Sparse spectral estimation from point process observations

We consider the problem of estimating the power spectral density of the neural covariates underlying the spiking of a neuronal population. We assume the spiking of the neuronal ensemble to be described by Bernoulli statistics. Furthermore, we consider the conditional intensity function to be the logistic map of a second-order stationary process with sparse frequency content. Using the binary spiking data recorded from the population, we calculate the maximum a posteriori estimate of the power spectral density of the process while enforcing sparsity-promoting priors on the estimate. Using both simulated and clinically recorded data, we show that our method outperforms the existing methods for extracting a frequency domain representation from the spiking data of a neuronal population