synaptic weight and baseline firing rate using point
process adaptive smoothing. Using simulations, we first show that this model
can accurately recover time-varying synaptic weights 1) for both depressing and
facilitating synapses, 2) with a variety of long-term changes (including
realistic changes, such as due to STDP), 3) with a range of pre- and
post-synaptic firing rates, and 4) for both excitatory and inhibitory synapses.
We then apply our model to two experimentally recorded putative synaptic
connections. We find that simultaneously tracking fast changes in synaptic
weights, slow changes in synaptic weights, and unexplained variations in
baseline firing is essential. Omitting any one of these factors can lead to
spurious inferences for the others. Altogether, this model provides a flexible
framework for tracking short- and long-term variation in spike transmission.
