The spiking dynamics of simultaneously recorded neurons from a small region of cortex reflect the local network structure of excitatory and inhibitory connections between observed neurons, as well as the time varying response of the neurons to their many unobserved and correlated inputs. Inference about the local network is easily contaminated by these unobserved nonstationary influences. We have been exploring conditional inference as an approach for statistically isolating local network dynamics from background nonstationarities. The approach is promising, but there remain many modeling questions and computational challenges.