I'm in the second half of an electrical engineering doctorate but have come to realize that mathematical statistics and the theoretical side of information theory might be more my calling. I am too far along in my research to pivot my doctoral thesis to this abstract of an area, especially considering I am in the engineering department.
I am relatively strong in math (Tall for a hobbit... taking the grad functional analysis sequence, albeit late relative to when math students see it) and have a (very conservative) original math side project, so I believe I am at least capable of understanding math research. However my environment is still most conducive to studying engineering problems, not math/stats ones.
If someone in this position wanted to research and publish in mathematical statistics later on, would an engineering doctorate be enough credentials to do so?
There are several reasons I ask:
- The amount of math knowledge implied by a typical engineering doctorate is not anywhere near the amount necessary to do research in statistics theory. (Not to say the EEs I have met here aren't extremely capable in their field, just most aren't focused on research level math).
- The direction my adviser and I are headed with my current thesis is interesting and useful. I'm not about to drop my engineering degree.
- If it isn't necessary I would rather not jump through all the hoops of getting a PhD all over again.