> Then I noticed that the way you talk about p-value doesn't sound very frequenty. I think a lot of people improperly understand the Frequentist/Bayesian divid

> Then I noticed that the way you talk about p-value doesn't sound very frequenty. I think a lot of people improperly understand the Frequentist/Bayesian divide; both look at likelihood functions but the Frequentists assert, as a matter of experimental interpretation, that the likelihood function should depend only on the observed data while the Bayesians are willing to admit "out-of-experiment" modifications to the likelihoods implied by the data (i.e. the "prior"). Frequentist arguments correctly point out that the prior is, from the isolated standpoint of the experimental observations, purely subjective and non-falsifiable. Bayesian arguments correctly point out that experiments are designed by humans in context, and that the context may imply a prior distribution that is not evident within the observations themselves. Neither is incorrect, but they answer different questions. Which question is the right one to answer is context-dependent. As a concrete example, consider an A/B test where A and B perform very similarly. Merely seeing A's performance against B does not carry the contextual information that A has consecutively beaten one hundred previous non-B competitors that sort-of-look-like B. The Frequentist will correctly argue that, if you don't explicitly model the A/B test generation process (as opposed to just the A/B test itself), then all the data can tell you based purely on the laws of probability is that A and B are likely to be pretty similar. The trouble faced by the frequentist is that it's pretty easy to model an individual A/B test for, say, binary outcomes, but it's very hard to explicitly model the generation of A/B test competitors. So the Frequentist says "all I can tell you and still be strictly objective is that A and B look similar". The Bayesian, rather than explicitly modeling the generation of tests as the Frequentist would like, wraps up that contextual knowledge into a subjective prior distribution that heavily weights A over B simply because A has won so many times before. The Bayesian's advantage is that the previously-blocking part of the probability modeling problem is punted into a subjective, experimenter-designed, input. This is a tradeoff, not an increase of correctness! It will "do the right thing" assuming the new B looks a lot like the old Bs, but will do the wrong thing if the new B is dramatically different and maybe looks a lot more like A with small tweaks. Bayesianism is not a universal solution to probability modeling problems, and Frequentism is not an obsolete unhip method.