DanielWarlock

I'm not know how good you are with math. But your last sentence is very naive. Understanding definition does not make things easy. For example see this exercise: World-class mathematicians specializes in group theory, you know. It is not easy. Have heard any mathematician specialize in adding two numbers together? No because adding two numbers together is easy. Even if you are leading expert in group theory, you don't get to make that kind of claim considering that (i) you have studied group theory for at least 5 years to be world-class expert as you are and that is just like a few topics not entire field of group theory (ii) if it is not too difficult, why are there still open problems? shouldn't have you solved all of them already, given that they are so easy?

I would caution any foray into abstract algebra for stats people. First of all, it is useless for most stats. Second of all, it can get out of hand, especially for "honour" abstract algebra unless you already had a formal training in pure math--a solid first two-years in analysis and algebra. From the look of the courses you have taken, I don't think you do. I was stupid enough to take honour abstract algebra in college with pure math people who had real training. The class was taught by an actual expert (Fiona Murnaghan) and I was destroyed. Class was 100+ people and by the time of midterm there was like 20 left. I got 31% on midterm. Granted, the average was 30% but I worked my ass off doing that stupid class and I was technically only taking 2 classes that semester. Some of those homework problems are extremely difficult to do with my math ability at the time. I ended up dropping that class. I took a non-honour version of that at another school last year and got 100% on every thing with minimum effort. So don't take the honour version.

You have had no formal training in math/stats. This may not be as bad as you think for some master programs but are you sure you can handle a phd tho, given that you are admitted? You can grab a few graduate level textbooks such as theory of point estimation by Lehman, probability and measure by Billinsley. See if you are comfortable with those. It could be a problem for someone who had no exposure to math. Remember: you will need to take courses on those in ANY PhD program and pass a test; this could be your undoing despite you being a star researcher. But I could be wrong. There was actually a high-school student who managed to take graduate probability class last semester from scratch. But that guy was a genius and you may be not; plus, he was an established researcher in some pure math domain, already published a dozen papers before college. So he had a lot of exposure to math already. All I'm saying is that you don't want to enrol to a PhD and have to dropout because you struggle with the classes or qual exam. It was a waste of time and money; and the struggle is bad for your mental health. You may want to do a master first at Berkeley or Harvard before applying for PhD--I see you did list those two schools and I think you will find yourself quite at home with their more "gentle" course requirement. Be cautious about going to Chicago or Stanford; the master programs there are also very hard (so I have heard)--you may also end up dropping out. In terms of less competitive programs, you may want to apply to UF. The feedbacks from one guy who just graduated there seems to be very positive. I actually applied to only one "safe" school and it is UF. I mean, I don't want to go much lower than UF since PhD is a big commitment. But that is just me. You can check out something like Florida State--they say there could be no funding for PhD! I don't see how it will work so choose not to apply. But at least something to put on your Radar. But my honest suggestion is to consider doing an MBA instead of a technical degree. Have you thought about that? You have been out of school for a couple years now and haven't had much math in the first place. Now you go back to school for stats and all of a sudden are expected to do integrals, derivatives, matrices etc. Is that what you want? because that is what you will get. You don't get to use sklearn to do regression anymore. You need to actually write down things in excruciating details such as doing matrix inverse, things that are not necessary for most practical applications (though necessary for academic research). Is that truly going to help your career and your start-up?

Ok another suggestion is that you should get your statement of interest proof-read by someone, preferably a native speaker. Your written English seems to be pretty off. This along with your low verbal score can really do some damage to your otherwise decent application.

Your profile is very strange. Why do you have 145 in GRE verbal? Is that a typo or you actually scored just that much? If so, I think you should at least redo it. 145 is like you got most questions wrong. It may raise some red flags. I have never seen anything like this. Also why are you applying to like 30+ schools? This is very unusual. Otherwise, it looks good, except that "advanced cal I" and "applied linear algebra" is graduate class? It is unheard of. If they are not actually graduate classes taken by PhDs, don't bluff on your application. It is really strange for graduate students to take classes on calculus and (applied) linear algebra. You may want to apply to some more elite master programs. You certainly have a shot at Columbia (stats master), JHU, Michigan (data science master) to say the least. But that verbal score, if not a typo, is a wild card. You should really redo it to get 150+.

If you truly love math and want to keep it going, then you need to give it a shot no matter what. It seems that you have funding for it so there is not much to worry about at all. You can at least apply and give up AFTER being rejected. It seems more logical to me unless application fee is a problem.

This is absolutely false at my program at least. Half of the class are international students whereas the competition among domestics is no less stiff. Some guys are domestics from Berkeley math, NYU math etc. Harvard math, MIT, Stanford etc. with 3.9+ GPA. Many outstanding applicants simply don't want PhD and apply to Masters at top schools so that they can transition to elite companies and live a comfortable life in 1-2 years. I don't think my profile is superior to theirs in any way. Top master programs are less selective compared to PhD mainly on their requirement for academic rigour and there is more flexibility, especially emphasis on your prospect to land an elite job. There is not much discount on GRE or GPA as far as I can see.

Professor Han Liu is very good. I read some of his papers about dimension reduction. He collaborated with another chinese guy at Princeton a lot -- So essentially studying with Prof Liu is comparable to studying with the other guy at Princeton. But if you go back to your home country, say China, to find a non-research job in industry, then all they know is Princeton (some may not even know Princeton!) and when you say you are from Northwestern it's like you did your PhD in wild west shooting buffalos (They call foreign universities they don't know "chicken university"). Your parents are embarrassed to talk about your school and your relatives and friends think of you as a failure, studying in your 30s at chicken university unmarried living on minimum wage. You can say it is all about science and not opinions of other people etc. But the truth is that it is very hard to land a faculty job no matter what and you will likely return to China after PhD to find a non-research job. One exception would be that you are truly genius and do manage to do great contribution to science. But the price to have that proposition tested out is enormous. How do you know you will not be a mediocre PhD if you are not even good enough for some of those PhD programs as a college student? One of my classmates (from Peking U Math!) at my Harvard master program was actually admitted to Northwestern PhD and didn't go. He would rather come to Harvard, pay tons of money, studying with less competent people such as myself, just so that his education background will be recognized. Another exception is that you absolutely cannot live without doing your research. Your love to your field is so crazy that the addiction cannot be contained and you don't care about anything just so that you can keep pursuing it. Then fine. You do it at chicken U or whatever. But this is very very rare even among the best scientists. Mostly, people work like crazy just so that they can prove they are the best. Perelman, probably the most powerful mathematical mind there is, retired from mathematics after he proved the conjecture, so did his predecessor Hamilton. More mundane examples are profs slow down research (sometimes greatly) after being granted a tenure. Students think they are "interested in" doing some area of research but when they actually do it, they do it out of necessity to get their degree and that becomes unbearable. I witnessed a stats PhD at Harvard broke into tears one day while saying "I hate this shit so much". My old boss dropped out of Waterloo PhD just because the psychological burden was too great and to watch his peers went on to live great life in industry broke him. He said "PhD was my darkest hours". So don't go to PhD unless you are absolutely sure you do it at place you are happy with. You sacrifice a lot and are doing mankind a favour by pursuing PhD, especially at a place with little recognition beyond academia.

I'm not sure about this. I was rejected from Stanford and Chicago so did all of my classmates here at Harvard. Acceptance rate at Harvard DS master program is already 7%. And Chicago and Stanford are absolutely lower. All I'm saying is that for data science/stats programs like Harvard and Berkeley they highly value your professional experience where Chicago and Stanford place high emphasis on your academic credentials. Classes at those two schools are way harder than Harvard and is not flexible at all. You need to do Probability and Inference etc. with PhDs in order to even graduate. I honestly am not sure if I was up to that task 1 year ago and no one will have confidence looking at my engineering transcript. I'm not sure about that even now as they say PhD classes at Harvard, which I took and struggled to a degree, are like joke compared to those schools. But essentially at Harvard or Berkeley you can take easier classes and go find a job so they are less obsessed with you being a math genius.

I don't think a real analysis course is absolutely mandatory, especially when your background is computer science instead math/stats. Graduate probability/stochastic calc and inference classes use real analysis extensively--so doing as well as you did in those classes should be a good indication of your math ability. I personally would also include books I have read such as Rudin, Royden, Folland, Stein etc to amend lack of pure math real analysis class. If you have "corroborated evidence" such as research work using knowledge of analysis, grad-level probability classes, I believe this statement will be taken into account.

I can't comment on your chance of getting into stats phd program because I'm also applying this year and have no idea. As to other questions, I personally think a C- in Mathematical Statistics is going to hurt at least a little because one class you will need to take in any graduate stats program is a graduate version of this. A C- is like a passing grade close to almost D so some people may question it a little bit. But this is not a death sentence because your performance on other math, stats classes are very strong, and your research is very strong too. I think you should add a note to explain why this class didn't go as well. That said, you must increase your quant GRE score for like ~10 points which seem to me is your other weakness. The practice test score is very good. Replicate that in a real test and you are good to go.

Abstract algebra seems to be completely useless for most statistics, unless you intend to work on some highly specialized areas of probability such as random walk on groups etc. If you are applying to top 10 pure math programs, I'd say you may be in trouble because abstract algebra is very essential for pure math and a B+ may put you at a disadvantage at top places. But for statistics I really don't see how it is a factor. That aside, you got B+ which is almost an A! It is not even that bad if at all. Many people would consider B+ to be an "honour grade". I would only worry about that if I had an otherwise perfect profile. But again, when your profile is that perfect on other aspects, no one will care. I strongly discourage you from including a note about grade deflation etc. because that may come off as pretentious considering that (i) there is no official, scientific quantifier as to what school has deflation; (ii) B+ is a very good score on a hard topic. It's like explaining I got 169 instead of 170 on GRE because there is a very unfair question. Makes no sense.

U Chicago actually said they rarely admit those who do not take and they have lots of applicants scoring above 90% or something along those lines. This (along with no close interest match) pushes me over the edge of not applying.

I think a disclaimer is due since this a public forum and I don't want to spread rumours about UofT: There is literately no scientific data that suggests it is "impossible" to do a funded masters at UofT as international student or that international students' profiles are discriminated in any way; all I'm saying is that on top of my head I can't think of any such example--but my knowledge only applies to a handful of people I know and should not be taken as a reference for your decision to apply. I don't want to deter people from applying to UofT just because of rumours or my personal experiences. There is nothing on my rejection letter that states my immigration status was a factor for rejection. As I said, I was not a math or stats major and didn't take the most relevant classes in college. It may be one reason why I was turned down. That aside, there are many masters at UofT that discloses immigration status composition of incoming cohort. Some, especially self-funded ones, do have a track record of admitting a lot of international students and they are quite good, selective based on academic merits and professional experiences. Some of them such as MMF do give data on composition of their enrolled students based on immigration status. This is what I would be looking at as reliable information. Please don't take anything I said into serious consideration.

I actually don't know much either. All I know is rumours. I myself was rejected for a master. That said, you may want to get in touch with your dream prof because I feel the system at UofT is a bit different than US or even waterloo. A lot of guys know their Prof and have worked together long before submitting an application for PhD. It appears that UofT "self-consumes" a lot of its own undergraduate students. It's not an official stance but most people at UofT seem to agree that UofT self-consumes more than other schools and it is helpful (to say the least for some programs) to have your prof to look after your application. Please know this is just opinion and rumours, not proven facts.

Exactly. That's the major reason I applied to Upenn instead of Chicago. I spent a summer with Rosenthal's PhD (Jun Yang if you know him) doing this approximate chain stuff. The idea was to generalize Rosenthal's 1995 quantitative bound so that it provides complexity instead of exact bound for higher dimensions. The catch is that Rosenthal's minorization and drift set-up blow up to 1 very quickly so in high dimension it falls apart. So Jun's idea is to add a "large set" in addition to "small set" so that all ill conditioned parts of state space are discarded. It's a neat idea but the amount of calculus is over the roof even for basic stuff like Stein-estimator and is really not practical at all. I thought a lot about this but didn't end up writing anything down. There are basically no good theoretic work on this neat enough for those who do not have expertise. Natesh Pillai and Aaron smith at UOttwa had a paper where the bound assumes a lot of things which are not practical to verify. The tools are modified from discrete chain literature such as conductance. We actually talked to Smith and he thought it was his "less proud" paper. I talked to Natesh and he was not even that interested in this anymore so we worked on this dual space/discretization projects which has essentially turns a continuous chain to discrete and thus has high-dimension application and is very easy to implement. I feel the subsampling routine with artificially defined "optimal weights" are the way to go. Take a look at this paper: https://www.tandfonline.com/doi/abs/10.1080/01621459.2017.1292914 Now, what if I want to do this with Bayesian posterior, or what if sample size are so large for the original logistic regression problem. The idea of monte carlo is essentially to address "big data" situation like this where the whole picture is unknown due to size of the problem but local information is available such as a subset of entire data. So long as you can find a set up, it will give you exact solution asymptotically. I will focus on talking about this kind of stuff because I thought even machine learning community would be interested.

Thank you for reminding me! Non-parametric Bayesian, Dirchlet, urn representation, Chinese restaurant is a standard area in MCMC. I almost forgot that. In fact, I think my current research may be extended naturally to such problems to obtain easy convergence diagnostics. Very interesting idea actually. I hope I thought of that 2 months ago. Another interesting thing you reminded me about non-parametric would be Gaussian process stuff. In general, the auxiliary dual space to original MCMC may be defined as space of functions/distributions rather than a partition cell of state space. I will see if I can work out some interesting use cases and will definitely keep that in mind when discussing potential with nonparametric faculties. Thank you very much. As a side note, I'm aware of the big data trend in Bayesian as far as sampling is concerned. The posterior becomes too hefty and parallelization does not seem to be a direct solution to that. There are some "subsampling", "approximate/perturbed chain" techniques and bounding techniques but still an open problem. Is there a way to address that using optimization? Industry standard seems to be just randomly pick a subset from all the data each time, sometimes with tailored hypothesis. A neat idea in regression I saw the other day is to assign a distribution to each multiplicative factor to draw sample from that as what you would you for computation. This distribution is chosen so that the variance of estimator for coefficients is minimized. I could see some adaptive algorithm being developed using analogous idea for Gibbs sampler for posterior Bayesian, i.e. each step is taken with consideration a subset of all data but the selection of this subset is adjusted gradually from uniform towards optimality. Oh well, I can go on and on about Monte Carlo. Might not even have a chance to work on these things if I failed my PhD application. We will see what happens.

I'm also applying this year. Your profile is comparable to mine, i.e. with more emphasis on research rather than grades. I know people who are on the opposite end with perfect grades in a bunch of graduate math classes (harmonic analysis, Lie algebra etc.) but no research experience or letters to testify. Their letters will be from math class instructor to further reiterate that they are "math geniuses". Yes on paper, they appear to be more "solid". But the admission needs to balance research interests of incoming cohort. And that is where they fall short. The purpose is not to fill the entire cohort with machine learning oriented people but is to ensure professors in each area will have some, even just remote matches, even more so they didn't admit any in previous years. For example, if there are +2 sampling, statistical computing, Markov models faculties, then they will very likely admit at least one person with experience and interests in that area. That way, your disadvantage compared to someone from pure math on baseline measures who think he is going to do machine learning or "big data" or theoretic probability in general will not be as bad. Also, competition between profile like yours and mine will be almost non-existent because your area of interests are completely orthogonal to mine. So I think the best strategy for profile like ours is specificity: talk about your area in statement competently, say by proposing research ideas in relation to your target faculties' sub-sub-field. But at the end of the day, they want to make sure you have as much competence with mathematics as possible. Personally, I think competence with math is crucial to publication in statistics. Some profs believe in that strongly but some do not actually care as much. The consensus at Harvard where I did my masters seems to be that probability/statistics is not math and a "probabilistic" thinking is more important. Entering PhD cohort at Harvard is not exclusively math geniuses--some do struggle with 1st year probability and inference classes believe it or not. I believe there are many applicants who are extremely competent with math but didn't get in because match of interests and other factors. That said, at top places like Stanford, you will still fall short because regardless of your area, some applicants' track record is good enough to apply to post-docs in his/her specialized area. (take a look at this guy: https://faculty.wharton.upenn.edu/wp-content/uploads/2016/11/CV_Bhattacharya.pdf?_ga=2.148566066.443551298.1571676683-1391157221.1571513002). Solving 4 world-class combinatorics problems and published in top math journals 2nd year in college.. I mean, I wouldn't be too surprised if he got a tenor-tracked position at lower-tier department fresh out of college. How do you compete with this stuff? You can have 100% in GRE math and take all math classes there are and still pale in comparison to such people. For example, I like to say my interests match Diaconis as I also worked on Markov chains but so do many other people and there is no way I can get in no matter what. And mind you there is going to be at most 2 such pure math geniuses to be admitted--they will absolutely admit people with less impressive baseline measures (if they have to) in other areas such as biostats, high-dim inference because there is only one Diaconis. My strategy is therefore to apply to 2-3 less elite places such as UF where there are several faculties that match your interest, and leave the rest to fate (or God if you are religious).

Bayessays. I checked the faculty but didn't see any MCMC people here. Which professor are you referring to? Thank you! Page I checked: https://stat.utexas.edu/people/core-faculty

I think you are right to a degree. First is the pragmatic reason, I chose to do 9+2 because my friend applied last year and he did exceptionally well by applying to only top schools, receiving only 2 out of 13 but very high-quality admissions (he applied to 13 programs in total). The reasoning was that I just need to be admitted to 1 school and to have too many safety choices would be a waste. Plus, safety is not really safe and reach may not be reach after all given all the other factors such as interest match. But I decided to also do UNC now and dropped Princeton from my list just because UNC has several MCMC faculties and Princeton had none. The new list is now: Harvard, Berkeley, MIT(CSE), Stanford(CSE), Columbia, Upenn, Duke, Michigan, UNC, UIUC, UF. Yes it is a top-heavy but I think the risk is not actually that bad: I should have 50% chance getting into each of the last three schools on average given that UNC and UF has several MCMC faculties. I will say 10% chance for Harvard, Duke, Michigan each on average (my advisor actually said 80% chance which I will take as hyperbole). Now I have like 9.1% chance being rejected by all these schools. I will not count my chance into Berkeley, MIT(CSE), Stanford(CSE), Columbia, Upenn just to offset what inflation I might have included. But Upenn, Columbia and Berkely all have dedicated MCMC faculties whereas MIT and Stanford need to admit people with interests in statistical computing and randomized algorithms; not as many stats people will apply to those programs so I might just get lucky from interest match. Now I have below 10% chance of failing completely. Let's say even if I was being conservative already, the actual odds are worse. The thing is that I already have operated under optimal conditions in undergrad and master level (best schools, best advisors, no financial worries) and have already worked my butt off in a way. This is not like someone from India or China who are very talented but are put into a disadvantage due to their background and origin. The point is that if I were still to be rejected by all these programs, then I am proven to be mediocre beyond reasonable doubt and would be better off doing less challenging works and leave research opportunities to others. That's why I said so be it.

That's exactly what I thought. I will not submit the score anywhere. Stanford average on that test is like 90%+ this year as well, that's with domestic included. This test has become quant section of general GRE. Given that everybody gets it perfect on courses and GRE, I think if I ever get in anywhere it would be because my research and reference. No need to divert attention to other stuff. We will see what happens.

I applied to masters at UofT, Waterloo, and UBC 2 years ago. My profile was comparable to yours except my GPA was higher (that said, my courses were like joke, i.e. engineering, and are much less relevant than yours). I was rejected by UofT but got into Waterloo and UBC with full scholarship. The rumour is that U of T master stats program very rarely admit international students. I heard that a guy, who was international undergrad at UofT at the time, was admitted to Princeton to do phd or something but was still rejected by the said program. No official statement on this and I presume some very outstanding applicants with right courses/connections may actually get in. But certainly it is unheard of as far as my knowledge is concerned. Most of my peers went to waterloo or US. Other funded MSc are similar: a guy almost made it but the prof broke off the arrangement in March due to funding issue! He was not even allowed to do it if he himself pays for his study. Fully funded at UofT being an international student is very hard. But let's assume you have funding. You can apply to the finance masters such as MMF, which almost exclusively admit international students and job prospects are very very good. Almost everybody can find a full-time, high-paying job in finance doing risk or something. But very tough to get in still. Most guys have 3.90+ GPA, or intern experience in RBC, Scotia etc. I didn't even apply because I was not thinking right. Now I regret it deeply. You should at least apply to MMF if you have funding. You can also apply to "MEng" in financial engineering--it is a less selective, self-funded program. From what I heard, GPA at your level is almost sufficient to guarantee admission. But support for landing internship is next to none, unlike MMF. Another good one is the new insurance master at Rotman: it is almost as easy to get in and has very outstanding job placement record. My friend went there 2 years ago and now is doing machine learning at top banks (and is getting married with a house!). His GPA/experience was not nearly as good as yours or mine. So you see, with right program and right efforts, your life will totally take off. There are many programs in Canada that you can apply to such as QMF at Waterloo--it was much cheaper. My old boss went there after dropping out of phd and find job very quickly afterwards and eventually become boss. He was like just 5 years older than me. I actually regret that I did not stick to Canada and went US where I worked a lot to no avail. Now I'm very stuck and broke, and may very soon be forced to go home (to China) to live off of my parents' pension if things go even worse. I had my chance and I blew it because of stupidity. So sticking to Canada is the key. As to other schools, you should not worry too much about your odds. I think you will likely prevail.

Thank you "Stat PhD Now Postdoc". I'd assume you are associated with UF given you detailed knowledge of the job placement. Do you think I should submit my GRE math score for UF and UIUC? My guess is that as they are less competitive than schools like Stanford or Chicago, a 76% may actually help my case at UF and UIUC? I could be wrong though since I have no idea what a typical pool of applicants would look like.

Yes. I went Monte Carlo/MCMC all the way since doing a thesis with professor Rosenthal. Both profs at Harvard are experts in MCMC as well and hopefully they will say I know what I'm doing (somewhat). I really loath taking courses, especially high-powered stuff such as "graduate real analysis I, II" or "graduate algebra I, II"--this is taught at Harvard by some crazy person and he went way beyond standard graduate text such as Royden, Rudin etc with PDE and harmonic XXX because math phds at Harvard are that good. In a perfect world, I'd taken such classes and got an A but it is simply too much stress and so unnecessary for someone who does statistics. Plus I'd probably have to do zero research to cope with classes and thus land bad letters. I read baby and papa Rudin on my own instead and studied linear algebra again in details in grad school. Even outperformed some (if not most) Harvard PhDs in their probability and inference classes. I totally flopped the math GRE despite my love for it. It has many clever problems with emphasis on basics. I still don't know how I can possibly fail that bad. I literally fell down the stairs seeing the score (resulting in minor injuries). oh well it actually doesn't matter that much. Not everyone is meant to be a scientist. I have decided to take my chance with 9+2 formula with UIUC and UFlorida. I don't actually want Chicago that bad upon looking at their faculties. It is also said that there is a "cut-throat" culture so I might not even survive even if I got in. UIUC is a good computer school (maybe chance to collaborate) and Florida has monte carlo people plus top-notch living condition. Both seem like great deals. The other 9 schools, Michigan and Duke to a lesser degree, are highly reputable--so no regret in missing out on the "prestige". And if I can't get in any of these, so be it. Time to go home anyways. Thank you for your advice, statfan and bayessays! Good luck with your research and stuff..

"A quick update: I got 760 on the Math subject GRE test, which is the 72th percentile. I don't know anything about abstract algebra, complex analysis and graph theory, so I consider it an ok but not great score. I already submitted to Stanford and UPenn, and I am wondering if I should submit it to schools..." Thanks statfan. I saw you probably had a similar profile as I do and probably similar math background (not in pure math). Did you send your GRE math score to all schools? What is your application results? Where did you end up?