To my mind this is essentially a well written and informative article. My only slight concern with the first draft of this article was that it might, in places, be a little 'hard going' for general readers with little prior knowledge of probability theory. The opening paragraph, for example, was very jargon laden. I have tried to address this a little in my edits by introducing what I hope to be an easily accessible example right in the opening paragraph, expanding on the authors' the prose a little here and there, and moving the figures closer to the text they refer to. I would consider my changes "minor editing suggestions". I hope the authors and readers find them useful.
This article gives an excellent introduction to the issue of sampling bias. It is very well structured and written and it explains concepts in a very intuitive way by making use of good examples. I have only a couple of minor suggestions:
- The information about the difference between sampling bias, sampling error, bias of probability function and limited sampling bias is a bit condensed. I was wondering whether the authors could make use of an example (maybe the example of the election poll they used before) to illustrate these biases.
- After equation (1), I guess I(X;Y) is not strickly zero when X and Y are statistically independent, for example, due to low sampling biases as later described. I would suggest something like: 'it is close to zero when X and Y are statistically independent'.
- At the end of the section on the effect of limited sampling on the determination of statistical and causal relationships, it is mentioned in one sentence how limited sampling bias can be corrected. I was wondering whether a bit more information could be given on how this correction is done, if it is possible to do so without extending much the article and getting into too many technical details.
- In the last paragraph, in most cases action potentials are no longer visualized with an oscilloscope, as it used to be in the good old times...
- I introduced some minor modifications directly in the text.