Bursts in gamma and other frequency ranges are thought to contribute to the efficiency of working memory or communication tasks. Abnormalities in bursts have also been associated with motor and psychiatric disorders. The determinants of burst generation are not known, specifically how single cell and connectivity parameters influence burst statistics and the corresponding brain states. We first present a generic mathematical model for burst generation in an excitatory-inhibitory (EI) network with self-couplings. The resulting equations for the stochastic phase and envelope of the rhythm’s fluctuations are shown to depend on only two meta-parameters that combine all the network parameters. They allow us to identify different regimes of amplitude excursions, and to highlight the supportive role that network finite-size effects and noisy inputs to the EI network can have. We discuss how burst attributes, such as their durations and peak frequency content, depend on the network parameters. In practice, the problem above follows the a priori challenge of fitting such E-I spiking networks to single neuron or population data. Thus, the second part of the talk will discuss a novel method to fit mesoscale dynamics using single neuron data along with a low-dimensional, and hence statistically tractable, single neuron 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 an E-I network of generalized integrate-and-fire neurons for which mesoscopic dynamics have been previously derived. We show that both single-neuron and connectivity parameters can be adequately recovered from simulated data.