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I was having a discussion with a statistics professor a while ago about the different 'flavours' of statistics (frequentist, Bayesian, ...). He posed that he would subdivide statistics in four categories: non-parametric-, robust-, frequentist- and Bayesian statistics. The subdivision is characterized by the amount of assumption the methods make about underlying distributions (non-parametric statistics makes none, while Bayesian makes those assumptions very explicit).

I was going to to ask if CrossValidated agrees with this subdivision, but since that is a subjective question I'll ask:

1) Is this subdivision widely recognized in statistics;

2) do 'real world' problem usually require one particular method? Ie, given some problem, is there a method most suitable for solving that problem or can multiple methods work for a given problem?

Thanks in advance.

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Subdivisions in statistics for CrossValidated is not good for community. People always confuses his problem that what kind of problem it is. Statistics Problem should be open for everybody who interested in statistics. Besides, divisions this community does not bring any benefit. – Randolph Chou Dec 30 '11 at 10:43
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I disagree, when applying statistical methods one needs to be clear about the framework in which the analysis is performed, and you can't do that without mentioning the subdivision of statistics into at least two fundamentally different categories (Bayesian and frequentist). However we should all be familiar with both frameworks so we know which is more appropriate for the application at hand. Understanding the subdivision is vital, so discussion is helpul. What isn't helpful is rigidly sticking to only one subdivision and ignoring the benefits of the other. – Dikran Marsupial Dec 30 '11 at 11:13
Tags function is enough for us to distinguish the problem categories. If subdivision is necessary, why don't we divide math stackexchange into applied math or pure math? Subdivision may affect the architecture of stackexchange system. Resources for upgrading system is needed. This is not easy to make a decision. One thing should be done is to analyze the related system data whether statistics community is separated or not. – Randolph Chou Dec 30 '11 at 11:51
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I don't think anyone was suggesting subdividing cross-validated, just a discussion of the subdivision of statistics. – Dikran Marsupial Dec 30 '11 at 12:30
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@MichaelBishop, maybe something like "philosophy of statistics" will do? – Stijn Jan 1 '12 at 10:07
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I wouldn't consider non-parametric or robust as being sub-categories of statistics in the way that frequentist and Bayesian are, simply because there are both frequentist and Bayesian methods for non-parametric and robust statistics. Frequentist and Bayesian are genuine sub-categories as they are based on fundamentally different definitions of a probability. Frequentists and Bayesians will both vary the strength of assumptions made depending on the requirements of the application.

So I would say that particular subdivision into four categories is not widely recognised in statistics. In my opinion, both Bayesian and frequentist methods can be used for most statistical problems, however they are not always equally useful, for example whether a frequentist confidence interval or a Bayesian credible interval is more appropriate depends on whether you want to ask a question about what to expect if the experiment were replicated, or what we can conclude about the statistics as a result of the particular experiment that we have actually performed (I would suggest in most cases it is the latter, but scientists generally use frequentist methods anyway).

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One thing that I think you've hinted at, but that might be good to flesh out further, is that much of the "delineation" between Bayesian and frequentist statistics lies in motivation, interpretation and philosophy. There are many instances in which either (a) the same exact formal approach can be given a Bayesian or frequentist argument (e.g., ridge regression) and/or (b) so-called Bayesian or frequentist methods arrive at the same solution, though the final interpretations differ (e.g., certain confidence/credible interval constructions). – cardinal Dec 30 '11 at 13:37
yes, absolutely (+1). I find the differences between frameworks a very interesting subject. My basic view is that you should adopt the framework that most directly answers the question you want to ask (framing the question accurately is very important!), which is often a matter of intepretation/meaning. However like many I often find myself using frequentist methods where they are not really appropriate as the Bayesian approach involves integrals that are just too difficult. The skill is to know when it is O.K. to settle for the "wrong" approach and when it isn't, which isn't at all easy! – Dikran Marsupial Dec 30 '11 at 14:01
@DikranMarsupial, thanks for your answer. Like you, I find the differences between frameworks, and the implications of using one over the other, really interesting. Would you know any books about precisely this subject? – Stijn Dec 30 '11 at 15:45
Sorry, I don't know any good books on the topic; I have found discussions on Stack Exchange (and with colleagues) the most informative source. – Dikran Marsupial Dec 30 '11 at 16:37
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I would not necessarily assert that those are the subdivisions present in statistics. If pressed, I'd argue that Frequentist versus Bayesian is the most clear division, although even that gets somewhat fuzzy at the edge cases and most people in practice seem to be a mix of the two.

Robust and parametric/non-parametric aren't really divisions as much as different tools for different problems. Admittedly, there are people who only work in problems that lend themselves to one or the other, but that's people, not the actual statistics - and I'd argue not even most people. To use an example, I'd argue there's no "Subdivision in carpentry" between hammers and screw drivers, even though I know a guy who hates using nails.

I'd say the far more profound division in statistics is how its viewed from the perspective of a mathematician versus a dedicated statistician versus a statistically-literate applied researcher.

To answer the second bit of your question: Sometimes

There are times when you must use one method - because that method was designed to work when others fail. Exact statistics come to mind. But there are many, many questions where multiple approaches work. For example, a project I'm working on could be approached using either Bayesian or Frequentist methods, and use either a parametric, semi-parametric or non-parametric approach. That's six possible combinations of tools, and credible arguments for each. In the end, I chose the method that would be the most useful for me, in this project.

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Thanks for your answer. Do you happen to know any books on the issue of knowing what method to use given some problem? I'm a math student with a focus on probability theory and feel that I'm lacking more 'practical' skills such as knowing when to apply some method, given some real world problem. Would you happen to know any literature on that problem? – Stijn Dec 31 '11 at 0:10

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