I'm trying to compose a guide on methods for (1) generating and (2) verifying theories about rare phenomena. I am interested in any sort of ideas and experiences.
Dear Chris, I am more daring about it: if you truly do research on rare phenomena, you have to develop new methods. By definition, innovation entails a real challenge, so that the standard methods, f.i. are useless vis-à-vis new problems, etc. I would be glad and proud if you work on developing those new methods in accordance with the fields, problems and heuristics you work with.
What is it that you want to examine and who is the one classifying it as rare? Sometimes these things- phenomena-, although rare to the outsider are often mundane matters to communities that they relate to.
Conducting research on rare phenomena entails a descriptive type of research in the first instance. This would involve identifying the characteristics of what would be explored later on to broaden our understanding of that phenomenon. Subsequently, the question of method can be adressed.
As Mohamed said you need to obtain a complete description of the rare phenomenon. It depends upon the type of phenomenon. For example if it is occurring currently then you may use a qualitative approach such as Ethnographic in order to get complete details of the phenomenon. Once you have a complete description then formulate a theory and then postulate a hypothesis and prove it through any of the research approaches. If it has occurred in the past, then use Historical research methods to gather the necessary information. Then continue from there.