Subdivisions in statistics 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.
 A: 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.
A: 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).
