Timeline for What's the difference between mathematical statistics and statistics?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2016 at 13:39 | comment | added | Nick Cox | It is important to me (not a matter of life or death, but still important) that statements here are clear and correct. Thanks for your summary. So long as any kind of consideration of data and their analysis is included in your very broad definition of mathematics, then I can agree. | |
| Apr 4, 2016 at 13:33 | comment | added | Digio | My point all along has been that every aspect of statistics is mathematical in nature, be it pure, applied, discrete, computational, etc. To be honest, it's not important. Thank you for replying to an old discussion just for the sake of arguing. | |
| Apr 4, 2016 at 13:04 | comment | added | Nick Cox | That helps me to see what you're getting at, but nevertheless it leaves what I consider my most important single point (second comment above) quite untouched. I don't see that the relevance and indeed importance of these computing issues undermines that in any sense. Indeed, these examples make your initial emphasis on pure mathematics as a basis for statistics seem more peculiar. Sure, applied mathematics depends on pure mathematics, but I don't think of computational complexity theory as pure mathematics. If you want to argue back, I am happy to let you have the last word. | |
| Apr 4, 2016 at 12:49 | comment | added | Digio | Let's take forward regression and variable selection as an example, the aspect of linear regression that most statisticians would view as empirical methods. Variable selection is mathematically a NP-hard combinatorial problem (can be reduced to the max-cut problem), which a deterministic algorithm would solve in exponential time. Forward selection and backward elimination are nothing more than a sort of generilised Hill Climbing, a local search heuristic "solving" a NP-hard problem in polynomial time. This makes little sense in the world of statistics, but it's not an empirical approach. | |
| Apr 4, 2016 at 10:38 | comment | added | Nick Cox | I just don't recognise the picture of statistics you paint and find your assertions implausible and unsubstantiated. For example, how do generalised linear models, or any other standard tool you care to use as an example, arise out of, or are even illuminated by, computational complexity theory? I am content to let my earlier comments. stand as expression of dissent and puzzlement. | |
| Apr 4, 2016 at 10:29 | comment | added | Digio | "but many principles such as strategy for model building are also based on empirical evidence or other imperatives" <- BTW, that is not true. What statisticians call "methods for model-building" has a very deep theoretical background in things such as computational complexity theory and algorithm theory, both studied in discrete mathematics and logic (the latter being a subfield of pure math)... | |
| Nov 19, 2015 at 10:58 | comment | added | Digio | By citing Rice I was meaning to support my claim that generic/core statistics (first half of the book) can be synonymous to ‘mathematical statistics’, which is what this question was about in the first place. The book also implies that empirical data analysis is not synonymous to applied statistics. This is not meant to be pejorative in any way. A biologist who uses hypothesis testing to prove the efficacy of a certain medicine is not a statistician (applied or otherwise) and has no interest in being one. This doesn’t change the fact that the methods he uses are mathematically valid. | |
| Nov 19, 2015 at 10:41 | comment | added | Nick Cox | I trust you are not implying, by the way, that those formally trained in mathematical statistics are somehow intrinsically superior to those who are not. I am certainly not a statistician in any formal or certificated sense, so these hints at class distinctions can be sensitive for me, and more importantly others too. A background in some science can also inform data analysis in a way that pure mathematics does not. | |
| Nov 19, 2015 at 10:35 | comment | added | Nick Cox | Neither of us is going to persuade the other to change their mind, but the discussion might have some small interest for others. But, FWIW, I have read all three editions of Rice's book and am even acknowledged in it, and I disagree again. Indeed the conjunction in his title Mathematical statistics and data analysis to me manifestly does not imply that data analysis is a subset of mathematical statistics, nor do the contents support that view. But I did not state, do not imply and have never thought that applied statistics is a discipline on its own, so there is no disagreement there. | |
| Nov 19, 2015 at 10:30 | comment | added | Digio | A source, which shares my view would be ‘Mathematical statistics and data analysis’ by J. A. Rice. Also, I don’t see how D. R. Cox’s use of the term “applied statistics” is in conflict with what I’m saying. The thing is that, academically speaking, there’s not such thing as “applied statistics” as a discipline of its own. It’s meant as a “specialisation” for someone who’s already fluent in the theory of mathematical statistics. The fact that some of the empirical methods of applied statistics can be used by people who are not statisticians in the context of data analysis does not change that. | |
| Nov 19, 2015 at 10:15 | comment | added | Digio | To address your earlier points, it all depends on someone's perception of where does Statistics start and end. We could argue forever on where does Statistics end and machine learning or data analysis begin, but I think we all agree on where does Statistics begin, and it’s with pure math. In that sense, mathematical Statistics is for me synonymous to "core Statistics", which can be focused on theory or application. Empirical methods such as model-building that you perceive as ‘applied statistics’ are, for me, part of ‘data analysis’ or ‘data science’ and not Statistics per se. | |
| Nov 19, 2015 at 8:55 | comment | added | Nick Cox | I would have to differ on "strictly". My own namesake Sir David Cox has written books with titles like theoretical statistics and applied statistics. Much of the content of the latter is not deducible from the former. Your comment doesn't really address my earlier points. | |
| Nov 19, 2015 at 8:49 | comment | added | Digio | Applied Statistics has no common definition among academic institutions and methods of teaching can differ significantly. However, in all occasions it consists strictly of applying of the mathematical principles established in theoretical statistics. This doesn't mean that the person learning/applying those methods is necessarily a mathematician (or even a Statistician in some cases). But it also doesn't make the scientific discipline any less mathematical. | |
| Nov 18, 2015 at 18:21 | comment | added | Nick Cox | I also would deny that all the principles of statistics come from pure mathematics. The argument can be protected by defining principle in a sufficiently narrow way, but many principles such as strategy for model building are also based on empirical evidence or other imperatives. Evidence on how procedures work with real data influences how they are (recommended to be) used, which is not directly deducible from pure mathematics. | |
| Nov 18, 2015 at 18:21 | comment | added | Nick Cox | It takes a lot of evidence to be clear on what is true throughout the world: but I just note that I frequently see distinctions between mathematical or theoretical statistics on the one hand and applied statistics on the other. To regard applied statistics as a subset of mathematical statistics just doesn't match the way the terms are used in my experience. | |
| Nov 18, 2015 at 17:01 | history | answered | Digio | CC BY-SA 3.0 |