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Do professors usually benefit from their undergraduate researchers?

Some do, absolutely. In fact, when I went up for tenure, I can safely say I made more than half my tenure case on the basis of work done with undergrads (and nobody could have told from the paper record). This was partly out of necessity: my department did no work in my area when I joined, so I had to create a presence from scratch, and it took a while to get the grad student pipeline going. But I also did it because I really love working with undergrads as much as I do with more senior researchers.Now, be aware that when people use the term "research" with undergraduates, they often mean two very different things:routine "work" (which I lump as "build me a GUI" or "be a code-monkey")actual research (as in, work on open questions that may not yield answers)Personally, I am very clear about distinguishing between these two, and when I speak of undergraduate research, I mean the latter: the kind where innovation happens, papers get written, etc. Henceforth I'll call this Research to distinguish it from the generic term. But a lot of faculty not only co-mingle the concepts, they in fact often mean the former.Once we get past that to actual Research, there are still multiple models. I have been through two different ones in my career. Sometimes, the undergrad works directly with the professor on a problem unrelated to what the PhD students and others in the group might be working on. In other cases, the undergrad works on a topic that more senior group members are working on, and then works with other group members in addition to (or even in place of) the professor. Each model has its strengths and weaknesses that I think you can infer.However, it is difficult to get enough work done with undergrads because of the short period of time that they're actually firing on all cylinders and able to contribute productively, without having graduated. I have evolved a very peculiar formula that works fabulously for me and may not so much for others. I'm not bothering to go into it because it involves a combination of my teaching schedule, Brown's academic calendar, the Brown student mentality, courses that I teach, and also a willful replacement of internal Brown Research "ceremony" (theses on bond paper, poster sessions, etc.) for genuine, externally-visible Research. When I can get these stars to align, I can actually take an undergrad all the way to publishing at major venues. I've typically had 1-2 such papers every year since about 2000 (and a few before that as a grad student).My advice to undergrads is this:Make sure you know what it is you want (to be a programmer/lab assistant/etc. or a genuine Researcher -- the latter may sound cool but not be so much fun in practice).If it's the latter, figure out the right professors to ask based not just on your interest but also your background. You can probably do development work for many, but Research only with very few -- people whose work you know through courses with them, for instance.Have a blunt conversation to make sure you know what kind of "research" you're getting into, and whether it's the one you want (in particular, if you want to do Research and what they're offering sounds like pure development, express your desires more clearly and ask more probing questions).Be prepared for a professor to say sorry, you're just not in a position to contribute to Research. Respect that answer. They may be wrong about you, but they are probably right in general.Good luck!

What are some statistical methods that have been created to attempt to determine causality (with only observational data, without a controlled experiment)?

In addition to approaches and methods referred to in some of the previous answers, I'm surprised that nobody has mentioned structural equation modeling (SEM) family of statistical methods, suitable for determining causality (to various degrees of validity, of course). I'm currently working on my dissertation, which uses SEM as a main statistical toolset and only secondary data, which, I believe, is roughly synonymous to observational data (in this context). What causal conclusions I will be able to infer from the results of the analysis, remains to be seen.In order to address parametric SEM's deficiencies, such as potential bias and misspecification, some semi-parametric approaches have been developed, including inverse probability weighting and g-estimation. I'm not familiar with these techniques, so I'm mentioning them here just for completeness.In the context of my reference to SEM, some people's work is more relevant and IMHO should be mentioned here (the following mentions are in no way meant to be even close to a comprehensive source, but simply an example). In particular, work of UCLA's Judea Pearl (Cognitive Systems Laboratory) and, in particular, his book "Causality: Models, Reasoning and Inference" (CAUSALITY, 2nd Edition, 2009). I'm sure that many people are aware of this book. However, I believe that much less people are familiar with another interesting book on the topic. This book is called "Causal Inference" and the authors are Harvard School of Public Health's Miguel Hernan and Jamie Robins. This book is expected to be published next year, but free drafts (in PDF format) and complementary materials are available on the book's website: Causal Inference Book.In addition to the above, I'd like to share some resources on the topic, which I find quite interesting and I hope will be useful to other people:1) Blog on causal analysis: Causal Analysis in Theory and Practice2) A University of Copenhagen's free course (on Coursera) "Measuring causal effects in social sciences": Coursera3) Posts on causal inference in Andrew Gelman and colleagues' blog: Causal Inference Archives - Statistical Modeling, Causal Inference, and Social Science

If someone renounces their citizenship why isn't there a generic passport provided by the United Nations, for example?

I renounced my US Citizenship and became Stateless 4–1/2 years ago. There are some 80 countries who signed the 1954 UN Convention on the Status of Stateless Persons.(Edit 07/07/2018: More details in my blog: Experience: My first International Trip using a “Stateless Passport”)That Convention creates various obligations for the countries that signed it. One of them relates to “Travel Documents” (essentially passports). In short, if a Stateless person is legally in the territory of one of those countries, the country is obligated to issue them a “Travel Document”. If one is illegally in one of those countries, the country is strongly encouraged to issue one (and as a practical matter would need to in order for the person to leave).Although the country I reside in (legally) is obligated to issue me a travel document they have not done so yet; as they have never issued one they don’t have a process. However, I traveled to a nearby country and received one 2–1/2 hours after I presented the paperwork they required.You can see in the OCR code “XXA” that is in the space for Nationality, and XXA is the code for Stateless Persons per the 1954 convention. XXB is for refugees, and XXX for those with unknown or unclear nationality. On one of the back pages (in very small print) it has a disclaimer stating that the document is not a national passport and has no impact or declaration of the nationality of the holder.It is essentially a passport in format, except for that disclaimer and the front saying “Titulo de Identidad y Viaje” instead of “Passport”. Additionally, and unlike a passport, it infers no obligations on the issuing country to the individual (ie: diplomatic protection, etc), and infers no obligations on the individual to the issuing country (allegiance, military service, etc).

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