I've just finished a module where we covered the different approaches to statistical problems – mainly Bayesian vs frequentist. The lecturer also announced that she is a frequentist. We covered some paradoxes and generally the quirks of each approach (long run frequencies, prior specification, etc). This has got me thinking – how seriously do I need to consider this? If I want to be a statistician, do I need to align myself with one philosophy? Before I approach a problem, do I need to specifically mention which school of thought I will be applying? And crucially, do I need to be careful that I don't mix frequentist and Bayesian approaches and cause contradictions/paradoxes?
Bayesian – How to Think About the Different Philosophies of Statistics: Bayesian vs Frequentist
bayesianfrequentistphilosophical
Best Answer
I think that the main takeaway here is this: the mere fact that there are these different philosophies of statistics and disagreement over them implies that translating the "hard numbers" that one gets from applying statistical formulae into "real world" decisions is a non-trivial problem and is fraught with interpretive peril.
Frequently, people use statistics to influence their decision-making in the real world. For example, scientists aren't running randomized trials on COVID vaccines right now for funsies: it is because they want to make real world decisions about whether or not to administer a particular vaccine candidate to the populace. Although it may be a logistical challenge to gather up 1000 test subjects and observe them over the course of the vaccine, the math behind all of this is well-defined whether you are a Frequentist or a Bayesian: You take the data you gathered, cram it through the formulae and numbers pop out the other end.
However, those numbers can sometimes be difficult to interpret: Their relationship to the real world depends on many non-mathematical things – and this is where the philosophy bit comes in. The real world interpretation depends on how we went about gathering those test subjects. It depends on how likely we anticipated this vaccine to be effective a priori (did we pull a molecule out of a hat, or did we start with a known-effective vaccine-production method?). It depends on (perhaps unintuitively) how many other vaccine candidates we happen to be testing. It depends on etc., etc., etc.
Bayesians have attempted to introduce additional mathematical frameworks to help alleviate some of these interpretation problems. I think the fact that the Frequentist methods continue to proliferate shows that these additional frameworks have not been super successful in helping people translate their statistical computations into real world actions (although, to be sure, Bayesian techniques have led to many other advances in the field, not directly related to this specific problem).
To answer your specific questions: you don't need to align yourself with one philosophy. It may help to be specific about your approach, but it will generally be totally obvious that you are doing a Bayesian analysis the moment you start talking about priors. Lastly, though, you should consider all of this very seriously, because as a statistician it will be your ethical duty to ensure that the numbers that you provide people are used responsibly – because correctly interpreting those numbers is a hard problem. Whether you interpret your numbers through the lens of Frequentist or Bayesian philosophy isn't a huge deal, but interpretation of your numbers requires familiarity with the relevant philosophy.