DanielWarlock

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.

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. 

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.   

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.  

Given your interest, I think Harvard is best fit. Imai has affiliation at Kennedy school, Neil Shephard is affiliated at economics. Murphy is also a big name here doing causal inference and reinforcement learning affiliated to CS department. There is no problem that you seek additional advisors at MIT or other Harvard departments. You can easily find someone at MIT to supplement for (3) (4). Everyone is saying Stanford stats but they are mainly about highly mathematical/theoretical high-dimensional stats and probability theory. So I guess you will need to go to their CS department to find advisors? Stanford probably is not that of a good fit for you. 

Given your interest, I think Harvard is best fit. Imai has affiliation at Kennedy school, Neil Shephard is affiliated at economics. Murphy is also a big name here doing causal inference and reinforcement learning affiliated to CS department. There is no problem that you seek additional advisors at MIT or other Harvard departments. You can easily find someone at MIT to supplement for (3) (4). Everyone is saying Stanford stats but they are mainly about highly mathematical/theoretical high-dimensional stats and probability theory. So I guess you will need to go to their CS department to find advisors? Stanford probably is not that of a good fit for you. 

Both schools are focused around the theme of high-dimensional stats. But risking oversimplification, a quick summary of their difference is: CMU is more "CS"; UChicago is more "mathematical". If you consider yourself more of a mathematician/probabilist, go to Chicago. If you consider yourself a computer scientist who looks at more applied stuff, then go to CMU. I will now further explain what I mean. 
CMU focuses more heavily on more applied, interdisciplinary stuff like neurosciences, astrostatistics, social sciences and yes sports analytics.  Of course, most of these are done under the tag of "high-dimensional statistics".  But I would even go so far to say CMU stats has more of a "CS flavour" if you know what I mean. On a related note, CMU is also much stronger on causal inference, which is also more "CS". I also feel the organization is very similar to what I see at EECS at MIT: they have all these themed working groups like "astrostats group", "causal inference group". So the community based activities like colloquium/talks, reading groups will be more specifically tailored to your subfield. 
Chicago is more theoretical and will probably be more so in the coming years based on their new hires. Maybe "theoretical" is not a good descriptor. What I mean is that their new hires now mostly have tags such as "physics", "statistical mechanics", "random matrices", "Fourier/harmonic analysis", "combinatorics", "random graphs". Chicago is definitely more mathematical and has a taste of more probabilistic things. They even hired student of Borodin who does hard-core math. 

Both schools are focused around the theme of high-dimensional stats. But risking oversimplification, a quick summary of their difference is: CMU is more "CS"; UChicago is more "mathematical". If you consider yourself more of a mathematician/probabilist, go to Chicago. If you consider yourself a computer scientist who looks at more applied stuff, then go to CMU. I will now further explain what I mean. 
CMU focuses more heavily on more applied, interdisciplinary stuff like neurosciences, astrostatistics, social sciences and yes sports analytics.  Of course, most of these are done under the tag of "high-dimensional statistics".  But I would even go so far to say CMU stats has more of a "CS flavour" if you know what I mean. On a related note, CMU is also much stronger on causal inference, which is also more "CS". I also feel the organization is very similar to what I see at EECS at MIT: they have all these themed working groups like "astrostats group", "causal inference group". So the community based activities like colloquium/talks, reading groups will be more specifically tailored to your subfield. 
Chicago is more theoretical and will probably be more so in the coming years based on their new hires. Maybe "theoretical" is not a good descriptor. What I mean is that their new hires now mostly have tags such as "physics", "statistical mechanics", "random matrices", "Fourier/harmonic analysis", "combinatorics", "random graphs". Chicago is definitely more mathematical and has a taste of more probabilistic things. They even hired student of Borodin who does hard-core math. 

I hope you all have been having a spectabulous Spring and are excited about your options for this Fall if you have been applying to schools this season.
I've been lucky to receive very good results for my PhD applications, and I do believe that I'm ready to make my decision. However, I would like to crowdsource my question just for that last drop of insight, and maybe also because I'm curious: which statistics PhD program between University of Chicago and Carnegie Mellon University would you be most inclined to choose (if those were both your best or only options)?
The typical points of comparison I've approached are along these lines: UChicago has a more comprehensive theoretical program with many courses and course options, offers somewhat safer summer funding to most students, and has collaborations with nearby institutions like Toyota Tech and Argonne; CMU has more freedom built into their program without qualifying exams or as strict and intense a course load, emphasizes interdisciplinary work and applied projects more, and is located in a safer and more affordable neighborhood.
I think that these may be enough to decide which department culture is more to one's general preferences, but it's not a total and unilateral comparison. I have met current students at both programs who faced the same decision, so I'm confident that there's no wrong answer. I can only truly learn about department culture by living and interacting in the respective environments. As such, I have come to a biased decision from these simple impressions alone and would like to see whether I'm approximately in agreement with the broader community of new grad students in my field.

I agree with bayessays, but I did want to add in one edge case -- I really wanted to go to CMU in part because of their strong collection of people working on applications in sports (more the students than the professors I think, but they host a summer research program for sports statistics too).  Of course, that's a niche interest, so YMMV.

Besides the very personal city preferences (Hyde Park isn't the most desirable place to live, but you have access to a much bigger city than Pittsburgh), I agree that the theoretical nature/intensity of the programs would be my biggest factor.  If I was very confident in my math abilities (such that I wouldn't be worried about failing quals) and I wanted to do very theoretical/mathematical statistics, I would go to Chicago. Otherwise I would probably go to CMU.  Of course, these are broad generalizations and if there were specific professors I wanted to work with at one, that would be a different story.  Either way, both great choices, congrats!

Both schools are focused around the theme of high-dimensional stats. But risking oversimplification, a quick summary of their difference is: CMU is more "CS"; UChicago is more "mathematical". If you consider yourself more of a mathematician/probabilist, go to Chicago. If you consider yourself a computer scientist who looks at more applied stuff, then go to CMU. I will now further explain what I mean. 
CMU focuses more heavily on more applied, interdisciplinary stuff like neurosciences, astrostatistics, social sciences and yes sports analytics.  Of course, most of these are done under the tag of "high-dimensional statistics".  But I would even go so far to say CMU stats has more of a "CS flavour" if you know what I mean. On a related note, CMU is also much stronger on causal inference, which is also more "CS". I also feel the organization is very similar to what I see at EECS at MIT: they have all these themed working groups like "astrostats group", "causal inference group". So the community based activities like colloquium/talks, reading groups will be more specifically tailored to your subfield. 
Chicago is more theoretical and will probably be more so in the coming years based on their new hires. Maybe "theoretical" is not a good descriptor. What I mean is that their new hires now mostly have tags such as "physics", "statistical mechanics", "random matrices", "Fourier/harmonic analysis", "combinatorics", "random graphs". Chicago is definitely more mathematical and has a taste of more probabilistic things. They even hired student of Borodin who does hard-core math. 

Very interesting story. Maybe he is not dead-set on getting a PhD? Yale stats is actually very good. With guys like Harrison Zhou, Zhou Fan and Van Vu, I can even see one choosing Yale over Stanford when admitted to both. Not to mention the tremendous cost of money and time and the uncertainty of actually getting into Stanford (or even Yale itself) 2 years later. Sounds like a terrible decision. 

Very interesting story. Maybe he is not dead-set on getting a PhD? Yale stats is actually very good. With guys like Harrison Zhou, Zhou Fan and Van Vu, I can even see one choosing Yale over Stanford when admitted to both. Not to mention the tremendous cost of money and time and the uncertainty of actually getting into Stanford (or even Yale itself) 2 years later. Sounds like a terrible decision. 

Very interesting story. Maybe he is not dead-set on getting a PhD? Yale stats is actually very good. With guys like Harrison Zhou, Zhou Fan and Van Vu, I can even see one choosing Yale over Stanford when admitted to both. Not to mention the tremendous cost of money and time and the uncertainty of actually getting into Stanford (or even Yale itself) 2 years later. Sounds like a terrible decision. 

Very interesting story. Maybe he is not dead-set on getting a PhD? Yale stats is actually very good. With guys like Harrison Zhou, Zhou Fan and Van Vu, I can even see one choosing Yale over Stanford when admitted to both. Not to mention the tremendous cost of money and time and the uncertainty of actually getting into Stanford (or even Yale itself) 2 years later. Sounds like a terrible decision. 

I personally would definitely go to UChicago. It is the most reputable and give you a leg up finding jobs in not only data analysts/statistician roles but also in finance, consulting, SDE etc whereas Duke, UNC, UW Maddison are strong in statistics but not as strong in other things (like finance). 
That said, if you would like to do a PhD, ETH Zurich may also be a good option because European masters, as far as I know, is research-based and you could very likely transfer into their very excellent PhD program and finish much faster.

The answer would be Stanford for me by a very long mile. The program is very elite, much more so than Berkeley's program in my opinion. The fact that you are from the Stanford program would be already impressive on your PhD application--not so much for Berkeley MA. The reason? Firstly, Berkeley MA admission is much less competitive. Simply getting into Stanford MS indicates you are elite undergrad, a class above anyone else from a master program. The distinction to me is very clear.
Second, Berkeley's master course is watered down from their regular PhD version. Sure, you can substitute for PhD equivalents on your own initiative but if you apply elsewhere people may just assume that you have less rigorous coursework.
To put it plainly, my first impression would be Stanford MS students are of a higher calibre. 
You do not need to worry about no "formal thesis" at Stanford. The thesis formality is simply putting together a document that, at master level at least, no one will care. It could be of very high calibre or just some reading notes, but the thesis itself as a document does not matter either way. The only way your master research factors into phd admission is (i) having a strong recommendation from renown profs who specifically comment on the quality of your work (ii) publish it at top venue of your field before phd application is due.  Both (i) and (ii) have nothing to do with whether you have a formal thesis or not. Actually it is better to not to have it because the only difference is you spending like two weeks to type it up from work already done. 

I went to Berkeley as an undergrad. It seems that Berkeley's program is designed to be two semesters long. They made the change to a shorter program recently to better serve students looking for industry jobs (~2016). In fact, MA students used to TA but no longer have time for anything but coursework. 
Also, I don't think a year is nearly long enough to do these things simultaneously: take PhD level courses (Berkeley PhD courses are no joke), connect with potential letter writers, and start a project. I would feel that you'd be fighting an uphill battle given that the MA website clearly states that: "(i)n extremely rare cases, a thesis option may be considered by the MA Chair".   In my experience, Berkeley doesn't make anything easy (you have to test in for their BA program for christ's sake lol) so when they say "it's extremely rare" I would take their word for it. ?
I would elect Stanford (longer program) or another option that enables you to connect more with potential letter writers and take more theoretical courses.  Like @DanielWarlock said, having a paper is not important. 

The answer would be Stanford for me by a very long mile. The program is very elite, much more so than Berkeley's program in my opinion. The fact that you are from the Stanford program would be already impressive on your PhD application--not so much for Berkeley MA. The reason? Firstly, Berkeley MA admission is much less competitive. Simply getting into Stanford MS indicates you are elite undergrad, a class above anyone else from a master program. The distinction to me is very clear.
Second, Berkeley's master course is watered down from their regular PhD version. Sure, you can substitute for PhD equivalents on your own initiative but if you apply elsewhere people may just assume that you have less rigorous coursework.
To put it plainly, my first impression would be Stanford MS students are of a higher calibre. 
You do not need to worry about no "formal thesis" at Stanford. The thesis formality is simply putting together a document that, at master level at least, no one will care. It could be of very high calibre or just some reading notes, but the thesis itself as a document does not matter either way. The only way your master research factors into phd admission is (i) having a strong recommendation from renown profs who specifically comment on the quality of your work (ii) publish it at top venue of your field before phd application is due.  Both (i) and (ii) have nothing to do with whether you have a formal thesis or not. Actually it is better to not to have it because the only difference is you spending like two weeks to type it up from work already done. 

The answer would be Stanford for me by a very long mile. The program is very elite, much more so than Berkeley's program in my opinion. The fact that you are from the Stanford program would be already impressive on your PhD application--not so much for Berkeley MA. The reason? Firstly, Berkeley MA admission is much less competitive. Simply getting into Stanford MS indicates you are elite undergrad, a class above anyone else from a master program. The distinction to me is very clear.
Second, Berkeley's master course is watered down from their regular PhD version. Sure, you can substitute for PhD equivalents on your own initiative but if you apply elsewhere people may just assume that you have less rigorous coursework.
To put it plainly, my first impression would be Stanford MS students are of a higher calibre. 
You do not need to worry about no "formal thesis" at Stanford. The thesis formality is simply putting together a document that, at master level at least, no one will care. It could be of very high calibre or just some reading notes, but the thesis itself as a document does not matter either way. The only way your master research factors into phd admission is (i) having a strong recommendation from renown profs who specifically comment on the quality of your work (ii) publish it at top venue of your field before phd application is due.  Both (i) and (ii) have nothing to do with whether you have a formal thesis or not. Actually it is better to not to have it because the only difference is you spending like two weeks to type it up from work already done. 

Hard to say now. Harvard's courses have become harder this year. The 2nd inference class now follows Van der Vaart almost exactly--we used to just cover MLE consistency/normality and some less theoretical Bayesian stuff like model comparison, mcmc. 2nd prob instalment also paces faster than previous iterations. Looks like Duke could indeed be the least demanding in terms of course work. 

The answer would be Stanford for me by a very long mile. The program is very elite, much more so than Berkeley's program in my opinion. The fact that you are from the Stanford program would be already impressive on your PhD application--not so much for Berkeley MA. The reason? Firstly, Berkeley MA admission is much less competitive. Simply getting into Stanford MS indicates you are elite undergrad, a class above anyone else from a master program. The distinction to me is very clear.
Second, Berkeley's master course is watered down from their regular PhD version. Sure, you can substitute for PhD equivalents on your own initiative but if you apply elsewhere people may just assume that you have less rigorous coursework.
To put it plainly, my first impression would be Stanford MS students are of a higher calibre. 
You do not need to worry about no "formal thesis" at Stanford. The thesis formality is simply putting together a document that, at master level at least, no one will care. It could be of very high calibre or just some reading notes, but the thesis itself as a document does not matter either way. The only way your master research factors into phd admission is (i) having a strong recommendation from renown profs who specifically comment on the quality of your work (ii) publish it at top venue of your field before phd application is due.  Both (i) and (ii) have nothing to do with whether you have a formal thesis or not. Actually it is better to not to have it because the only difference is you spending like two weeks to type it up from work already done. 

I once faced a similar situation (plus Berkeley, minus Columbia). Columbia is very attractive to me, contrary to popular opinions here. If I had an offer from Columbia, I would be tempted to say the least simply because of the location. Imagine living at downtown Manhattan with Columbia's low-cost student housing. Columbia also appears to have a rigorous format with 2 quals (1 qual immediately when you start in September) and 3 separate specialty tracks: probability, math stats, and data science (including ML, applied statistics) headed by Blei. Here, the 2nd qual tests you on your specialty field. Classes such as probability, math stats, applied stats are 3-semester sequences instead of the usual 1-year load elsewhere and they restrict undergrad/master enrolment so that the courses can be taught at a high-level of rigour for just PhDs. I feel that the curriculum is much more in-depth than what we have at Harvard because Harvard often have about half of the class being undergrad (so all of our classes require minimal to none measure theory but Columbia is full of them). Basically Columbia program gives you more clarity in terms of concentration from the start. I think you will likely go to the data science track so I say a bit more: you get a joint degree in statistics and data science so there are mandatory credits in computer science classes, mathematics etc. 
Harvard is a trade-off in terms of location. It is 20mins drive from downtown Boston and Cambridge itself is not bad at all. 15 mins walk to MIT (if you take classes or do research there, you can get a very cheap blue bike student pass). It is nowhere near NYC experience but still above average in terms of location convenience. Harvard programming is moderate: 1 qual at the middle of 2nd year, mandatory class in prob, inference etc--a total of 7 mandatory classes, which appears to me to be less demanding than Columbia. In terms of applied work with Bayesian analysis, Professor Jun Liu is a big expert. Prof. Sam Kou also does a lot of applied work with Bayesian. Pierre Jacob is a big computation expert but he also does methodology work on stuff like model comparison, nonparametric Bayesian. Xiao Li now works with astronomy stuff a lot, which is also applied work I guess? He calls it "working with astronomically large data". Not sure how much of it is Bayesian but I'm sure you can make it so if you want to. 
Duke's location is not very appealing to me because of the remoteness. But if you like quiet, idyllic type of environment, Duke might be a good fit. I feel Duke program is in between Harvard and Columbia, with 2 quals (occurring later than Columbia) but less advanced coursework. I don't know much about Duke other than that. I just remembered that director Dunson told me students have flexibility with coursework and working with other department (e.g. CS and Math). 

The department hooked you up with a fellowship, specifically for disadvantaged students. That's easily worth 10-15hours/week. Most of us had teaching assistantships and they were really annoying. Grading, teaching labs, answering student emails everyday, office hours... it was a major distraction. Perhaps they see potential in you and think you could use the extra 10-15/hours week to catch up? To say they don't support you at all seems like a stretch.
The women in our department were actually less pressured to "take" service work (not that we had a choice) and more likely to get a fellowship that didn't require teaching. And to be blunt, most of the US women in our department were from fairly affluent families, went to good expensive private colleges. At the same time, we had a guy who grew up in a trailer in rural Alabama, went to a weak state school, and ended up being one of the department legends since he absolutely crushed research and got a really prestigious post-doc and later TT position at a top-15 school (he recently got promoted to Asoc prof). He struggled big time his first year, failed the qual the first time, but with 70-80 hours/week year-round, he shined. Yet he had none of the advantages a woman from a middle-class family has like women-only fellowships or affirmative action.
We can theorize all we want but practically speaking, it's not going to change your situation. Spending time pondering the fairness of the situation is fine, but ultimately it's not going to get you the PhD. My suggestion is to hunker down and study hard, hard, hard. 60-80hours/week minimum. Study during winter and spring break. Take a few weeks off in the summer and then hit the books again. The PhD requires a high-degree of self-sufficiency. When you do your dissertation/research down the road, you'll be pretty much on your own. Take up a hobby that you can do for 1 hour/day like running, walking, cycling, cooking etc. to burn off some steam.
One final piece of advice would be to wait before making too much noise. Give it at least one full year. Things may start to "come together". Causing too much noise (unless of course, you have a clear example of sexism/anti-woman bias in the department) is not going to win you any friends among the faculty. Right now you're speculating.
I'm done with this thread- best of luck!