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.

  • $\begingroup$ That seems true on its face, but I doubt there are any probabilists who don't actually know any statistics. $\endgroup$ Commented Jul 2, 2015 at 22:50
  • $\begingroup$ Knowing statistics would help probabilists to gain insight or something like that? $\endgroup$
    – Integral
    Commented Jul 2, 2015 at 22:53
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    $\begingroup$ 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. $\endgroup$ Commented Jul 2, 2015 at 22:57
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    $\begingroup$ I would even question how much probability so-called statisticians actually need to know, at least to have statistician as your job title. $\endgroup$
    – dsaxton
    Commented Jul 2, 2015 at 23:19
  • $\begingroup$ @gung do you mind in writing your comment as an answer? Maybe with some more details if you have some. $\endgroup$
    – Integral
    Commented Jul 3, 2015 at 0:40

1 Answer 1


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.

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    $\begingroup$ 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. $\endgroup$
    – Nick Cox
    Commented Jul 3, 2015 at 11:18
  • $\begingroup$ 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. $\endgroup$
    – TPArrow
    Commented Jul 3, 2015 at 12:28
  • $\begingroup$ @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). $\endgroup$
    – Integral
    Commented Jul 3, 2015 at 16:12
  • $\begingroup$ 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? $\endgroup$
    – Integral
    Commented Jul 3, 2015 at 16:17
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    $\begingroup$ @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. $\endgroup$
    – Nick Cox
    Commented Jul 4, 2015 at 0:34

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