Pursuing Stats

[Vince Silvia]

I'm about done with a Master's in Computer Management and Information Sciences (same as my Bachelor's) here in the Midwest, and I've been giving some serious consideration to applying to PhD programs in Statistics. My major issue, however, is that my degree is a business degree, and as such, isn't very strong in a math background. I asked the MS Stat program coordinator where I'm lacking specifically, and he suggested I take Calc II, Calc III, Linear Algebra, and a Logic and Reasoning class. Does this sound sufficient, or should I take as much math as I can before applying (i.e. Discrete Math, Differential Equations)?

For the record, what I do have in math background is pretty spotty at best, with a C in Calc I and a D in Calc II from the University of Missouri at Rolla (when I was there in 2000-2001, now it's Missouri S&T), and a C in Discrete Math from my current school, SIUE (as an undergrad, though). Additionally, as an undergrad at SIUE, I took an Intro to Statistics class and got an A.

So, with all that said,

A) What's my best plan to get my maths up to snuff?

B ) Are there stat-related programs that I should be focusing on where my impending Master's degree might hold more weight? I've seen some schools that offer Business Statistics, for example, but I don't know what the differences might be besides the obvious.

C) I haven't taken the GRE, but I got a 700 on the GMAT (if that offers any sort of comparison), and am currently holding a 4.0 GPA in Grad School to go along with my 3.2 GPA in undergrad. Where should I be looking in terms of programs? Top, middle, bottom? Any specific recommendations?

D) Am I crazy for thinking I can pick up relatively higher-level math despite at least 8-9 years away from any knowledge of the subjects (if any, really), or succeed as a PhD candidate in Statistics?

Thanks in advance.

Vince

Edited March 21, 2011 by Vince Silvia

[coffeeintotheorems]

For a PhD in Stats, you absolutely must know your Calculus I-III and basic Linear Algebra inside-out (except maybe line integrals?) I don't know if you need a full Discrete Mathematics course, but you absolutely must know basic counting and combinatorics inside-out. Then you should apply your knowledge by taking basic courses in Probability and Mathematical Statistics--both of which require the aforementioned courses as prerequisites.

How you learn these subjects--from a local university or community college, or by self-study--is up to you, but you have to do them.

Differential Equations is a traditional topic that complements the Calculus sequence. It's not often explicitly used in Stats and you probably wouldn't need it for applications, but it would at least be an important addition to whatever theory you learn. (An example, for those in the know who might be reading this: there is an analogy between Laplace transforms and the 1:1 correspondence of Moment-generating functions to distribution functions.)

"Logic and reasoning" is important, but I'm not 100% sure you need to take a class on it. Your study time would be better spent developing other mathematical skills, and you can learn applied "logic and reasoning" best in the school of hard knocks (i.e. by using common sense.) It would help to know basic symbolic logic, though, e.g. why the contrapositive of a statement is equivalent to it, or why DeMorgan's Laws work on unions and intersections of sets.

Sounds like your current GPA and GMAT are pretty solid, and if you have applied work experience that will also be good on the professional end of things.

Edited March 21, 2011 by coffeeintotheorems

[emmm]

GIven your previous experiences with math classes . . . are you SURE this is the route you want to take? I agree with needing to know calculus and linear algebra inside out. That, in itself, will take a lot of work, and should give you a sense of how seriously you want to pursue this goal. In addition, you may be at a disadvantage during the admissions process with your old grades on your transcript. The A in Intro to Stats won't help you much -- that mostly just uses arithmetic. I would also say that a 700 score in any sort of quantitative standardized test may not be suficient. My sense is that successful math/stats applicants almost uniformly have 770+, with most at 800, on the GRE. Not sure how the GMAT works. I think it will be an uphill batle, but you probably already know that. However, I think people should pursue whatever goals they want for themselves, and I have great admiration for those who do, so . . . Good Luck!

[Sleepy]

I personally spoke over the phone with a member of a committee from a good school from which I was rejected and he told me that the only reason I wasn't accepted is because I did not take Real Analysis and if I make a commitment to take it, he will change my status from rejected to deferred. The lesson is: take Real Analysis. I've spoken to many people who told me it wasn't important at all to the degree program but that I will not get into many schools without it (I couldn't take it since it is only offered during the day and I can't exactly quit my job)

[Bobbi]

Are you sure you're even interested in Statistics? That's a lot of work to enter a program that you ultimately might not even enjoy. I majored in Statistics as an undergraduate, and it was awful. Statistics is nothing like that intro course you took and got an A in.

[coffeeintotheorems]

Actually, emmm has a point. I had assumed an overall GMAT score of 700 was good because I believe its math section to be far superior to the GRE quant section based on what I've seen from a friend who was studying for it (haven't taken it myself.) Vince, what was the quant score on your GMAT, and what was its percentile?

For entrance to a Stats program, you *will* have to take the GRE. Mathematically speaking it's an utterly vapid test, but scoring in the high 700s on the quant section is a basic hoop that every applicant must jump through. With long, proper training you should be able to do it, but that should be much lower on your priority list--you need to take Calculus, Linear Algebra, etc. before even considering applying and prepping for the GRE.

I personally spoke over the phone with a member of a committee from a good school from which I was rejected and he told me that the only reason I wasn't accepted is because I did not take Real Analysis...

This is correct if you wish to have a competitive application for a top school or second-tier school. I'm guessing Vince isn't planning on applying to any school in the top 20. (I mean no offense by this; I'm just being realistic about the rigor of the background you would need to get into a top program.)

Real Analysis should not even be on this guy's radar. If you find calculus difficult, real analysis will end you. I guarantee it.

[illu]

First of all, do you even like statistics? Why do you like it?

Here's, in my opinion, the set of courses you should have for PhD:

1. Multi-variable calculus (vector calculus is not important, but you probably want to take it for the heck of it), and linear algebra

2. Introduction to mathematical statistics (on the level of Hogg and Craig is good; Wackerley et al. is a bit too weak, in my opinion)

3. Introduction to regression analysis (at the level of Kutner's book is good)

4. Measure theory (on the level of Stein & Shakarchi, Royden, Folland, Pugh, etc.; they are about the same)

Don't bother with differential equation. It's useless for statistics.

[Xero735]

You should also have a fairly strong background in linear systems and linear programming

[Vince Silvia]

First of all, thanks for the responses.

I wouldn't say that I'm SURE about pursuing stats, but I like what I know of statistics. Admittedly that's not a whole lot, but I like the idea that complex situations or whatnot can be modeled or predicted in a calculable or numeric way, if that makes any sense. For example, one year, I was getting tired of making crappy March Madness picks time after time, so I tried to devise a statistical method to compare the matchups and make my picks. I've tweaked it over the last 4-5 years and just wrote some code to run simulations (of 10000 "games") using a normal probability distribution for a couple of the stats to make my picks. I think it's fair to say it's something I'm pretty interested in overall, even if I don't know a lot of it, but that's kind of the point.

I spoke to friend of mine a while ago about this possibility, and she was confused by my motivation. She's pursuing her PhD in a different field because she wants to be able to teach at the University level, and she needs a PhD to do that. I told her that my reasoning for potentially pursuing a PhD is because I want to know more about Statistics and be better at them. What that additional knowledge or understanding brings me isn't as important to me. Maybe it's strange, but I'm just sort of interested in certain things, and I want to know more about them. Statistics happens to be one of them.

As to my poor undergraduate grades, I blame my youth. I wasn't terribly motivated as an undergraduate, in all honesty, because it felt like something I was supposed to do as opposed to something I wanted to do. Then, 5 years after graduating, I wanted to get a Master's degree in CMIS for the same reason I'd like to pursue Statistics - because I wanted to be better at various disciplines in it. I've been working full time the whole time I've been in grad school, and I've been able to maintain a 4.0 in a more intensive program than the undergrad, so I don't know that even I trust the accuracy of my undergrad grades.

My plan was to start taking Calc II this summer and progressively take more potentially required classes until either A) I've passed them all to my satisfaction (or enough of them to where I can start applying to programs), or Realized that they're beyond me and my goal is unrealistic. I was going to try either way, so I appreciate the input.

[Xero735]

Then I would suggest going for your masters at the very least. You would be going up against frankly people like myself that have been very motivated have given countless talks, have potential publications, multiple degrees in the field, and have spent the last decade studying this material. What this means for you is first and second tier programs are out of the picture and while you have a shot at some programs, admissions in the past several years have been ruthless and you need to look towards low-tier schools. What schools have you considered?

[coffeeintotheorems]

For example, one year, I was getting tired of making crappy March Madness picks time after time, so I tried to devise a statistical method to compare the matchups and make my picks. I've tweaked it over the last 4-5 years and just wrote some code to run simulations (of 10000 "games") using a normal probability distribution for a couple of the stats to make my picks.

This is a good start; it's pretty important to start off with a sense of purpose. Before you pursue a stats degree any further, you should be have a few very clear application ideas and career goals. Going through such a program, while rewarding, will be very demanding for you both intellectually and financially.

Also, the fact that you're a programmer is good and means that you'll be more ready for applied work if you can master the mathematical and abstract concepts.

I spoke to friend of mine a while ago about this possibility, and she was confused by my motivation. She's pursuing her PhD in a different field because she wants to be able to teach at the University level, and she needs a PhD to do that. I told her that my reasoning for potentially pursuing a PhD is because I want to know more about Statistics and be better at them. What that additional knowledge or understanding brings me isn't as important to me.

It sounds like your main motivation is curiosity rather than a specific career. In this case, you might want to just study on your own for a few years before thinking about pursuing a degree (unless you somehow have access to an endless pit of money.) The main reasons for a PhD in Stats are 1) to teach and do theoretical research at university (like your friend), and 2) to obtain one of various jobs that involve the title "Statistician," "Epidemiologist," etc. If you're just intellectually curious for now and want to use stats for side projects, then it'll be better to crack a few books, take low-cost courses, and save the MS plans for later.

Maybe it's strange, but I'm just sort of interested in certain things, and I want to know more about them. Statistics happens to be one of them.

If you think that is "strange" then you're posting on the wrong forum . A majority of the people here were math majors in undergrad; you generally don't do that if you aren't "interested in certain things" for their own sake, without regard to financial rewards.

My plan was to start taking Calc II this summer and progressively take more potentially required classes until either A) I've passed them all to my satisfaction (or enough of them to where I can start applying to programs), or Realized that they're beyond me and my goal is unrealistic. I was going to try either way, so I appreciate the input.

Wait, your Calc I is perfectly solid, right? As in, you can do it in your sleep, right? I don't care about your damn "grade" (although you should aim for As)--I care about whether or not you've developed an intimate understanding of the subject.

I don't think you're goal is unrealistic, especially given that you like to explore things on your own. I do, however, think you have a long (but rewarding) road ahead of you in your quest to develop these new skills.

Let's face it: math is hard. Always has been, always will be, and there are no shortcuts.

[Messed_up_thrice]

Any school that takes itself seriously will expect you to have thru Calc III, an intro to linear, an intro to proof writing, a year long sequence in Prob/Mathematical Statistics, and a year of Analysis to be admitted as a PhD student.

The Analysis might be optional but definitely expect to have to take it during your first year if you enter without it.