Homework7 4 - Githubissues

dduyh commented 5 years ago

I have some confusion about the problem 4 in homework 7. What does that mean by "the phase is drawn uniformly between 0 and 2pi for each trial"? Does that mean the theta changes randomly through time? Is that still a Poisson or inhomogeneous Poisson process?

wenquan commented 5 years ago

You are right. The average number of spikes $\langle n \rangle$ can be done in two parts.

First, perform an average over a time period T.
Second, perform an average over different $\theta \in [0, 2\pi]$ .

You will find that the results are the same as homogeneous poisson process, because the average over \theta will cancel out the second term.

However, this is not the case when you compute the variance $\langle n^2 \rangle - \langle n \rangle^2$ . The reason is that there would be a $\cos^2(\omega t+\theta)$ term.

Enjoy.

dduyh commented 5 years ago

I got it! So that r(t) means every time I start to test a new trial, the phase will be changed randomly, right?

Wenlab / Computation-Neuro-Course

Homework7 4 #24