PhD Stats/Biostats - research interest in statement of purpose?

[DMX]

I'm in the process of writing my statement of purpose and I've stated that my research interests are in Markov Chain Monte Carlo methods that mirror physical processes (e.g. simulated annealing, quantum annealing). Specifically, I'm interested in to what extent they mirror the actually annealing processes, and statistical properties of why they work so well. This interest was inspired from a project that I did in one of my classes.

Some concerns:

- am I being too specific with regard to my research interests? Should I make my SoP more 'generic' (e.g. 'given the amount of data we are inundated with in the modern world, I believe that the development and application of sophisticated statistical models are paramount')?

- could I be seen as too 'naive'? I've only taken a few courses in MCMC methods and perhaps these questions have already been answered, or are unrealistic to be answered (an analog might be a PhD CS applicant writing in his SoP that he's interested in developing Artificial Intelligence that can feel emotion. while this would be a specific research interest, it reeks of naivete).

[DMX]

By "naive" I'm worried as my research interests coming off as too "pie-in-the-sky"

[cyberwulf]

Though it's really not a huge deal because personal statements won't make or break your application, I would aim for somewhere between a specific project idea and "I want to do some kind of statistics!". I think your best bet would be to mention that you're really interested in MCMC methods, and in particular simulated annealing, but stop short of laying out the specific research questions you think you'd like to answer. As I said, it's not likely to matter much, but you want every admissions committee to think they have a shot of attracting you to their school. If you are very specific in your statement, a good place which doesn't have people in that specific research area might see you as a longshot to come to their department and decide to pass in favor of someone else.

It's good to show that you've thought about interesting potential research topics, but ultimately most students end up working on something very different than what they imagined entering graduate school. Hence, it's important to convey that you're also broadly interested in statistics/biostatistics and would be happy working in other areas.