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Also keep in mind that when most of this forum talks about academia, they are talking about jobs at PhD-granting institutions.  In that case, the above paths are the likely ones. I also see people do a year or two doing post-docs at Microsoft research or something similar and then becoming professors. 
But it is *very* possible to work in industry for years or even decades and get a job at a small liberal arts college or less prestigious state school. I see it all the time.

Thanks so much for sharing your story. 
I guess workloads for TA appointments are not so different between schools, but I am also a workaholic and hope to be a faculty in the US in the future. So I'm also considering RA opportunities or students' research history as well. I'm currently contacting a graduate from the department who's doing a postdoc to learn more about the culture. There are several professors who study the areas I am interested in. I've not considered the program size, thank you for adding a new view.
Hope you and your family can successfully begin your life there!!

I've seen a few cases where it happened.
1. One guy worked at a well-known tech company in a research-type role, and part of his job was publishing and presenting papers, so he got a TT job the first year he applied. It was a so-so state school with a combined Math/Stats department that I believe offers an MS in Stats. Not exactly a "prestigious" position but it was near where him and his wife grew up, so it was a no-brainer for him.
2. Another guy worked in a run of the mill R&D data analyst type role, got hired as a department "instructor" at a local university (basically a teaching-only position, usually 1-3 year contracts), did research on his own, published a ground-breaking paper as well as a couple other solid papers in his free time, got a TT job a year or two later.
3. I've heard of at least one person going back to do a post-doc and eventually getting a tenure track job.
It's very impractical to do this. I agree with @Stat Assistant Professor that you'll need some sort of springboard to get back into academia. Keep in mind also, as an example: going from making $150k/year in an area like Chicagoland, with great benefits & 40-50 hours/week workload, to a post-doc (requiring a move) making $50k/year working 60-80 hours/week, and then getting rehired at $80k/year in a publish or perish environment (in a possibly awful location) would be an enormous financial and QOL hit, all for the possibility of tenure in 5-7 years. If you have kids, or a spouse that's unwilling or unable to move, it may be totally impossible to make this work. There's a reason why hardly anyone does this.

I made my decision already, so I'll give some input on what factors were the most important for me.
1) Work-life balance. Obviously, it's important to enjoy life for the next 4-5 years, which may be difficult to do if you have to spend excessive amounts of time on school. All PhD programs will take a significant amount of time and effort, but there are definitely some that will take more time and effort than others, depending on who you are. Since I am married and planning on starting a family during my PhD program, I didn't necessarily want to choose a program that I thought would consume my life. However, since I tend to be kind of a workaholic, I probably would have chosen a more intense and time-consuming program if I were single.
To judge work-life balance, I looked at things like coursework requirements, average time spent on GTA type work, the qualifying exam process, etc. You can get a good idea about a lot of this stuff from most departments' websites, but you may also need to talk to current grad students to get a better idea of what it's like.
2) Program fit. Make sure you do some research into department culture. How do the professors and students interact with each other? Is the department one you would like to be a part of? A department that has a great culture where you fit in well will certainly make your life better than a department that isn't a good fit for you, even if there is a disparity in program ranking.
I made sure that every school I applied to had plenty of potential advisors with whom I would like to work if I ended up going there, so that is something to consider in choosing a school as well. If you go somewhere with only 1-2 potential advisors working on some hot topic you're interested in, you may have to compete with a lot of other students to be able to work with that advisor.
As a part of program fit, program size may be an important factor to consider. I am currently at a university with a large number of statistics undergraduate students (we have over 500 undergrad statistics majors right now). Thankfully, I have had a lot of great interaction with professors even though we have a large department; however, I have heard that this is not always the case at other universities with large departments, so it's one thing I've kept in mind. Large departments can be great for their resources and research opportunities, but it may also be easy to get lost, and you may have to compete with a lot of others to get time with professors.
There are plenty of other factors to consider like location, funding, job placements, etc. All the programs I applied to are in places that I would enjoy living in for different reasons, so this wasn't a major concern for me. The monthly stipend amount (and summer funding availability) is also pretty important, but all the offers I received would have been plenty to live off of in each area, so funding wasn't really a huge deal for me either. Job placements are important, but since I'm 90-95% sure I want to go into industry, I don't think it really matters where I go for my PhD since everywhere seems to do well in terms of industry placements.
Good luck on your decision!

I've seen it happen (PhD->industry->academia), but usually, the scenario was like this. The person got their PhD and decided to go work in industry. They didn't like it and discovered that they preferred academia, so they went to do a postdoc instead after 1 year out in industry. Then after the postdoc, they got a faculty position.
It's much less common for people to return to academia after a number of years. I've seen it happen but this almost always entailed taking a (non-tenure track) lecturer position somewhere, or sometimes a job at a teaching-oriented college. The reason it's harder to return after many years (for research universities anyway) is because academic hiring is based so heavily on your research output (i.e. your publication record) and the department's needs. If you've been working in industry for longer than a year, it is very difficult to keep writing papers and publishing (whereas if you've been out of your PhD for only a year, you could still have fairly recent papers from your dissertation that have been published or that you're working to get published somewhere).  It's also hard to keep up with current trends in academic research if you've been out for a very long time, and those tend to change rapidly these days. If your research area isn't at least a moderately sized area of interest to the statistics/biostatistics/machine learning research communities, then it will be hard to get hired. 
However, I suppose you could theoretically be competitive for academic positions after years spent in industry if you were in a role where you could continue publishing. Or you could also be competitive if you were to go do a postdoc after years spent in industry and used the postdoc as a springboard for getting back in into academia. I think I may have seen a couple of people do this (do a postdoc after years spent in industry). It should be noted that these people usually did Biostatistics postdocs and then went into Biostat departments. 

Just wanted to give a quick shoutout to @bayessays for being around and giving solid input/advice to a lot of people on here.

The Feeling when acceptances/waitlists have come out for CMU and you still haven't heard back:

In your case, I would find a department that has diverse research. I was in your same position, so I chose the department that (1) had a great culture and location and (2) had someone doing research in many diverse topics with little intersection. That really gave me a lot to choose from when year 3 came around. 
Other points to consider:
Have any departments given you a research assistantship years 1-2? If so, that's pretty substantial. When I was a year 1-2 teaching assistant, I easily spent 10-15 hours/week teaching labs, grading, office hours, answering emails, etc. This was a major time suck and distraction, although I kind of enjoyed it. While I generally don't recommend looking at financial aid packages since it's a short-term thing (as long as they are at or above subsistence level), if one package is substantially higher than the others, you can save the excess money in a Roth IRA over 5-6 years which could easily be worth six figures when you retire. I really regret not putting at least $1-2k in a Roth IRA each year when I was a PhD student.  Location matters, if you're into "culture" and sports and whatnot. I wasn't. All I needed was a gym, a running trail, a liquor store, and a dive bar. Which meant I would be happy anywhere. Some people need to be near museums, theatres, sports games, or whatever. Also consider weather - if you're a lifelong Florida resident, going to the University of Wisconsin, Michigan, or Minnesota could make for some very rough and depressing winters. If you're planning on going into industry, you may want to consider a university that's near a lot of companies. This will make getting internships slightly easier since there's no relocation involved. You may want to consider the culture of the departments as well. Some departments are super social and fun. Others are super lame.  Best of luck to you.

That's pretty amazing that your program admits people without having taken linear algebra - I've never heard of such a thing and it does sound sort of ridiculous to expect people to just catch up in that case.
The first few years of graduate school can be overwhelming for a lot of people, as you feel there is just *so much* to learn.  When I was getting my MS, I felt like I had to learn everything from the most basic level to fully understand it, and make sure I knew all the math that led up to it.  But I think a perspective change might be helpful, in that you really only need to do well enough to pass the classes (and exams, which in some departments are awful - if you go to one of these departments, I'm sorry for your terrible luck.  Kicking people out of school because of a single 3-hour test is terrible.  Maybe you should transfer to a more welcoming program that doesn't weed out domestic students like this -- they exist!).
I just returned to schools after 5 years off.  I barely remember how to do integration by parts - but when a problem comes up with a weird integral I try it out.  I don't know what the the power series for e looks like off the top of my head, but I know enough that when I see a weird series I can look it up and maybe see that it's in a nice form.  I certainly don't know any properties of a trace of a matrix.  I barely know how to take partial derivatives to do the Jacobian transformations of random variables in Casella Berger.  And this time around, I'm not even going to try to trace back my math education to the beginning to re-learn every little skill that would lead me up to this point.  Just learn to do the problems in the books, on your homeworks, and I'd highly recommend searching for lecture notes/stack exchange conversations that give clearer explanations than your professors might give.

I didn't actually attend the visit day, so I'm not sure how many acceptances CSU has sent out so far. The deadline for accepting the first round offers though is on Monday (the 22nd), so I imagine they will likely send out more offers after that.

I think I have seen some similar posts on here before concerning whether to accept such an offer or try to reapply next year after doing additional coursework, research, etc. But I guess it comes down to preference and timing. I was accepted into some top-ranked program but ultimately chose to attend a lower-ranked one owing to the research fit, the desirable location, the offer quality, and the program structure. Going in, I had not expected to end up where I did, so I would not discount a program just because of its ranking. It seems that you have a strong profile, and, as was mentioned, this year might have been more competitive than others, but by waiting and reapplying, you still run the risk of not being admitted again, at least not to the very top programs. I am sure that it will be beneficial to take analysis, and knowing more linear algebra is always helpful, but I would still consider whether this alone will be enough to tip the scales in your favor at the top programs. But you know best your situation and your ambitions. Even at the top programs, securing a tenure-track position after graduation depends also on what you are working on and the connections you make, so while top programs might offer better access to these things, I don't think choosing a lower-ranked program precludes a successful academic career, especially if you go in with the intention of going into academia after graduation.

How "low" are you talking? Fwiw, I went to a PhD program ranked ~40 in USNWR, and we have placed PhD grads in TT faculty positions at Duke, University of Minnesota, UT Austin, etc. And I have also seen people who got their PhDs from Baylor, University of Cincinnati, and University of Illinois at Chicago (*not* UIUC) get TT jobs at Texas A&M, University of Florida, and Iowa State.  
It's not *just* about where you get your PhD. For example, Dave Dunson has a PhD from Emory (a very solid biostats program but not a Stanford/Berkeley/Harvard), and Michael I. Jordan (considered one of the top researchers in statistics/ML) has a PhD in cognitive science from UCSD. Both of these guys are extremely renowned in the statistics field.  I can also think of other outstanding researchers who don't have PhDs from "top" schools who have done quite well in academia.
I don't want to dismiss rankings completely, but pedigree really is only one factor (and byfar not the most important one). Hiring committees *really* care about your past publication record, your future potential, your postdoc experience (a very productive postdoc at a prestigious institution can help you a lot), your letters of recommendation, your PhD advisor and influential scholars who can vouch for you, your teaching experience, etc. These are all things that are taken into account for academic hiring.

CSU had a virtual visit day on Feb 15th and they invited me to it in my admission offer. Missouri's offer didn't say anything about a visit day, but I'm sure you could ask to set up some sort of virtual meeting with a professor and/or current grad students. I did that with Baylor.

I received the offer letter from JHU biostat PhD this afternoon.

The results page has an acceptance from an international student, so I would assume they've sent out at least some offers to international students. The first round of offers has an exploding deadline on February 26th (or some of the offers did), so my guess is that they'll send out more offers at the end of February/early March

Just got an unofficial acceptance from NC State in an email from Graduate program director. Finally some relief! 

I am stuck in an airport with nothing else to do and not enough WiFi for Netflix so I figured I would start an advice thread on all things Statistics PhD admissions that I have learned from the process.  I wanted to share all the things I wish I knew when I was applying.  Anyone else feel free to add to it.  I wrote this from a general statistics perspective but some of this probably will be similar in biostats and perhaps even math.   
Admissions - Where to apply
The best indicator of how you will do is looking at the past profiles that are most similar to you.  You will unlikely find a perfect match, but try to look at similar applicants first and then see what kind of programs they got into.  Expect a lot of randomness and try to have a more balanced list than I did.  Also know that safety programs really don’t exist and lower ranked programs (particularly smaller ones) can be just as hard to get into as large high ranked programs.  There are programs that you have a higher probability of getting admitted at then others.  Also research fit is very important so consider that if you have known interests.
Admissions - What to Expect When you are Expecting to go to Graduate School
TL;DR Expect a lot of waiting.  
I am going to be totally and completely honest with you about my experience applying for graduate school.  For undergrad I was admitted two weeks after I applied and had an departmental scholarship two months after that.  I knew I was going there because it was my first choice and I had automatic acceptance.   So I have never not know what I was doing next.  This whole process of not knowing where I am going to be in Fall 2018 for over a year now has been hard.  I still don’t know where I will go.   I have watched results tell me that I was waitlisted and rejected before I knew officially and checked admissions portals multiple times a day.  To protect my sanity and prevent me for spending my entire life on the gradcafe I blocked it from 9-5 every day on my laptop.  I highly recommend it.   I have cried more than I ever have in my life and have questioned myself almost daily.   My impostor syndrome has been awful.  I have doubted whether or not I am ready to jump into a PhD program at 21.   I have questioned why programs admitted me and felt intimidated by the people at visits who already have masters degrees.  I have read all the profiles dozens of times and knew that most domestic students with my level of research experience typically do well but I didn’t think I would do as well as I did.  I have questioned if I really do know what I want to do and whether or not being able to pursue my research is a deal breaker.  I have struggled over how to decide and what qualifies as a deal breaker.   If you had/have any of these feeling you are not alone.
Interviews
I interviewed two times (three if you count Baylor) so thought I would share my experience.  
For Duke the interview was very informal and was more about me as a person than me as a prospective admit.   I was asked what my hobbies were (which totally threw me off) and we talked about life at Duke and in the research triangle. It was about 20 minutes long and with a single assistant professor on the AdComm who was the original reviewer for my application. I was asked for more technical details on my research but that was the only thing application related we talked about.  
For Virginia Tech, they just asked if I had any questions and I asked about funding and their completion rate.  It was implied that funding was competitive and I was told the completion rate was “around 30%” because a majority of people fail quals.  They were definitely trying to court me calling me their “top applicant” and “favorite application” and I really though I had gotten the fellowship.   I had an single semester of support with the possible option of renewing but it didn’t have the language that my other offers did which offered more security.  I mainly applied for the fellowship so when I didn’t get it I wasn’t very interested.
Baylor was a causal visit and I meet with everyone at the department that was there. It wasn’t really an interview.
Visits
I have completed three visits so far and I wanted to help answer the what do I wear question that I had.  On both my prospective student weekends there was a range from button down and tie for men and nice blouse and heels for women to tee shirts and jeans.  The average was around business causal and that’s what I would recommend you do.  Don’t worry about knowing anyone research interests and memorizing CVs if they aren’t your POIs.   All my meetings with professors started with a basic explaination of their research and since you will likely be supported by a TA ship your first year you don’t need to find an advisor right off the bat.  I didn’t really take notes and made a list of people I liked.  You will have information overload and it takes time to fully realize the pros and cons after visiting.
Program Impressions
Next I wanted to share my impressions of programs based on my interactions with them.  
Baylor
Baylor is my favorite program so I am biased.  Demographically it is a majority domestic program (~75%) with about 40-50% women.  Waco is very much a college town but it still has a lot of things to do.  They told me 82% of their students graduate in four years with almost all of them finishing by year 5.  Their placements are mainly in industry with a lot of people at Eli Lilly which is huge supporter of the program and has funded RA positions and grants for the faculty.  It has 3 Bayesian statisticians and 5 other faculty members doing different things.  The main fields of application are biostats and environmental statistics.  They have a nice bank of computers for faculty and students to use to run simulations on.  I think it is severely underrated.  On the Academic side of placements they occur mainly at state universities and liberal arts colleges.  They offered to buy me a plane ticket but instead they reimbursed me for mileage which was over $300 plus a nice hotel room.   It’s a great department that is totally underrated.  
UT Austin
It may be a young department but it is growing fast.  They have a ton of people doing Nonparametric Bayesian statistics with some machine learning and hierarchical modeling mixed in.  It is entirely Bayesian to the point of the visitors being told that if you want to be a frequentist don’t come here.  A lot of the faculty is double appointed in both stats and the business school but they are committed to the Stats PhD program.  It seemed to be about 40% female and a slight international  majority but the domestic and international students were really integrated with each other which doesn’t always happen. Austin is a very expensive city (at least for Texas) and most of the graduate students I talked to spend around $700-1000 on housing a month, my stipend offer was $2000 a month so that seemed expensive. They also have a lot of computing resources for research. They are very proud that their first graduate got a job (post doc I think?)  at Berkeley straight out of a PhD (who wouldn’t be)  My visit was completely funded.
University of Missouri - Columbia
Also know as Mizzou,  the University of Missouri is state university in a college town.  Columbia’s airport is awful (I have been stuck here for 5 hours since there are only like 5 flights a day), but Columbia is a nice city that is bikeable and the bus system is apparently good.  The department has a wide variety of research  but it probably more Bayesian than classical and more focused on environmental statistics than most programs.  Demographically it appeared to be about half and half domestic and international but not a single international student did anything at the visit until the free dinner where they didn’t sit with the prospective students.  A grad student made a comment that they never want anything to do with us (referring to the domestic students).  This is a lot different than UT and Baylor where  all the graduate students knew each other pretty well.  The faculty do seem nice and hierarchical modeling was a common theme from the research presentations.  Their placement was a mix of academic and industry and generally good for a mid tier program.  My visit was completely funded.
Virginia Tech
I never actually visited but it I didn’t like the completion rate and the potentially unstable funding package.  The professors seemed nice but I am kinda bitter about how they called me their top applicant and then didn’t even give me two semesters of funding.  I am sure it is not a bad place but I was no longer interested when I began to get my other packages.  Their academic placements aren’t great as well.  I personally wasn’t interested in visiting given my concerns but they offered to fly me out on a paid visit.  
I talk about TAMU when after my visit.  

Looking at results over previous years, it does seem to me that many of the programs I applied to (like TAMU and UIUC) normally would have sent out several acceptances by now. Perhaps some programs are somewhat behind schedule this year.

Me when UWashington acceptances came out and my inbox was empty:
It is the evening of the day
I press refresh on gradcafe
Rows of green I can see
But not for me
I sit and watch
As acceptances go by
 
My gpa can’t buy anything
I just wish I was better at proving things
All I hear is the sound
Of emails going around
I sit and watch 
As acceptances go by
 
It is the evening of the day
I press refresh on gradcafe
Seeing profiles like I used to do
they think are new
I sit and watch
As tears go by

I got an acceptance from Baylor this morning! Deadline is February 26th since first year students start in July, so I'm hoping to hear back from other schools before then. Funding is $20,700/9 months, and they also offered an additional $7k fellowship for the first year for having a "strong application".

I got an acceptance from Baylor this morning! Deadline is February 26th since first year students start in July, so I'm hoping to hear back from other schools before then. Funding is $20,700/9 months, and they also offered an additional $7k fellowship for the first year for having a "strong application".

I got an acceptance from Baylor this morning! Deadline is February 26th since first year students start in July, so I'm hoping to hear back from other schools before then. Funding is $20,700/9 months, and they also offered an additional $7k fellowship for the first year for having a "strong application".

I got an acceptance from Baylor this morning! Deadline is February 26th since first year students start in July, so I'm hoping to hear back from other schools before then. Funding is $20,700/9 months, and they also offered an additional $7k fellowship for the first year for having a "strong application".

I got an acceptance from Baylor this morning! Deadline is February 26th since first year students start in July, so I'm hoping to hear back from other schools before then. Funding is $20,700/9 months, and they also offered an additional $7k fellowship for the first year for having a "strong application".

I got an acceptance from Baylor this morning! Deadline is February 26th since first year students start in July, so I'm hoping to hear back from other schools before then. Funding is $20,700/9 months, and they also offered an additional $7k fellowship for the first year for having a "strong application".