I’m preparing a journal article on a novel method. There are several related methods publicly described on preprint servers such as arXiv or bioRxiv.
Is it permitted to cite works that have not been peer reviewed and is it appropriate to acknowledge them? I wish to discuss and critique them as they are critical to the novelty of our work.
I consider it not only permitted to discuss and critique crucial related work in preprints, but obligatory. That it hasn't been peer-reviewed should mildly inform how sceptical we are when considering such work (only mildly, because we shouldn't blindly trust that peer-review would find all flaws).
If a journal has policies dictating otherwise, the journal is wrong in having them.
That's an interesting question.
It certainly is not forbidden, but as others have said, journal rules may apply. On the one hand, the contribution should be given, but on the other hand, there is no peer review and thus no independent evaluation. On numerous occasions, I had to remove such preprint citations because the work I cited was fundamentally flawed. Thus, I tend to not cite work that is only published in preprint venues unless it has an immediate and obvious connection to my work.
I try to find a version that has been published and more often than not the paper has been submitted to some peer-reviewed workshop (or similar), that has no archival proceedings.
This may depend on the journal you're submitting to, or even on individual editors. I have seen journals in which preprints on such servers were cited, but I also once had a request by an editor to remove such a citation. The first thing to do is to see whether the policy of the journal has anything on the matter. If not, personally I'd include these works in my submission because the worst that can happen is that the editor asks to remove them. I cannot imagine that anyone would reject a paper because of this. (Note that in my field papers are hardly ever accepted as they are in the first go, so a request like this wouldn't lose you time; this may be different in some fields/journals.)
