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Deducing the structure of neural circuits is one of the central problems ofmodern neuroscience. Recently-introduced calcium fluorescent imaging methodspermit experimentalists to observe network activity in large populations ofneurons, but these techniques provide only indirect observations of neuralspike trains, with limited time resolution and signal quality. In this work wepresent a Bayesian approach for inferring neural circuitry given this type ofimaging data. We model the network activity in terms of a collection of coupledhidden Markov chains, with each chain corresponding to a single neuron in thenetwork and the coupling between the chains reflecting the network'sconnectivity matrix. We derive a Monte Carlo Expectation--Maximizationalgorithm for fitting the model parameters; to obtain the sufficient statisticsin a computationally-efficient manner, we introduce a specializedblockwise-Gibbs algorithm for sampling from the joint activity of all observedneurons given the observed fluorescence data. We perform large-scalesimulations of randomly connected neuronal networks with biophysicallyrealistic parameters and find that the proposed methods can accurately inferthe connectivity in these networks given reasonable experimental andcomputational constraints. In addition, the estimation accuracy may be improvedsignificantly by incorporating prior knowledge about the sparseness ofconnectivity in the network, via standard L$_1$ penalization methods.

A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data