Thank you for agreeing to help edit Probability Surveys.
(1) The Big Picture.
In judging a submission, the most important single question to keep in mind is: if I had a graduate student working on a related topic, would I encourage them to read this paper? That is, a typical survey paper should provide a bridge between textbook material and current research, and should be useful and interesting and comprehensible even to people slightly outside the specific topic under consideration.
(2) Clarity.
Even well-written research papers require effort to read line-by-line. But a well-written survey paper should be easier to read. If reading is hard work, ask yourself: could this be explained better? or could it be cut out? In particular, the abstract and introduction should be accessible to a wide audience.
(3) Correctness.
Often it will be clear that the author is an expert, in which case referees need not put much work into assessing technical accuracy.
(4) Focus and Completeness.
Does the paper start with a clear description of the topic it intends to survey, and does it in fact do a good job of selecting the most important and interesting parts of the topic to discuss?
(5) Your Report.
Authors are rarely enthusiastic about doing major re-writes, so we try to avoid recommendations for major re-writes. Usually a referee can decide after a quick reading whether the paper is “basically acceptable” or not. If not, then a quick report and explanation to the Associate Editor is sufficient; it is not necessary to write a separate report to the author. If acceptable, it is worth reading the paper again for the purpose of making suggestions to the author.
Concrete suggestions of the type
- could you add a section explaining the connection of this topic with topic X
- the material in section 5.3 seems too technical; can you omit it?
are more helpful than comments of the type
- I found section 2.11 confusing
For acceptable papers, focus on a report to author; the separate report to editor can be brief.
(6) Timing.
Please submit your report in 6 weeks if at all possible. If you need more time, let the Associate Editor know.
Thank you again for your help. Good refereeing is the key ingredient of a successful journal.