Competitive profile for Statistics Grad School

[tcbh]

Hi, I'm a 2nd year math major (stats minor) interested in applying to Statistics grad schools down the line. The problem I'm having is in choosing how to balance math classes vs. statistics classes and schoolwork vs. research (and what types of research?)

In terms of classes, I'm probably going to take an introduction to Measure Theory next quarter. But how useful would classes like Topology, Complex Analysis, Set Theory, Grad level Measure Theory, and Grad level Probability be? The alternatives would probably be taking a couple extra statistics electives.

In terms of Research, how useful would it be to do work in Applied Math? Or doing some statistical analysis for researchers in a completely separate field? Or is it much more useful to do straight statistical research?

Lastly, what's a typical undergrad GPA for a top 10 or top 20 program? Is there much of a difference between the two levels?

(apologies if any of these questions are naive or asked too frequently. It seems like it's hard to find concrete information on what grad schools expect, and instead people always say just to "do what you're interested in.")

[PompousPilots]

Math major with a stat minor is perfect.

Set theory, grad-level measure theory, and probability are worth taking. I wouldn't spend any time on Topology or Complex Analysis.

Any stat elective would be good, too I'm sure.

Applied math or stat research would be better than statistical consulting.

I don't know about typical GPA's, though, sorry. I wouldn't worry about that if I were you. Just take the right classes and research, and do your best. You're starting early, so you're in great shape.

[tcbh]

Math major with a stat minor is perfect.

Set theory, grad-level measure theory, and probability are worth taking. I wouldn't spend any time on Topology or Complex Analysis.

Any stat elective would be good, too I'm sure.

Applied math or stat research would be better than statistical consulting.

I don't know about typical GPA's, though, sorry. I wouldn't worry about that if I were you. Just take the right classes and research, and do your best. You're starting early, so you're in great shape.

Thanks for the reply. It's interesting that you say the Measure theory class would be useful but to not take Topology, since undergrad Topology is listed as a prereq for graduate measure theory (which is a prereq for Probability). Maybe I should look into whether that's enforced and how necessary it's really thought to be.

[floffel]

I'm not sure it's worth taking grad level measure theory/probability if you are already planning on going to grad school in Statistics. Most PhD programs assume you will take this material your first year, and even if you take it now you'll probably want to take it again to make sure the material is very fresh when you take quals, and because classes like that are pretty foundational for most programs. More math is never a bad thing, even if the areas aren't that relevant to Statistics. I'm assuming you've done real analysis and linear algebra. Functional analysis, fourier analysis, and complex analysis would all also be useful courses for Statistics. Also, definitely take some Statistics classes (probability doesn't count). I think it's important to show a genuine interest in Statistics rather that just one-dimensional mathematical aptitude.

For research, working with a statistician would be best, but either of the other options you mentioned would certainly still be valuable. Research experience is definitely an important part of the picture.

Lastly, like anything else GPA of course matters, but how much depends on the quality of your undergrad program, letters of recommendation, research, etc. Good grades are obviously desirable, but average grades can be made up for by great letters, experience, and enthusiasm.

[thom1820]

Unrelated, but PompousPilots, could you tell me when you heard from NC State and how (website, letter, etc.)? I applied there and haven't heard anything. I applied to the Masters program though, so things could be different for me, but I'm still curious.

[tcbh]

I'm not sure it's worth taking grad level measure theory/probability if you are already planning on going to grad school in Statistics. Most PhD programs assume you will take this material your first year, and even if you take it now you'll probably want to take it again to make sure the material is very fresh when you take quals, and because classes like that are pretty foundational for most programs. More math is never a bad thing, even if the areas aren't that relevant to Statistics. I'm assuming you've done real analysis and linear algebra. Functional analysis, fourier analysis, and complex analysis would all also be useful courses for Statistics. Also, definitely take some Statistics classes (probability doesn't count). I think it's important to show a genuine interest in Statistics rather that just one-dimensional mathematical aptitude.

For research, working with a statistician would be best, but either of the other options you mentioned would certainly still be valuable. Research experience is definitely an important part of the picture.

Lastly, like anything else GPA of course matters, but how much depends on the quality of your undergrad program, letters of recommendation, research, etc. Good grades are obviously desirable, but average grades can be made up for by great letters, experience, and enthusiasm.

Thanks for the response. I have taken Linear Algebra (1 quarter introduction focusing on solving problems, 1 quarter focusing on theory and proofs) and Real Analysis (2 quarters). I've also taken 2 quarters of calc-based probability and a quarter of calc-based Statistics. I'm hoping to have all or most of the core statistics classes done before I graduate too. The biggest question I had was depth in math vs. breadth in Statistics. It seems like either way is good, which is comforting to know when picking a path.

[PompousPilots]

Unrelated, but PompousPilots, could you tell me when you heard from NC State and how (website, letter, etc.)? I applied there and haven't heard anything. I applied to the Masters program though, so things could be different for me, but I'm still curious.

about three weeks ago via email. good luck to you.

[hedgie]

I am pursuing a Stats PhD as well and will finish an undergrad in Math with a focus in stats and was wondering everyone's opinion on whether a Master's in Math or Stats would be better for applying to PhD program's. Due to life circumstances I am stuck somewhere for a year and figured I could pick up the Master's to strengthen my profile.

In the Math program I would take the grad sequence of Math Stats I & II, Real Analysis I & II, and some courses that will be less relevant as my school does not offer much more that is as applicable. Maybe a grad level probability course but that's it. I also could take 1-3 courses from the Stats Grad department if I went this route.

I could also not pick up the masters's and take grad level complex analysis, stochastic processes, RA I & II, Math Stats I & II, and some courses from the stats grad department.

I had been advised by a few people to skip a lot of the math (except stats applicable) and just do a Masters's in stats and pick up the RA sequence.

Any input would be great! Thanks if you have the time.

[biostat_prof]

<br />Thanks for the response.  I have taken Linear Algebra (1 quarter introduction focusing on solving problems, 1 quarter focusing on theory and proofs) and Real Analysis (2 quarters).  I've also taken 2 quarters of calc-based probability and a quarter of calc-based Statistics.  I'm hoping to have all or most of the core statistics classes done before I graduate too.  The biggest question I had was depth in math vs. breadth in Statistics.  It seems like either way is good, which is comforting to know when picking a path.<br />

It's very difficult to give a general answer to this question, because every admissions committee is going to look for something slightly different. Having said that, in general, you are probably better off taking more upper-division math courses. The biggest concern of most admissions committees is that you won't be able to pass your qualifying exams if you can't do the math. Also, there is a mindset (incorrect in my opinion) that you can teach a person to do applied statistics or computational work but mathematical ability is something innate, and if you're not a strong "math person" than you'll never be able to do high-level theoretical work. Also, nearly every statistics graduate program will require you to do some sort of coursework in theoretical statistics and probability, but the applied curriculum varies greatly from school to school. Thus, if you take more applied statistics courses, you may have a bunch of applied courses on your transcript in areas that you will end up never using in grad school. (Well, pretty much every program will require a course in linear models, but otherwise there is a lot of variation.) So in general, I would definitely error on the side of more math (or theoretical statistics/probability). Analysis, measure theory, theoretical statistics, and measure-theoretic probability would all be fantastic, as would advanced linear algebra. You probably won't get much mileage from complex analysis or topology, though. Also, if you are interested in applied statistics, you should look into the possibility of taking some computer science courses. Demonstrating programming ability will probably help you more than applied statistics courses for the reasons I listed above.

As for research, I would say that it is far more important to find a project where you can make a major contribution and get a strong recommendation than it is to find a project in a specified area. You would be better off working in an area that is only tangentially related to statistics if it will result in a first-author paper and a superb recommendation than a project where you're basically just making photocopies for a superstar statistician, if that makes sense. The main thing is to demonstrate that you can do independent research, so anything you can do to provide evidence of that would be a good idea.

Let me know if you have any other questions. I don't check this board frequently, but I'll try to answer your questions when I come on here.

[biostat_prof]

<br />I am pursuing a Stats PhD as well and will finish an undergrad in Math with a focus in stats and was wondering everyone's opinion on whether a Master's in Math or Stats would be better for applying to PhD program's.  Due to life circumstances I am stuck somewhere for a year and figured I could pick up the Master's to strengthen my profile.<br /><br />In the Math program I would take the grad sequence of Math Stats I &amp; II, Real Analysis I &amp; II, and some courses that will be less relevant as my school does not offer much more that is as applicable.  Maybe a grad level probability course but that's it.  I also could take 1-3 courses from the Stats Grad department if I went this route.  <br /><br />I could also not pick up the masters's and take grad level complex analysis, stochastic processes, RA I &amp; II, Math Stats I &amp; II, and some courses from the stats grad  department.<br /><br />I had been advised by a few people to skip a lot of the math (except stats applicable) and just do a Masters's in stats and pick up the RA sequence.<br /><br />Any input would be great!  Thanks if you have the time.  <br /><br /><br />

I'm still a little unclear about which courses you would take for which degree. And are you considering just taking some additional courses without getting an MS as well?

If real analysis is the only relevant math course in the math MS program, then maybe a stat MS is a better option, assuming that you can still take real analysis. Although if you can take any courses in measure theory/mathematical statistics/measure-theoretic probability, that will help you as well. I wouldn't bother with complex analysis, and stochastic processes is questionable. If you list exactly which courses you would be taking for the two degree programs, I can try to give you better advice.

[hedgie]

I'm still a little unclear about which courses you would take for which degree. And are you considering just taking some additional courses without getting an MS as well?

If real analysis is the only relevant math course in the math MS program, then maybe a stat MS is a better option, assuming that you can still take real analysis. Although if you can take any courses in measure theory/mathematical statistics/measure-theoretic probability, that will help you as well. I wouldn't bother with complex analysis, and stochastic processes is questionable. If you list exactly which courses you would be taking for the two degree programs, I can try to give you better advice.

Thanks! Stochastic is questionable if it helps or not? First for my undergrad do PDE's (still for my undergrad), linear optimization or abstract algebra help at all?

The two MS options are as follows (the math maybe an MA I haven't looked):

Math Master's:

- Real Analysis I & II

- hopefully a graduate level probability course at a nearby school (mine does not have one)

- Math Stats I & II

- Maybe a Numerical Analysis sequence or linear/non-linear optimization would be the choices of other require sequence.

- Complex Calculus

- Some elective (Probably can take 2-3 classes from the stats department)

Applied Stat's MS:

- Applied Regression Analysis

- Applied Multivariate Analysis

- Math Stats I/II (taught from the stats dept...and known for being less math heavy than the one from the math dept)

- Stat Methods

- Applied design of experiments

- Then some elective courses in data mining, time series analysis, sampling techniques

One other option I have is potentially go to a school not too far away and take all Math Stats I/II, some graduate sequenced probability theory based on measure theory (3-4 course sequence), real analysis I/II, and I am not sure what else there.

I had assumed the last option if possible is my best, but what about between the Stat's MS and Math Master's. I could take the Real Analysis I/II as my electives for the Stats MS.

Sorry if that is confusing, let me know and I'll try to clean up the post. Thanks for the time/advice!

[tcbh]

It's very difficult to give a general answer to this question, because every admissions committee is going to look for something slightly different. Having said that, in general, you are probably better off taking more upper-division math courses. The biggest concern of most admissions committees is that you won't be able to pass your qualifying exams if you can't do the math. Also, there is a mindset (incorrect in my opinion) that you can teach a person to do applied statistics or computational work but mathematical ability is something innate, and if you're not a strong "math person" than you'll never be able to do high-level theoretical work. Also, nearly every statistics graduate program will require you to do some sort of coursework in theoretical statistics and probability, but the applied curriculum varies greatly from school to school. Thus, if you take more applied statistics courses, you may have a bunch of applied courses on your transcript in areas that you will end up never using in grad school. (Well, pretty much every program will require a course in linear models, but otherwise there is a lot of variation.) So in general, I would definitely error on the side of more math (or theoretical statistics/probability). Analysis, measure theory, theoretical statistics, and measure-theoretic probability would all be fantastic, as would advanced linear algebra. You probably won't get much mileage from complex analysis or topology, though. Also, if you are interested in applied statistics, you should look into the possibility of taking some computer science courses. Demonstrating programming ability will probably help you more than applied statistics courses for the reasons I listed above.

As for research, I would say that it is far more important to find a project where you can make a major contribution and get a strong recommendation than it is to find a project in a specified area. You would be better off working in an area that is only tangentially related to statistics if it will result in a first-author paper and a superb recommendation than a project where you're basically just making photocopies for a superstar statistician, if that makes sense. The main thing is to demonstrate that you can do independent research, so anything you can do to provide evidence of that would be a good idea.

Let me know if you have any other questions. I don't check this board frequently, but I'll try to answer your questions when I come on here.

Wow, lots of advice here. Thanks for the help.

[rockrs]

It's very difficult to give a general answer to this question, because every admissions committee is going to look for something slightly different. Having said that, in general, you are probably better off taking more upper-division math courses. The biggest concern of most admissions committees is that you won't be able to pass your qualifying exams if you can't do the math. Also, there is a mindset (incorrect in my opinion) that you can teach a person to do applied statistics or computational work but mathematical ability is something innate, and if you're not a strong "math person" than you'll never be able to do high-level theoretical work. Also, nearly every statistics graduate program will require you to do some sort of coursework in theoretical statistics and probability, but the applied curriculum varies greatly from school to school. Thus, if you take more applied statistics courses, you may have a bunch of applied courses on your transcript in areas that you will end up never using in grad school. (Well, pretty much every program will require a course in linear models, but otherwise there is a lot of variation.) So in general, I would definitely error on the side of more math (or theoretical statistics/probability). Analysis, measure theory, theoretical statistics, and measure-theoretic probability would all be fantastic, as would advanced linear algebra. You probably won't get much mileage from complex analysis or topology, though. Also, if you are interested in applied statistics, you should look into the possibility of taking some computer science courses. Demonstrating programming ability will probably help you more than applied statistics courses for the reasons I listed above.

As for research, I would say that it is far more important to find a project where you can make a major contribution and get a strong recommendation than it is to find a project in a specified area. You would be better off working in an area that is only tangentially related to statistics if it will result in a first-author paper and a superb recommendation than a project where you're basically just making photocopies for a superstar statistician, if that makes sense. The main thing is to demonstrate that you can do independent research, so anything you can do to provide evidence of that would be a good idea.

Let me know if you have any other questions. I don't check this board frequently, but I'll try to answer your questions when I come on here.

Dear biostat_prof, thanks for the useful opinion. I think everyone on the forum will be grateful for the above post. In relation to it, I would like to ask you a few questions, if you would have the time...

1) Given the mindset you mentioned for the innate math ability. How do adcoms treat bad grades in first university year in core math and then good ones in next years as well as an excellent MS? (I am international student)

2) What exactly the GRE general quant score is used for. Could the good score help if I have some bad grades or something? I have heard that the GRE quant is not relevant unless you score under 750 and this may lead to doubts in one's abilities.

Thanks in advance.

[biostat_prof]

Thanks! Stochastic is questionable if it helps or not? First for my undergrad do PDE's (still for my undergrad), linear optimization or abstract algebra help at all?

The two MS options are as follows (the math maybe an MA I haven't looked):

Math Master's:

- Real Analysis I & II

- hopefully a graduate level probability course at a nearby school (mine does not have one)

- Math Stats I & II

- Maybe a Numerical Analysis sequence or linear/non-linear optimization would be the choices of other require sequence.

- Complex Calculus

- Some elective (Probably can take 2-3 classes from the stats department)

Applied Stat's MS:

- Applied Regression Analysis

- Applied Multivariate Analysis

- Math Stats I/II (taught from the stats dept...and known for being less math heavy than the one from the math dept)

- Stat Methods

- Applied design of experiments

- Then some elective courses in data mining, time series analysis, sampling techniques

One other option I have is potentially go to a school not too far away and take all Math Stats I/II, some graduate sequenced probability theory based on measure theory (3-4 course sequence), real analysis I/II, and I am not sure what else there.

I had assumed the last option if possible is my best, but what about between the Stat's MS and Math Master's. I could take the Real Analysis I/II as my electives for the Stats MS.

Sorry if that is confusing, let me know and I'll try to clean up the post. Thanks for the time/advice!

Yeah, I think the statistics MS is the better option of the two choices listed above. Complex analysis almost certainly won't help you, and numerical analysis/linear optimization probably won't be useful unless you decide to pursue a few very narrow specialties. Real analysis and mathematical statistics will be useful, but it sounds like you can get that from the stat MS anyway. And the stat MS will also give you exposure to some core stat courses that you will probably encounter in grad school. Having said that, real analysis would be a far better choice for your elective courses in the statistics program than a class in data mining/time series analysis/sampling. Honestly, unless you are applying to a department that is strong in one of those areas, none of those courses will probably help you that much, but almost every school will expect you to have taken real analysis. If you can get some exposure to measure theory as well, that would also be useful. (You will often get this as part of an advanced probability course.) As I said earlier, there is a common mindset that anyone can learn to write SAS code to do time series analysis, but not everyone is smart enough to do complex theoretical math, so analysis/measure theory would be better electives than other applied statistics courses.

I hope that helps. Let me know if you have any more questions.

[biostat_prof]

Dear biostat_prof, thanks for the useful opinion. I think everyone on the forum will be grateful for the above post. In relation to it, I would like to ask you a few questions, if you would have the time...

1) Given the mindset you mentioned for the innate math ability. How do adcoms treat bad grades in first university year in core math and then good ones in next years as well as an excellent MS? (I am international student)

That's hard to say. If you got bad grades in first-semester calculus many years ago and good grades in more advanced courses more recently, I doubt it would hurt you that much. (It might be worthwhile to explain what happened in your personal statement, though.) Having said that, if the bad grades were in a really critical class like analysis or linear algebra, I would give some serious thought to retaking the class (if you haven't done that already). There simply isn't much margin of error for international applicants these days, so a bad grade in a core class might very well doom you, particularly at the most competitive schools.

2) What exactly the GRE general quant score is used for. Could the good score help if I have some bad grades or something? I have heard that the GRE quant is not relevant unless you score under 750 and this may lead to doubts in one's abilities.

Thanks in advance.

Again, this is something that varies greatly from department to department (and from admissions committee member to admissions committee member). In general, I think what you say is correct: A very low score will raise some eyebrows, and an 800 will bump you up a bit, but generally it's used as a "weeder" if it's used at all. (Basically, they use low scores to filter out uncompetitive applications, and that's about it.) But it really varies. I talked to one person on our admissions committee who said that they give higher priority to people with 800 scores. Another person said that they don't consider it at all unless the score is very low. And anecdotally there is an undergraduate at my school who had a sub-750 math GRE score and they still have been accepted to virtually every program to which they applied. (Although this person had a nearly perfect GPA and incredible recommendations/research experience, and they still got rejected at some of the top-ranked schools.) If you have some questionable math grades, I do think it would be worthwhile to study until you're confident that you will get a nearly perfect score on that exam.

[hedgie]

Yeah, I think the statistics MS is the better option of the two choices listed above. Complex analysis almost certainly won't help you, and numerical analysis/linear optimization probably won't be useful unless you decide to pursue a few very narrow specialties. Real analysis and mathematical statistics will be useful, but it sounds like you can get that from the stat MS anyway. And the stat MS will also give you exposure to some core stat courses that you will probably encounter in grad school. Having said that, real analysis would be a far better choice for your elective courses in the statistics program than a class in data mining/time series analysis/sampling. Honestly, unless you are applying to a department that is strong in one of those areas, none of those courses will probably help you that much, but almost every school will expect you to have taken real analysis. If you can get some exposure to measure theory as well, that would also be useful. (You will often get this as part of an advanced probability course.) As I said earlier, there is a common mindset that anyone can learn to write SAS code to do time series analysis, but not everyone is smart enough to do complex theoretical math, so analysis/measure theory would be better electives than other applied statistics courses.

I hope that helps. Let me know if you have any more questions.

Thank you! I had planned on doing Real Analysis I/II as my electives in addition to the electives I listed out if I did the MS in Stats. Do you think I'd be better served if I could go to the program, not too far away which has measure theory in a sequenced grad course combined with RA versus the MS in Stats with electives in Real Analysis I/II? So it'd probably be a Math MS with the opportunity to get into their Stats PhD program which is unranked, but the placements of their grads has been good, and I am unsure of their research areas yet relative to my interests.

I do have a couple of other follow up questions if you have the time to answer them. In finishing my undergrad work would abstract algebra, and partial differential equations be more useful than CS courses. I had been under the impression the adcom's look favorably on the Math's (as you also pointed out) and that CS beyond an intro to programming course was in about all that is necessary for the Stats PhD, the other languages one would learn on their own. Originally I had thought of not taking PDE's and abstract algebra (as well as one other math course) and getting a minor in CS, which would get me to a data and algorithm's course, and some C++, but I do not know how helpful that would be or not for the Stats PhD. Is it correct to think I would be better off with the math?

Thanks for your time and advice, and thanks in advance.

[biostat_prof]

Thank you! I had planned on doing Real Analysis I/II as my electives in addition to the electives I listed out if I did the MS in Stats. Do you think I'd be better served if I could go to the program, not too far away which has measure theory in a sequenced grad course combined with RA versus the MS in Stats with electives in Real Analysis I/II? So it'd probably be a Math MS with the opportunity to get into their Stats PhD program which is unranked, but the placements of their grads has been good, and I am unsure of their research areas yet relative to my interests.

I do have a couple of other follow up questions if you have the time to answer them. In finishing my undergrad work would abstract algebra, and partial differential equations be more useful than CS courses. I had been under the impression the adcom's look favorably on the Math's (as you also pointed out) and that CS beyond an intro to programming course was in about all that is necessary for the Stats PhD, the other languages one would learn on their own. Originally I had thought of not taking PDE's and abstract algebra (as well as one other math course) and getting a minor in CS, which would get me to a data and algorithm's course, and some C++, but I do not know how helpful that would be or not for the Stats PhD. Is it correct to think I would be better off with the math?

Thanks for your time and advice, and thanks in advance.

Once again it's hard to compare the two programs without knowing exactly which classes you would be taking and exactly what type of funding (if any) you would receive at either school. In any event, I can definitely tell you that programming will almost certainly be more useful than abstract algebra or PDE. I've never heard of anyone using abstract algebra or PDE in a statistics PhD, whereas programming skills can be very useful for some types of applied statistics. Granted, the areas where you would need to do C/Fortran programming in statistics are fairly narrow, so I wouldn't make these classes a priority, but I would definitely take more programming rather than abstract algebra or PDE.