HW 4.1: Inverse Gaussian model for interspike intervals

This problem is worth 30 points.

Data set download

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Consider a 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) The data set contains the times of spikes recording for the RGC. Compute the interspike intervals (ISIs). An ISI is the amoung of time between spikes. Make an exploratory plot of the ISIs.

b) As a first model for modeling interpike intervals, we can model spiking as a Poisson process. Propose such a model (complete with priors) and infer the relevant parameter(s). Be sure to do prior predictive and posterior predictive checks.

c) Another model that is prevalent in the literature is to model ISIs with an Inverse Gaussian distribution. Use an Inverse Gaussian likelihood and appropriate priors and infer the relevant parameter(s). Again, be sure to do prior predictive and posterior predictive checks.