Stat Assistant Professor

And even after a journal article gets accepted, it might take another year to get it published in a volume (due to the backlog of other accepted articles before it that haven't yet been published). So for an Annals of Statistics, JASA, or JRSS-B paper, you could be looking at three years from initial submission to publication.  That's why some faculty opt to publish some of their work in conferences -- the review times and revision times are all in a fixed time window before the actual conference, and then the proceedings are published shortly after that. Journals are often a bit more thorough than conferences IMO (though nobody denies the quality work in some of these conferences, journal articles go through a much lengthier process, so they often contain more simulation studies and empirical analyses, more theorems, more exhaustive treatment of the problem, etc.) 

So yeah, I definitely recommend checking the faculty webpages, CVs, Google Scholar, and arXiv (https://arxiv.org/multi?group=grp_stat&%2Ffind=Search) to make sure that they are being reasonably productive even if they don't have a lot of new papers in press/published on their CV. It's not super uncommon for there to be a year with no publications followed by a year with like, 5-6 papers (the faculty who have multiple papers *every* year likely have a ton of collaborators, postdocs, and PhD students working with them). So definitely check to make sure the faculty are at least revising their work and putting out new work (i.e. preprints).  

I would look more into it. Some faculty do not update their webpages very frequently, so they may have not just updated their website and/or CV. If they have a Google Scholar page, then that might be a good place to check to make sure that they are still being reasonably productive.
For top journals, the publication pace can be a bit slow -- partly because there are often multiple rounds of revisions (e.g starting with "reject with encouragement to resubmit," then "major revision" if the first revision was satisfactory, etc.), and also because they give the authors one year to submit/resubmit. Given this, I wouldn't consider one -- or even two -- years without any publications in press/published to be a huge red flag, as long as the work is "in revision" for quality journals. However, if it is more than 2 years with *nothing* (no preprints or new papers in press), then that is potentially concerning. However, before jumping to conclusions, I would check to make sure that this is really the case, and not just the faculty member failing to keep their personal website and publicly available CV up-to-date.

Another metric to assess this is the acceptance rate of the journal/conference. The most prestigious venues will have lower acceptance rates. That's partly why the folks who publish a lot in conferences list the acceptance rate on their CV -- to indicate how highly selective it was.

I think that's pretty much it. Reputation of journal/conference, impact factor, and number of citations are all the "standard" metrics. So besides the 'top' journals (AoS, JASA, Biometrika, JRSS-B), you'll also see some high-quality work in places like Statistical Science (e.g. the original paper on GAMs appeared in Statistical Science), Biometrics, Biostatistics, Statistica Sinica, Annals of Applied Statistics, Technometrics, Scandinavian Journal of Statistics, Journal of Computational and Graphical Statistics, Bayesian Analysis, etc.

I think this is quite frequent. Even some young or recently appointed assistant professors seem to be lagged in track of their newest publications or study on their cv / website. Thank you for the good point. I guess checking google scholar together helps a lot.

I don't think they're necessarily directly comparable, since Annals of Statistics pertains mainly to mathematical statistical theory (and is indeed the most prestigious stats journal for statistics theory). I would say among methodologists/theoreticians, Annals of Statistics is considered more prestigious.
 However, Annals of Applied Statistics is considered a top-tier journal and has had some very influential papers appear in it. For example, the original Bayesian additive regression trees (BART) paper (BART is one of the top-performing ML methods for prediction) and the pathwise coordinate optimization paper by Friedman et al. appeared in Annals of Applied Statistics. 

If you don't feel super strongly about a topic, I'd personally lean towards choosing a school based on location, ranking, environment, etc.  One thing I would look at when choosing a department is the level of research and the journals they are publishing in and how that matches with your career goals.  If you want to be a professor, you want to work with someone publishing in top stats journals.  Some lower-ranked programs don't have many people doing this.
Some people I know had a strong passion when they went into grad school (eg spatial statistics, or clinical trials, etc) and chose the advisor that they came to the school specifically for.   This is a minority, in my experience.
A lot of people don't have strong preferences.  For instance, if you want a pretty "standard" job, like being a data scientist or working as a biostatistician at a medical center, it really doesn't matter that much what your specific dissertation was on.  Even for an academic job, some people just choose a good professor they feel they will be productive with.  And thus some people just sort of fall into their positions with their RAships, or based on taking a class with someone they like, etc.
Some people don't have a strong passion for a specific topic, but choose a hot topic that may land them the type of job they want.  If you want to be a researcher at Facebook or Google, studying network science/causal inference/deep learning might be a good idea.  Or some people might think genetics sounds cool and they start doing research in genetics.
Of course the topic you choose for your dissertation has some importance and you have to find something that is interesting enough to you that you enjoy it.  But I recommend not stressing too much about this if you don't already *have* a strong preference.  You'll never find the "perfect" research topic, and you will learn a lot by working on different topics and can always change directions during a post-doc or later in your career, too.  I wish I had spent more time earlier in my career just jumping into research instead of stressing about what I'm going to work about in the future.  But going to a department with a variety of options never hurts.

Yeah, Harvard is really, really strong in the areas of causal inference and MCMC. For deep/maching learning and probability theory, I would say that Columbia, UC Berkeley, and UPenn Wharton have an edge over Harvard (e.g. you've got David Blei at Columbia, Michael Jordan and Martin Wainwright at Berkeley, Edgar Dobriban and Weijie Su at UPenn, etc.). There is also a large group of probability theory researchers in the Statistics Department at UCB, which is somewhat unusual nowadays (typically there is only one or two faculty in a Stats department working on pure probability theory topics).

I think your math background probably has a lot more to do with your results than the lack of a GRE score., as the Berkeley professor told you. I agree with @Stat Assistant Professor that you are unlikely to vastly improve your profile in a year. If you do well at a good but not great PhD program, you can also get a post-doc after to improve your profile, which may be a better use of a year of your life than just waiting for the chance to be admitted to a better program.

No worries, not insulted at all. Nobody denies that the "top" programs have more famous faculty and/or faculty who are consistently publishing in top journals. Therefore, your chances of getting an academic job may be positively correlated with program ranking.  However, that is only one factor; it's really on you and your track record. If you didn't attend a "top" university for your PhD, you can partly compensate for that with a prestigious postdoc, letters from famous people in the field who are familiar with your work, etc. 
Only you can decide for yourself if it is worth it to reapply again next year. It can be very costly and time-consuming to reapply, but the payoff could be greater if you can get better results. I think the most crucial things to consider is: if you reapply again next year, will you be a *much* more competitive applicant? And what can you do to significantly bolster your application in one year's time that you haven't already done? (e.g. can you get a higher GRE score, better recommendation letters, more research experience, etc.?) Most PhD programs in Stats don't care that much about the Math Subject GRE, and a couple points higher on the GRE probably won't make or break your application. If there's not much that you can do (e.g. because you are an international student and did not attend a "top" university in your home country), then I would just take one of the offers you do presently have.

No worries, not insulted at all. Nobody denies that the "top" programs have more famous faculty and/or faculty who are consistently publishing in top journals. Therefore, your chances of getting an academic job may be positively correlated with program ranking.  However, that is only one factor; it's really on you and your track record. If you didn't attend a "top" university for your PhD, you can partly compensate for that with a prestigious postdoc, letters from famous people in the field who are familiar with your work, etc. 
Only you can decide for yourself if it is worth it to reapply again next year. It can be very costly and time-consuming to reapply, but the payoff could be greater if you can get better results. I think the most crucial things to consider is: if you reapply again next year, will you be a *much* more competitive applicant? And what can you do to significantly bolster your application in one year's time that you haven't already done? (e.g. can you get a higher GRE score, better recommendation letters, more research experience, etc.?) Most PhD programs in Stats don't care that much about the Math Subject GRE, and a couple points higher on the GRE probably won't make or break your application. If there's not much that you can do (e.g. because you are an international student and did not attend a "top" university in your home country), then I would just take one of the offers you do presently have.

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.

I should qualify as well that if you're aiming to get a job at (say) Stanford or Harvard or one of those very elite schools, then your chances of doing that coming from a "lower" ranked program are probably slim, unless you're seriously amazing (very productive, tons of top publications, etc.). However, pedigree should not preclude you from getting an academic job at a fairly good school nonetheless. Even the vast majority of PhD graduates from the "elite" schools who go into academia will end up at flagship and public universities (there are only so many jobs at the "elite" schools, after all).

I should qualify as well that if you're aiming to get a job at (say) Stanford or Harvard or one of those very elite schools, then your chances of doing that coming from a "lower" ranked program are probably slim, unless you're seriously amazing (very productive, tons of top publications, etc.). However, pedigree should not preclude you from getting an academic job at a fairly good school nonetheless. Even the vast majority of PhD graduates from the "elite" schools who go into academia will end up at flagship and public universities (there are only so many jobs at the "elite" schools, after all).

Agree bigtime.
The most important factor for TT jobs is research. Having a good advisor helps - by good I mean one that publishes a lot and is at the forefront of his/her research, sets you up well to do research on your own going forward, and has some name recognition. Higher-ranked departments tend to have more good advisors. But even lower/middle ranked departments will have a few solid, well-known guys. 
Ultimately, someone super-motivated and ultra-hard working can overcome the setbacks of being at a lower-ranked department.

I was admitted to a very good program years 10+ years ago. Admissions were less competitive then. Before the fall semester, I emailed all the profs and for their syllabus so I could see what topics they would cover. I immediately recognized I had a few weaknesses:
I only took one semester of linear algebra way back freshman year of undergrad, and I didn't do particularly well I didn't have a good foundation in theory in statistics I realized it was going to be rough. So I bought a Linear Algebra textbook and Casella/Berger and studied for 4-6 hours/day from June-August prior to starting the PhD. I watched online lectures, did problem sets, etc. This gave me an enormous boost my first year in the PhD program and made the qualifying exam a piece of cake down the road.
The point I'm making is that you've gotta get on this yourself. The profs I had in my first and second year couldn't care less if someone was struggling in their coursework - they cared about cranking out publications and getting their PhD candidates competitive for academic jobs. When we did the written quals, graders didn't have the names of the students on the exam paper, and each of the 8 problems was graded by a different faculty member to wash out any biases. There was no affirmative action on the written qual.
Our cohort started at 6/4 men/women. 3 didn't make it and coincidentally they were all women (2 American and 1 Chinese). The Chinese woman had mental health issues while 1 American woman failed the written qual 2 times and the other never got into the groove of research and left before her oral prelim.
I can say this has been my experience as well. The gap between US and international students narrowed bigly by year 3 and when looking at academic job placements in our cohort, the guy that got the "best" academic job was from the US, and he failed the qualifying exam the first time he took it.

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.

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.

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.

I think working with an Assistant Prof is probably fine. I have seen some TT faculty who had Assistant Professors as their PhD supervisors and who still landed many campus interviews for tenure-track positions. The most important things to consider when working with an Assistant Professor are:
whether their research is a good "fit" and whether they can help you to be competitive in the job market for academia or industry (either because they can help you publish in the top tier journals/conferences or because they have solid industry connections), and whether they are productive enough (by your department's standards) to earn tenure. If both criteria apply, then I say go for it. Besides, getting a TT position is the sum of many different parts, not just one thing. If your research is in a "hot" area that a hiring department currently lacks expertise in or if their job ad expresses special interest in recruiting applicants from your subfield, then I would think that you would enjoy certain advantages, regardless of who your advisor is. I also think that adcoms consider the strength of the recommendation letters too, not just whom they're written by.
It is a good idea to try to get your work noticed, though, so you can hopefully get a letter of recommendation from somebody who is influential in the field. One of my letter writers when I was on the market was from a pretty prominent name in the field, and this person was neither my PhD or postdoc supervisors... but I interacted with this person fairly regularly and they were familiar with my work, so they were able to write a very good letter for me. I believe that helped a lot.

I'm sorry to hear that you are dealing with this. I don't really have much advice on how to rectify the specific issues with your department, but I do want to make a few observations.
1) It is true that international students typically have more extensive math backgrounds and are thus better prepared for the rigors of PhD coursework in statistics (e.g., it's commonly the case that a lot of international students have already taken classes at the level of Casella & Berger mathematical statistics, measure theory, etc., so in some sense, they already know the material in first-year courses). However, the gap between international and domestic students tends to narrow considerably by the third year, sometimes by the second. And by the time you start research, the majority of students are going to start out at the same level (i.e. not really knowing what they're doing).
2) If you make it past coursework and quals, then it's really the research that matters. This is what determines if you can earn your PhD -- and if you opt to stay in academia, this is what you will be judged on, not whether you earned an A or B in a core class (and if you're interested in teaching as LACs/regional comprehensives, then they will also judge your ability to teach and engage with undergraduate students). It is not unheard of for top-performing students in classes to struggle with research and take longer to finish, or for students who barely made it through quals to find their groove and excel at research. I've seen that firsthand at my own PhD institution where somebody who won "Outstanding First Year Student" struggled immensely with research and took a long time to finally finish. And other students who failed quals twice (failed first year exam once and failed PhD qualifying exam once) were still able to finish -- and even landed a TT faculty position later.  
3) Those of us in academia have all failed. Even if we didn't fail classes, we probably got papers rejected, grant proposals rejected, turned down for postdocs and faculty positions we applied to, etc. So if you're 'struggling' and faced with failure, you're definitely not alone.
I hope that you are able to resolve your difficulties. It is a tough situation to be in, and I am not really sure how to resolve it. Just know that if you can manage to get through the coursework, it's not all hopeless. 

I'm sorry to hear that you are dealing with this. I don't really have much advice on how to rectify the specific issues with your department, but I do want to make a few observations.
1) It is true that international students typically have more extensive math backgrounds and are thus better prepared for the rigors of PhD coursework in statistics (e.g., it's commonly the case that a lot of international students have already taken classes at the level of Casella & Berger mathematical statistics, measure theory, etc., so in some sense, they already know the material in first-year courses). However, the gap between international and domestic students tends to narrow considerably by the third year, sometimes by the second. And by the time you start research, the majority of students are going to start out at the same level (i.e. not really knowing what they're doing).
2) If you make it past coursework and quals, then it's really the research that matters. This is what determines if you can earn your PhD -- and if you opt to stay in academia, this is what you will be judged on, not whether you earned an A or B in a core class (and if you're interested in teaching as LACs/regional comprehensives, then they will also judge your ability to teach and engage with undergraduate students). It is not unheard of for top-performing students in classes to struggle with research and take longer to finish, or for students who barely made it through quals to find their groove and excel at research. I've seen that firsthand at my own PhD institution where somebody who won "Outstanding First Year Student" struggled immensely with research and took a long time to finally finish. And other students who failed quals twice (failed first year exam once and failed PhD qualifying exam once) were still able to finish -- and even landed a TT faculty position later.  
3) Those of us in academia have all failed. Even if we didn't fail classes, we probably got papers rejected, grant proposals rejected, turned down for postdocs and faculty positions we applied to, etc. So if you're 'struggling' and faced with failure, you're definitely not alone.
I hope that you are able to resolve your difficulties. It is a tough situation to be in, and I am not really sure how to resolve it. Just know that if you can manage to get through the coursework, it's not all hopeless. 

Agreed, UCSC is a very good program, and they have decent academic placements (if you're interested in that). They've placed some PhD graduates at University of Chicago (Matt Taddy), University of Florida, and other good places in the past. The Statistics Department is relatively new (it was part of the Applied Math department until around 2019), which is why UCSC may not be ranked in the USNWR.  
If you aren't interested in Bayesian statistics *at all* though, then you probably shouldn't apply there. One thing I would note though... if you decide to go into industry, I'm not sure how much of your PhD dissertation research you would really use for the "typical" jobs anyway (regardless of whether you study Bayesian or frequentist stats for your dissertation). Unless it's a very research-oriented industry job like Microsoft Research, Google Brain, or something of that sort, you probably will not use a ton of the stuff you learned in your research.

Agreed, UCSC is a very good program, and they have decent academic placements (if you're interested in that). They've placed some PhD graduates at University of Chicago (Matt Taddy), University of Florida, and other good places in the past. The Statistics Department is relatively new (it was part of the Applied Math department until around 2019), which is why UCSC may not be ranked in the USNWR.  
If you aren't interested in Bayesian statistics *at all* though, then you probably shouldn't apply there. One thing I would note though... if you decide to go into industry, I'm not sure how much of your PhD dissertation research you would really use for the "typical" jobs anyway (regardless of whether you study Bayesian or frequentist stats for your dissertation). Unless it's a very research-oriented industry job like Microsoft Research, Google Brain, or something of that sort, you probably will not use a ton of the stuff you learned in your research.

I think there are a few MS programs in Statistics that are truly competitive (in the U.S.A.)... Stanford, Yale, and Duke seem to have small Masters cohorts and are fairly selective. I would say that this is the exception rather than the rule. Even at some very elite institutions like University of Chicago and Columbia, it is not hard to get admitted to their Statistics MS program. 
Now, with the pandemic leading to so much virtual learning, I anticipate that schools will expand offerings for completely online Statistics MS programs, so there is even less need to be very selective about cohort size for Masters students.