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Actuary looking to apply for statistics PhD


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Hello, I'm an actuary that am looking to apply for a PhD in Statistics. Could I please ask for advices on what school I'd have a good shots on?

Undergrad: University of Waterloo, Statistics (A-)

Masters: University of Toronto Part-Time Statistics (in progress)

Grades (masters so far): Time-Series (A), Applied Stats (A+), Data Visualization (B+)

Work: Full-time actuary (work full-time and studying part-time together)

Other experiences: joining research oversight groups with the Society of Actuaries

 

I want to study in a warm and big city (Toronto is cold!). I've been looking at these places so far:

Top Choices (i.e. pipe dreams):  Berkeley, UWashington, Rice

Good Choices (i.e. hope to get in): UCLA, UC Davis, UBC

Back up (?): UTAustin, UFlorida

I haven't contacted any professors in the school above. Any advices would be appreciated. Thanks so much!

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You'll need to post a more detailed profile (look at other threads for a template) that includes your math background and grades in math classes.  Even those backup schools are very competitive and you'll need calc 1-3, linear algebra, real analysis at a minimum to be competitive.  You'll also need to take the GRE.  My guess is that these will all be reaches for you, and my suggestion will probably be that you apply to lower-ranked biostatistics programs.  But post the full profile and we can give you more help.

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Thanks bayessays, looks like I can no longer edit my original post so here's a more detailed version:

 

Undergrad: University of Waterloo, majoring in statistics, graduated in 2017

Undergrad Grades:  Calc 1 (B+), Cal 2 (F -> A+), Calc 3 (A), Lin Alg 1 (C), Lin Alg 2 (A-), Comp Sci 1 (B), Comp Sci 2 (B), Probability (A+), Statistics (A), Math Finance (A+), Optimization (B+), Actuarial Math (A), Math Investment (A), Math Stat (A+), Stat Business 1 (A+), Life Contingencies (A), Applied Probability (A+), Computer Simulation (A+), Stat Business 2 (A), Loss Model 1 (B), Loss Model 2 (A), Quant Risk (A-), GLM (A), Statistical Classification (B+), Forecasting (A-)

I did not take real analysis during undergrad.

Co-ops: Did 3 internships in actuarial related roles

 

Masters: University of Toronto, majoring in statistics (part-time, in progress)

Masters Grades (so far): Time-Series (A), Applied Stats (A+), Data Visualization (B+), Machine Learning (TBD), Applied Stats 2 (TBD)

 

Work: Actuary (details below)

  • Working full-time while studying part-time concurrently
  • Build GLM models using R, perform actuarial studies using SAS
  • Participate in research oversight groups with the Society of Actuaries

GRE: Have not written

 

Changing my schools to be more realistic. I am currently looking for backup schools, so probably rank 50-100 ones.

Top Choices (i.e. pipe dreams):  UWashington, Rice, UCLA, UC Davis

Good Choices (i.e. hope to get in): UTAustin, UC San Diego

Back up (?): To be decided

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Washington is more than a reach - it would be a total waste of money.  I also think your chances at UC Davis, UT Austin, and UCLA are close to zero.  UCSD doesn't have a statistics program; if you mean the math PhD with specialization in statistics, that would also be a waste, but you may want to look into their new PhD in biostatistics.

UCSB might be reasonable to apply to, but it will not be a safe school.  Your math background is weaker than statistics programs require, and your grades are uneven as well.  Unless you take some more math (including real analysis), I think your best bet is to apply to biostatistics programs outside the top 50 on US News.

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Okay, thanks for your comments! That's actually pretty good to hear since I still have an elective to take for my grad school, I'll take real analysis then.

Unfortunately, I don't want to stay in finance so I am not planning to specialize into that field. I'm planning to go to the industry so I'm not too picky on school ranking (of course higher is better lol). I'm pretty surprised I'm at UofT to begin with lol.

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35 minutes ago, bayessays said:

Washington is more than a reach - it would be a total waste of money.  I also think your chances at UC Davis, UT Austin, and UCLA are close to zero.  UCSD doesn't have a statistics program; if you mean the math PhD with specialization in statistics, that would also be a waste, but you may want to look into their new PhD in biostatistics.

UCSB might be reasonable to apply to, but it will not be a safe school.  Your math background is weaker than statistics programs require, and your grades are uneven as well.  Unless you take some more math (including real analysis), I think your best bet is to apply to biostatistics programs outside the top 50 on US News.

Completely agree with this assessment. I went to U of T for my undergrad and also had background from finance. I did my masters at Harvard with full A's in standard phd sequence (math stats, probability). My GPA is much better (near 4.0), with strong letters. Still I was rejected at schools at the rank of ~50, e.g. University of Florida as well as mid-ranged schools such as UWM. A major flaw is my math background which is still stronger than yours. The point is mid to low ranked schools care A lOT about math abilities such as real analysis but I don't have it. 

You are definitely NOT safe at ~50 rank level. And I would say UT Austin, Penn state, UWM level school is the "pipe dream"/"top choice" level.   

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12 minutes ago, DanielWarlock said:

Completely agree with this assessment. I went to U of T for my undergrad and also had background from finance. I did my masters at Harvard with full A's in standard phd sequence (math stats, probability). My GPA is much better (near 4.0), with strong letters. Still I was rejected at schools at the rank of ~50, e.g. University of Florida as well as mid-ranged schools such as UWM. A major flaw is my math background which is still stronger than yours. The point is mid to low ranked schools care A lOT about math abilities such as real analysis but I don't have it. 

You are definitely NOT safe at ~50 rank level. And I would say UT Austin, Penn state, UWM level school is the "pipe dream"/"top choice" level.   

Thanks for sharing, wow I'm actually quite surprised to hear since you seem to have perfect grad school profile. Yeah I'll talk to my advisor about taking real analysis course for my elective. Good things I asked here first!

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Posted (edited)
24 minutes ago, catarctica said:

Thanks for sharing, wow I'm actually quite surprised to hear since you seem to have perfect grad school profile. Yeah I'll talk to my advisor about taking real analysis course for my elective. Good things I asked here first!

I doubt that one course in real analysis will change things drastically. I had overlapping courses with actuarial students at UofT including the "Elements of analysis": MATH 336 H1. This is the real analysis class for actuarial students at uoft and I'm worried you may take it. Don't! Take MATH 357H1 instead. I also had complex variable (334) btw. Got 100 in both of these classes --no help to my application at all. The truth is that most people in those classes are definitely not math-savvy and have no clue so the instructor has to go extremely slow and review calculus stuff all of the time. The most advanced thing we learned was just calculus materials like sequence convergence, series, mean value theorem and we don't learn those very well.   In fact, a lot of classes at uoft is made easy and "useless" for you future academic careers as a PhD in stats, except for those for pure math specialist: e.g. MATH 357H1, Math 347H1.   MATH 336 H1 don't even teach standard real analysis material like Azera-Ascoli, Weierstrass but 357 does. I thought admission at other schools don't know the difference but I was wrong. I was immediately questioned for taking "computation based" math classes. Someone even said I would be better off taking hard, proof-based classes with a less perfect score. Absolute truth. I got 95% on my linear algebra class (designed for engineers)--I didn't even understand eigenvalues beyond the definition. So you see how those marks you got on your transcript are questionable . 

Also a definite way for us non-math majors is to take GRE math subject tests. I can tell you that it will definitely help boost your profile if you score anywhere above 90%. A hard task but getting high mark is not the only objective. I took it twice with one year span in between. Did poorly both times (74% and 79%) so didn't end up submitting it. But I don't regret studying for it one bit as it really prepares you for grad school if you are not solid in calc and linear algebra. Similar to you, I worked in risk management and most my work consisted of excel and writing simple programs. Taking GRE math really taught me calculus and linear algebra before grad school. I self-studied from classic books like linear algebra done right, baby Rudin, Dummit and Forte, Munkres etc. Of course, a "crash education" in math like this is not comparable to a 4-year, solid math education but it's absolutely helpful for my grad school and allowed me to read some theoretical papers.  

Edited by DanielWarlock
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I'm doing masters now so I'm sure if I get to take real analysis course they'll be more rigorous. I'm not sure about taking math GRE though since I'm also working full-time and it's already hard to find time to do part-time school on top. Thanks again for the detailed response.

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Posted (edited)

The major problem in your profile is your weak math background. At the minimum, you would need two semesters of real analysis and/or some other proof-based courses. However, I don't see any proof-based courses in your profile. The actuarial science program at Waterloo is intended for people who wanna become an actuary. Unfortunately, the mathematical training you obtained from the program is not enough for you to apply for statistics PhD. You would've been better off if you majored in pure math/applied math/CO. However, if you can make up the required mathematical background, you will not be at a disadvantage when it comes to admission. If you could take a few courses in real analysis/measure theory and get A's in them, then you might have a chance at some of the top 50's such as CSU/FSU/Iowa. You should also have a good shot at Waterloo. Given your math background, I wouldn't suggest you take the math GRE subject test. Only if you have had most of the pure math courses should you consider taking the test.

Edited by Casorati
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15 hours ago, Casorati said:

The major problem in your profile is your weak math background. At the minimum, you would need two semesters of real analysis and/or some other proof-based courses. However, I don't see any proof-based courses in your profile. The actuarial science program at Waterloo is intended for people who wanna become an actuary. Unfortunately, the mathematical training you obtained from the program is not enough for you to apply for statistics PhD. You would've been better off if you majored in pure math/applied math/CO. However, if you can make up the required mathematical background, you will not be at a disadvantage when it comes to admission. If you could take a few courses in real analysis/measure theory and get A's in them, then you might have a chance at some of the top 50's such as CSU/FSU/Iowa. You should also have a good shot at Waterloo. Given your math background, I wouldn't suggest you take the math GRE subject test. Only if you have had most of the pure math courses should you consider taking the test.

Not the OP, but I am stats phd applying for fall 2022. Is one semester of Real analysis (no measure theory, but used rudin) enough if I took bunch of other math classes?

Thanks

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8 minutes ago, Aspiring_stats_student2312 said:

Not the OP, but I am stats phd applying for fall 2022. Is one semester of Real analysis (no measure theory, but used rudin) enough if I took bunch of other math classes?

Thanks

Absolutely, especially for a domestic student.  For lower-ranked programs, it wouldn't necessarily even be the end of the world if you didn't have real analysis.  But OP has essentially no theoretical math background, which is why these programs are not just unlikely but impossible given his current profile.

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2 minutes ago, bayessays said:

Absolutely, especially for a domestic student.  For lower-ranked programs, it wouldn't necessarily even be the end of the world if you didn't have real analysis.  But OP has essentially no theoretical math background, which is why these programs are not just unlikely but impossible given his current profile.

Thank you!

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Thanks again everyone for your inputs. UofT offers graduate real analysis (with measure theory) and graduate probability course in fall. Guess I'll bite the bullets and take them first. Since I'm actually interested in biostat, I'll look into applying them too.

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1 hour ago, catarctica said:

Thanks again everyone for your inputs. UofT offers graduate real analysis (with measure theory) and graduate probability course in fall. Guess I'll bite the bullets and take them first. Since I'm actually interested in biostat, I'll look into applying them too.

If you have never taken any upper-level math or a first course in real analysis, you are going to have a really bad time in these courses.  They're also overkill.  You just need to take an undergraduate level real analysis class.

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17 minutes ago, bayessays said:

If you have never taken any upper-level math or a first course in real analysis, you are going to have a really bad time in these courses.  They're also overkill.  You just need to take an undergraduate level real analysis class.

I second this. I took grad classes in measure theory and probability as an undergrad, but it took a lot of preparation.

I completed an "intro to proofs" course and 3 semesters of undergrad analysis before I even thought about touching anything at the graduate level. That was in addition to theoretical classes in linear algebra, numerical analysis, undergrad probability, etc. I definitely would have failed without all that prep.

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Posted (edited)
2 hours ago, bayessays said:

If you have never taken any upper-level math or a first course in real analysis, you are going to have a really bad time in these courses.  They're also overkill.  You just need to take an undergraduate level real analysis class.

I don't think it's impossible but rather depend on OP's "math maturity" and how these classes are taught at that particular year. OP is an actuarial not a musician. Actuarial studies is a mathematics degree at Waterloo. They do already know a great deal about theoretical things like SDEs. 

With certain math maturity, one can certainly take these de factor self-contained classes that tend to be taught from scratch even at graduate level.  Every year, a couple sophomores or even freshmen take grad probability and grad real analysis with us. Last year we even had a junior as teach fellow for graduate real analysis class. So it is very likely OP would be able to take these classes. If not, OP will always have a chance to drop out. I don't think it's a big deal.

Edited by DanielWarlock
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@DanielWarlockYou're vastly overestimating the average student's math abilities.  Yes, there are some exceptional cases.  I'm sure at Harvard there were exceptional cases.  But 95%+ of people who complete Waterloo's statistics major (I am looking at the requirements) would have literally zero idea what is going on in a graduate real analysis class.

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Posted (edited)
3 hours ago, DanielWarlock said:

I don't think it's impossible but rather depend on OP's "math maturity" and how these classes are taught at that particular year. OP is an actuarial not a musician. Actuarial studies is a mathematics degree at Waterloo. They do already know a great deal about theoretical things like SDEs. 

With certain math maturity, one can certainly take these de factor self-contained classes that tend to be taught from scratch even at graduate level.  Every year, a couple sophomores or even freshmen take grad probability and grad real analysis with us. Last year we even had a junior as teach fellow for graduate real analysis class. So it is very likely OP would be able to take these classes. If not, OP will always have a chance to drop out. I don't think it's a big deal.

If the OP has taken the equivalent of Math 55 he/she should definitely go for it. Harvard's the odd case as their undergraduate pure math first year math class literally has its own wikipedia page lol

https://en.wikipedia.org/wiki/Math_55

Edited by trynagetby
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Posted (edited)

Regarding the objections, I must reiterate that it depends on (i) math maturity (ii) how that class is taught at that particular year.

The difference could literally be 6 hour/week v.s. 60 hrs per week for the same class with different instructors. Same thing goes with one's math maturity. 

From what I know, if Zhou Zhou or Rosenthal still teaches grad probability at UofT, it might be very  doable. I heard that Zhou Zhou is drier/technical but Rosenthal on the other hand should stick to his book "A first look..." and has a reputation of being lenient and less technical. Take a read and see if that works for you.  There seems to be a separate offering at math department now by D. Panchenko. Never took a class from the man but his books are among the best expository materials, written in astounding lucidity. He himself is a brilliant researcher with deep work in spin glass and inequalities. I personally would cherish an opportunity to take class with a master like that. Don't be too obsessed with grades. 

No ideas on real analysis. 

Edited by DanielWarlock
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Zhou is teaching again this year I heard. Either way, I can take classes slowly since I’m studying part-time. I’m honestly more concerned about long work hours leaving little time to study.

Since I’m quite interested in statistical genetics, I will actually look seriously at biostats too. If that’s the case I can choose to study less theoretical courses. That will give me more time to prepare GRE as well. Overall picking what to study is a good problem for me to have lol.

 

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The bigger point is being missed here.  Nobody is talking about grades here or worrying whether @catarctica will do poorly in the grad classes, as @DanielWarlock states.  Most graduate classes are jokes and everyone gets As.  So nobody will take an A in graduate probability or analysis seriously anyways -- it will raise more questions than it solves because the admissions committee won't believe you have the actual skills to succeed in this class.  It is also very likely to not be productive for you personally.  If you want to have a serious shot at a statistics PhD program, you need to take some more undergraduate math classes like analysis, and anyone telling you differently is doing you a disservice.  OP, if I am wrong and you are a math genius, forgive me, but just be aware that this is not the route 99.9% of people would recommend for you.

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Posted (edited)

@catarctica Are you taking classes with Prof. Sheldon Lin at UofT? He is a world-class actuarial, a professor in the statistics department, and had done his PhD in mathematical analysis. I can't think of a better person to resolve your conundrum. He is very friendly to undergrad/master students and knows uoft curriculum inside out (including Zhou's class and all those analysis classes) -- he used to spend an hour discussing my application with me even though he barely knows me. You should try to talk to Prof. Lin and listen to what he says. He should know as an actuarial, where, who and what you should apply to and what you should say in your letter. I'm not sure you will get good results applying to bio-stats if you have done nothing about it. Unless it is your absolute true passion, I caution you to consult Prof. Lin first. In fact, I think your best chance is to apply to departments with people who have joint interest in actuarial/finance and statistics.

By the way, in Canada, it's best that you send an inquiry emails to specific profs you would like to work with before applying. You are already a grad student at uoft, why don't you work with someone first and transition to their phd? This is the easiest route to land a phd offer at top ranked university. Why risking going to a low-ranked or even unranked school in the US?

Edited by DanielWarlock
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Unfortunately I never take classes with Sheldon before. When the campus is open, I'd drop by to see him then. He sounds like a really good person.

That's true about working with a prof and transition to uoft too. Part of me wants to try living in a new city but yeah I totally agree with what you said.

Noted on school, grade and courses too. I will try to get academic advisor's inputs and other people I know for their opinion as well. But this forum has been great in letting me know which direction to prepare.

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