Realistic computational models of neuronal activity typically involve many variables and parameters, most of which remain unknown or poorly constrained. Moreover, experimental observations of the neuronal system are typically limited to the times of action potentials, or spikes. One important component of developing a computational model is the optimal incorporation of these sparse experimental data. Here, we use point process statistical theory to develop a procedure for estimating parameters and hidden variables in neuronal computational models given only the observed spike times. We discuss the implementation of a sequential Monte Carlo method for this procedure and apply it to three simulated examples of neuronal spiking activity. We also address the issues of model identification and misspecification, and show that accurate estimates of model parameters and hidden variables are possible given only spike time data.
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