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.
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).