KS plot

What's the intuition behind the uniform ticks? Why do they set $b_k=\frac{k-0.5}{n}$

Without understanding the isi... data too much, theyve rescaled and ordered the z so theyre assuming theyre drawn from a uniform distribution. To visualize this, you could say how different they are from an evenly sampled unit interval, so in other words the b's. If the z samples are roughly evenly spaced then they'll lie on the 45 degree line If not, then they wont.

In their diagram, would the y-axis be empirical cdf and the x-axis be the theoretical cdf?

Thanks, I'm getting confused with some plots. Some of the KS tests plots theoretical cdf against empirical cdf? How does that work, supposed you have 10 data points 0.1,0.11,...,0.2 and you want to test if it's uniform distributed. For the first data point it's empirical cdf would just be 1/10 or (1-0.5)/10 depending on how you define the empirical cdf. Would the theoretical cdf then be F(0.1)? where F is the cdf of the uniform distribution

Thats basically what the posted plot is doing, as far as I understand you. The cdf of a uniform is a linear ramp, so the 45 diagonal which is why the b's are uniformally sampled from [0,1] as they represent the (cumulative probability of the) expected value of the ith sample.

For your example, so a uniform on [0.1,0.2] and say you had 10 samples, then their expected values would be 0.105, 0.115,...0.195
so the (scaled) bs in your plot.

I'm still not really following, I'll attach an example. Could you help clarify my confusions, thanks.
The rescaled ISI in this case should theoretically follow an exponential distribution of unit parameter as shown in figure 15A.
First thing I'm confused on, the y-axis should be named 'empirical cdf' rather than cdf shouldn't it?
What is figure 15B? What exactly is the 'model cdf'? Is it just the exponential cdf plotted against the empirical cdf derived in figure 15A?