  To understand how rich dynamics emerge in neural populations, we require
models exhibiting a wide range of activity patterns while remaining
interpretable in terms of connectivity and single-neuron dynamics. However, it
has been challenging to fit such mechanistic spiking networks at the single
neuron scale to empirical population data. To close this gap, we propose to fit
such data at a meso scale, using a mechanistic but low-dimensional and hence
statistically tractable model. The mesoscopic representation is obtained by
approximating a population of neurons as multiple homogeneous `pools' of
neurons, and modelling the dynamics of the aggregate population activity within
each pool. We derive the likelihood of both single-neuron and connectivity
parameters given this activity, which can then be used to either optimize
parameters by gradient ascent on the log-likelihood, or to perform Bayesian
inference using Markov Chain Monte Carlo (MCMC) sampling. We illustrate this
approach using a model of generalized integrate-and-fire neurons for which
mesoscopic dynamics have been previously derived, and show that both
single-neuron and connectivity parameters can be recovered from simulated data.
In particular, our inference method extracts posterior correlations between
model parameters, which define parameter subsets able to reproduce the data. We
compute the Bayesian posterior for combinations of parameters using MCMC
sampling and investigate how the approximations inherent to a mesoscopic
population model impact the accuracy of the inferred single-neuron parameters.
