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While I was reading this topic, it looked clear to me that statisticians must know some theory of probability (maybe even a lot of probability, depending on the problem).

But the inverse is not so clear. A probabilist is concerned with deducing mathematical statements about probability from other mathematical statements. Thus, we could say that probabilists work just like any other mathematician. From this point of view, there is no need for a probabilist to know statistics.

I want to know how much this is true? And how much is a probabilist losing if they do not know any statistics?

PS: I accept personal experiences/opinions, or you can talk about someone you know. I want to have a better understanding of how probabilists use and care about statistics.

kjetil b halvorsen
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Integral
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  • That seems true on its face, but I doubt there are any probabilists who don't actually know any statistics. – gung - Reinstate Monica Jul 02 '15 at 22:50
  • Knowing statistics would help probabilists to gain insight or something like that? – Integral Jul 02 '15 at 22:53
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    I should think so. I also think it would just be very difficult to get through a Ph.D. in Mathematics, specializing in probability, without learning some statistics along the way. I've met several probabilists who were pure mathematicians working on probability & weren't very interested in statistics, but they still knew statistics. – gung - Reinstate Monica Jul 02 '15 at 22:57
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    I would even question how much probability so-called statisticians actually need to know, at least to have statistician as your job title. – dsaxton Jul 02 '15 at 23:19
  • @gung do you mind in writing your comment as an answer? Maybe with some more details if you have some. – Integral Jul 03 '15 at 00:40
  • It isn't much of an answer. I would wait for someone more knowledgeable & with something more interesting to say to come along. – gung - Reinstate Monica Jul 03 '15 at 00:52
  • Not knowing statistics, probabilists will be losing the opportunity to work on problems statisticians care about, and thus lose the opportunity to publish work that has an impact in that field. The extent to which probabilists are likely to care will vary, though. I do agree with the other posters that there will be few who know really little statistics. – Christoph Hanck Jul 03 '15 at 03:37
  • How would an "isolated" (from applications) probabilist figure out what's a worthwhile problem to work on? – Glen_b Jul 03 '15 at 04:57
  • A probabilist looks for answers to questions such as "What is the probability that $10$ independent tosses of a fair coin result in $6$ Heads?" whereas a statistician seeks answers to questions such as "Is reasonable to assert that a coin is fair given that $10$ tosses resulted in $6$ heads?" – Dilip Sarwate Jul 03 '15 at 12:50
  • @DilipSarwate I think I know what you are getting at, namely does one start with data to analyse or with a probability problem. But any statistician or statistically-minded person I know would regard the probabilist's question here as a good, sharp question to ask that is relevant to analysing data. Your statistician's question could just provoke endless (quasi-)philosophical debate on what is meant by "reasonable to assert". I am a statistically-minded geographer, and here I would rather work out the probability directly! – Nick Cox Jul 03 '15 at 13:06
  • dsaxton wrote "I would even question how much probability so-called statisticians actually need to know, at least to have statistician as your job title." Nowadays, all someone needs in order to have statistician, data scientist, or machine learning expert in their title is to have used R, SAS, SQL, or Python. There's no need to know any probability, statistics, math, modeling, or principles of floating point numerical calculation. Software experience is proof enough of your qualifications for the job. – Mark L. Stone Jul 04 '15 at 17:11
  • What is the point in knowing how to use a software if you don't know how to interpret the outputs? Even more, how do you expect that a person with no knowledge of statistics will collect data and write a program to work on that data? – Integral Jul 04 '15 at 17:29
  • I'm voting to close this question as off-topic because it is about "probabilists" rather than about statistics and it explicitly is inviting opinion and speculation. – whuber Jul 04 '15 at 19:34
  • I hope it's not closed, because this way you are taking away my chance to have an understanding about the difference between this two type of professionals. I think it's clear that probability and statistics are very tight, quoting the first comment: " I doubt there are any probabilists who don't actually know any statistics". The best way to understand this differences is to talking directly with people who actually work with this. – Integral Jul 04 '15 at 20:05
  • If you do not help me with your "opinions" and "speculations" I'll have to rely on my own poor opinions and speculations, until have a chance to talk to people and know their opinions. I'll be limited to people working where I study, because the global help (here) refused to give some light in my doubts. This is only going to hold back my advance for some time. I really hope you rethink this, thanks. – Integral Jul 04 '15 at 20:09
  • Integral wrote "What is the point in knowing how to use a software if you don't know how to interpret the outputs? Even more, how do you expect that a person with no knowledge of statistics will collect data and write a program to work on that data?" That is my point. That is exactly my point. I described how it is, not how I think is should be. – Mark L. Stone Jul 05 '15 at 01:12

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The point is that both probability and statistics are using the same base, mathematics. probability and statistics are complementaries. Let me explain that more. If you have a need for a tool, then you ask an engineer to design a tool for you. In our case a statistician find a need for a method and mathematicians work on that. In group of mathematicians, people who have more experience in probability saying probabilists develop methods.

It is nearly impossible for an engineer to design a tool without knowing the concept behind that and for a theoretician to develop a theory without having a question to answer. That is similar for statisticians and probabilists (and vice versa).

All in all, both groups must know about each other.

TPArrow
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    The spirit of this is right, especially the conclusion. However, I'd quibble with the wording here: in practice now, people who call themselves "mathematicians" rarely invent new statistical methods (Terence Tao is one outstanding exception); statisticians and indeed non-statisticians and non-mathematicians often do that too. But this isn't really an answer to the question of _how much_ statistics probabilists need to know. – Nick Cox Jul 03 '15 at 11:18
  • Thanks @NickCox. Agree. In my answer I tried to briefly look at the subject. Determining how much in this case is nearly impossible in my view. I think just knowing the importance of connection of probability and statistics is enough in this case. – TPArrow Jul 03 '15 at 12:28
  • @NickCox You bring Terence Tao to the discussion, this is good because he wrote a book (Topics in random matrix theory) which doesn't seen to use statistics, only probability theorems. In fact any book of random matrices, random polynomials, random walk on some geometric object and so on, they don't use statistics. This is one thing that made me create this discussion: these books are about using theory of probability on mathematical objects, and because of that there is nothing or almost nothing of statistics in these books (or articles). – Integral Jul 03 '15 at 16:12
  • So I could study only probability theory and understand 100% of these books, which are, by the way, advanced reading. This is a point I'm concerned with: I can read advanced probability books without knowing statistics. And if I do understand at all what I'm reading, I think it's possible for me to develop tools (deducing theorems) in some of these areas. If I lose something in not knowing statistics, certainly it's the opportunity to read good books and articles of probability, and work something after reading. So what is that I'm losing? – Integral Jul 03 '15 at 16:17
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    @Integral I think this is getting too difficult to develop as it is morphing into a question about what you are missing personally. That is naturally your concern but it doesn't make the question very suitable for a forum. – Nick Cox Jul 04 '15 at 00:34
  • @NickCox The answer can be more general (or vague), what I just said is an example of how some probability books don't address too much statistics. The answer may be your own experiences, or about people you know. I just want to have a better understanding of how probabilists uses and care about statistics. – Integral Jul 04 '15 at 00:58
  • I am not antagonistic, and indeed you're raising very interesting issues, but a personal view is now that this is too broad and fuzzy to be a good question here. – Nick Cox Jul 04 '15 at 01:02