77 Estimating spiking rate
We will do a very simple experiment in which we take a sample of retinal tissue and expose it to a constant light source. We measure the spiking activity of a single retinal ganglion cell (RGC) over a time interval.
a) Obtain a maximum likelihood estimate of the spiking rate assuming that spiking is a Poisson process. Use the interspike intervals (ISIs) in your analysis. Also report a confidence interval.
b) Researchers often determine a spiking rate directly from data by creating time windows, counting the spikes in the window, and then dividing the number of spikes in the time window by the width of the window. So that this is equivalent to finding a MLE of the spiking rate \(\beta\).
c) Now assume a Gamma model for ISIs. This is often used by neuroscience researchers to handle non-Poissonian data. Obtain parameter estimates with confidence intervals.