Hi all. I am coming into this from a fairly unique path and I would be very grateful for any opinions on how crazy or not I am to pursue a PhD in statistics. I absolutely loved math in HS, and was always told I should be an engineer. That's how I went into college and I kind of got tunnel vision towards getting an eng. degree. Courses in the math department seemed intriguing, but with the time commitments of engineering I focused on just taking the ones I needed.
Out of university I worked a year at Carnegie Mellon writing reduced-order battery models which involved some data processing and monte carlo experiments. I touched on statistical methods from an applied side. I have since gone to work as a mechanical engineer in hydropower since 2019. I enjoy building things to an extent, but I spend my intellectual free time reading and trying to understand election models, pandemic models, sports performance models, etc. I still love math, but it has taken me this long to realize it's an option to actually study it. I am taking a general stats/probability course at the local university because I have no formal stats instruction yet.
I would very much like to pursue a PhD in statistics. I think research driving scientific models would be the most impactful way I could contribute to society. I intend to apply for Fall 2022. I know my undergraduate course load is weak and my current job is not in data science/stats, but I'd like to believe I have something to offer in practical experience and perspective. Am I crazy to think I could switch gears like this? Thank you to anyone willing to share their thoughts.
Undergraduate institution: Princeton University
Major: Mechanical and Aerospace Engineering
GPA: 3.82/4.0
Relevant courses:
Multivariable calc (A-) ; Algorithms and Data structures (A-) ; Linear algebra (A-) ; ODEs (A-) ; Math in ENG II [PDEs/Complex analysis] (B+)
My remaining engineering coursework was mathematically technical, but the above are the only math-specific courses.
Course plan to take in 2021: Currently enrolled in Engineering Stats at local University. Plan to take a course in R this summer.
Coding: Python, Julia, Matlab
Research experience: 1. 2-semester undergraduate senior project in fluid mechanics. 2. 1 year of data-based Li-Ion battery modeling at Carnegie Mellon as post-bach
Work Experience: Mechanical Engineer at water resources/hydropower company (since AUG 2019)
Letters of Recommendation: I expect to get one from the professor under whom I worked at CMU. The second would likely come from my supervisor at my current job.
GRE: Not taken(will take it in 2021)
GRE math: Not taken(will potentially take it in 2021)
Honors: Magna cum laude, Tau Beta Pi
type of student: Domestic white male
Type of PhD: Statistics
Research interests: Probabilistic modeling (climate forecasting, epidemic, biostats)
School I am planning to apply: Penn state, UVA, Northeastern, UPenn - tentative list at this point
I really don't know what schools I am competitive in because this is not my field. I have also seen on here people referencing "top programs" vs "20-40 ranked" or similar. I'd be curious to know if this is common knowledge or if there is a specific ranking (USN&WR?) that these types of comments refer to.