Initial agenda: the warm-up

Here are some warm-up tasks:

1. Run through a single complete instance of Kramer's FDR (false discovery rate) mechanism for a small random network with correlated noise. (Basically, replicate Section IV.A of Kramer2009.)
1. Consider the null distribution of $C_{ij}$ for colored noise, and as a function of the signal length $n$.
2. Also, examine the distribution of $s_{ij} = \mathrm{max}_\tau|C_{ij}(\tau)|$ whose CDF $P[z]$ is given in Eq. 4 of Kramer2009.
2. Run through many instances of the inference on many small random networks, to verify if the expected number of spurious edges is consistent on multiple instances of the inference task (where ground truth is known).
1. I may want to explore the parameter space a bit, considering the accuracy of the inference as a function of the coupling strength $\alpha$, as well as the general validity of FDR.
3. Acquaint myself with Izhikevich's synthetic neuron simulation routine, for the generation of simulated neural data. Note that Izhikevich's script is referred to in a few computational papers on network inference.
4. Acquaint myself with the "frequency domain bootstrap" method in Kramer2009, which will be relevant for experimental cases where one cannot simply analytically estimate or simulate a distribution.

I am also interested in coupling measures that are not the sample cross-correlation (many are listed in Kramer2009). In particular, I am interested in asymmetric measures that can yield directed dependencies. On this thought, a concept that is repeatedly mentioned in the literature is "Granger causality."