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Undergrad Institution: UK Top 5/6 (Although this is misleading as I believe 5th-8th are seen as interchangeable in the UK, if not (controversially) 3rd-8th)
Major: Mathematics and Philosophy
Concentration: Statistics, Pure math (mostly analysis)
GPA: (Converted) 3.90~4.00/4.00 (4.00/4.00 according to the guideline of my UG institution. Also, only the upper division classes count towards the GPA)
Graduated: 2018
Awards: Nothing besides Dean's list for the final 2 years
Type of Student: International Asian (East Asian)
Relevant Courses:  (Grad classes) Measure & Probability theory (A+), Ergodic Theory (A+) Advanced Bayesian Inference (A+) (Undergrad classes) Functional Analysis (A+) Linear Algebra (A) Differential Eq (A+) Markov Chains/Processes (A+), Multivariate Analysis (A), Advanced Logic (A+) Dissertation (A+)
 
GRE: (V)166 (97%)/(Q)177(97%)/(W)4.5(82%)
GRE Subject Math: 820 (82%) - will retake as I ain't got much to do before applications
 
Programs Applying:  PhD Stats mostly
Research Experience: 
 - Year-long dissertation (mainly) on (Hilbert) Sobolev gradient flows and their applications in image processing (Applied math-PDE). This is tightly linked to my current research interest. 
 - A project in the Advanced Bayesian inference module on MCMC approach to Bayesian network inference (mostly a survey of two main approaches)
 
This is my biggest concern as I missed the opportunity to do undergraduate research internships partly due to personal complications but mostly because of my lack of focus and organization. There seem to be many who end up with publications and more with at least a meaningful experience of being part of serious mathematical/statistical research. The closest thing to an official recognition of research experience is a consolation letter for my dissertation for 'almost' winning the prize. I did go theoretically deep as I could with my dissertation but for the most part it was deciphering already published papers and deriving middle steps that's rarely mentioned only because people in the field all would know without having to spell it out.
 
Recommendation Letters: Two from professors of the pure math grad classes. One should be close to very good and the other probably at least good . Another from my dissertation supervisor (Applied math) which would be close to very good and the last from statistics professor for the grad class in bayesian stats (cannot gauge the quality of the letter but he's a very nice person). Pure math professors are senior while appliedmath/stats are junior faculty members.
 
Research Interests: Intersection of the Wasserstein space and Bayesian inference (In particular, Approximate Bayesian inference such as Variational Bayes, Monte Carlo methods). 
 
Miscellaneous
 -I switched from Political science & Philosophy to Math & Philosophy before going into honours (upper division). My grades in the first two years are inconsistent especially in philosophy & poli sci as I had quite strong opinions in social science back then. My math grades are less inconsistent but have a pity-pass (D) in 2nd year introductory statistics and a B in upper division real&abstract analysis  which I took in my 2nd year (sad but no regrets as that allowed me to take grad classes later).
 
 -Took a couple years of leave of absence due to personal matters.
 
Applying to (probably)
 
PhD Statistics:
UW-Madison
Harvard
Chicago
Iowa
Duke
Berkeley
UNC Chapel Hill
Michigan
 
Phd Math:
CMU
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Remark: Although I'm personally not very comfortable with big-name universities, the above were pretty much the only ones I could find (after reading papers in spare time) with researchers in the field I hope to go into. Application of optimal transport theory/Wasserstein space in statistical inference seems to be pretty big in France (which is a shame because the only french I know is 'can I get the bill please') but not so much in the States, especially outside the top 20. That is one of my concerns as I don't feel like any program in the list is even close to being a safety for me, and I've realized how difficult admissions can be in the last application cycle.
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   Hello, I've been reading posts in this form in the last application cycle which turned out very badly, so I posted desperately looking for an advice on this forum. Last year I've applied to 5 PhD programs in the range of Chicago~Northwestern (in terms of USNEWS ranking) and I was rejected at all programs, with only one waitlist (ironically) from Chicago (and the waitlist that year seemed fairly long). The possible reasons are inconsistent transcripts especially in the first two years, lack of research experience, and possibly not very strong letters of recommendations. Last year I applied after returning from a two-year-long leave of absence so I had to ask for letters only after 2 months of trying hard to make an impression. I was told by the professors that the letters were very strong, but they probably did not have that much to write even if they had the best intention. In terms of letters I think it is reasonable to expect significant improvement. Also, I bumped up my GPA +0.2-ish in my final year so the transcripts would seem more consistent.
 
 Funding is a very important factor which is why I'm (forced to) only look into PhD programs. It'd be nice if I could take more classes and get a real research experience from a Master's it is unlikely that I would be able to do so unless I get a stipend. I will apply to MS programs with generous funding (McGill, Bonn, BMS Phase I) but it seems the competition for scholarships is nearly as fierce as those for PhD programs :(
 
  Also I'm planning to write to professors working in the field of my interest asking if they are taking in new PhD students. Websites (of the professors) often refer to the department's page for prospective applicants, and I'm not sure if that's a kind way of saying 'don't email me unlesse you are admitted' or just 'don't email me if you are going to only read the abstract of my work and ask to weigh your chances'. I'd be very grateful to hear thoughts of anyone with similar experience/plans. 
 
 Again, I am desperately looking for an advice, so any input will be much appreciated! :)
 
   
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Are you specifically mentioning your research interest in your application? It's so incredibly narrow that I think it would set off alarms at most departments that you won't be happy doing anything else; it comes off as a bizarrely niche interest. Maybe broaden your statement to say your interested in theoretical and Bayesian statistics.

 

Have you looked at UT Austin? Stephen Walker there is a top theoretical Bayesian. 

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I agree with bayessays.  Your research interest seems very narrow.  I would broaden my statement.  I would also see if you can get a LOR from a stat professor.  Your qualifications seem in general to be excellent.

Oftentimes math and stat professors don't interact much

 

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13 hours ago, bayessays said:

Are you specifically mentioning your research interest in your application? It's so incredibly narrow that I think it would set off alarms at most departments that you won't be happy doing anything else; it comes off as a bizarrely niche interest. Maybe broaden your statement to say your interested in theoretical and Bayesian statistics.

 

Have you looked at UT Austin? Stephen Walker there is a top theoretical Bayesian. 

Thanks bayessays.  Maybe I'm overcompensating for the fact that I felt like I lacked depth in my mentioned 'research interest' last year, and only now I see that it could work against me. Do you think it could hurt carefully expressing the excitement about the possibilities in a very narrow field after showing  general interest in a broader field (Bayesian statistics)?

 Also, will definitely look into his work. Cheers :)

  

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4 hours ago, Gauss2017 said:

I agree with bayessays.  Your research interest seems very narrow.  I would broaden my statement.  I would also see if you can get a LOR from a stat professor.  Your qualifications seem in general to be excellent.

Oftentimes math and stat professors don't interact much

 

Thanks Gauss2017. One of my letter writers is in stats (Bayesian). As you said, it'd be nice if I had more people from stats writing for me. The stats classes were larger (thus harder to get a good rec), I took less of them, and I've already graduated so sadly I can't change much about that. :( Thanks for your input!

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I wouldn't email professors until after you are admitted.  It's not likely it will improve your chances or even that you will get a meaningful response.   I sent some readmission emails and no one answered me.  After visit days I did get some responses.

I am not familiar with what your specific research interests but Florida, UT (like bayessays said),  Texas A&M, and Missouri have a few Bayesians. 

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