Is the frequentist framework more appropriate than the Bayesian one, according to Popper's theory? According to Karl Popper, only falsifiable hypotheses are truly scientific (quoting Wikipedia): 

no number of positive outcomes at the level of experimental testing
  can confirm a scientific theory, but a single counterexample is
  logically decisive: it shows the theory, from which the implication is
  derived, to be false.

In keeping with these theoretical premises, which statistical framework is more appropriate, the frequentist or the Bayesian?
 A: Karl Popper has argued for a general mindset that should be employed by a scientist.  The frequentist null hypothesis testing was designed in a way that is consistent with this kind of thinking about scientific method. However this does not mean that is is the only way how you could conduct hypothesis tests!  In Bayesian framework you could use Bayes factors to compare the "null" model with alternative model so to falsify your hypothesis (this is how most Bayesian equivalents to frequentist tests, like BEST, work).  So you can perform hypothesis tests in Bayesian framework and Karl Popper has nothing to do with Bayesian vs. frequentist debate.
A: It depends on what you mean that Popper had nothing to with debate.
IN some sense it is half correct
In other sense, its WRONGER THAN WRONG; ultimately,he rejected priors or inductive logic; and he was intimately connected with these issues. The foundations of probability is generally considered to be his best work.


*

*Developed and helped make rigorous Von Mises frequentist theory

*Developed  A confirmation Logic, using Popper Functions.

*Argued against Inductive logic, and standard bayesian inference; that is nonsense (see his paper on this

*Developed his own probability calculus similar to A Renyi

*Ultimately was interested in the debate, because he rejected both conceptions; arguing to a return to Kolmogorov interpretation of probability= the neo-classical physical interpretation called propensity theory

*Connected these issues to QM

*Generally considered to amongst the greatest mathematical philosophers of probability (if not the greatest in some cases) and probabilistic logicians

*More than half of his best work (read David Miller, who was close confident, contribution in the newly published cambridge companion to Popper)

