It is important to know the meaning of this word to understand the subsequent discussion, but also the meaning of the words theory and hypothesis has to be clear in our minds. So, a theory
“In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with scientific method.”
And hypothesis is,
The singular observation of a black swan show that 'all swans are white' is false.
The purpose of most of statistical inference is to facilitate decision-making (Roberts, 2007). The optimal decision is the Bayesian decision.
The likelihood principle, by itself, is not sufficient to build a method of inference but should be regarded as a minimum requirement of any viable form of inference. (Rossi et al., 2005).
In conclusion, I think that the ideas of Popper are not wrong and are useful in some aspects of sciences but the Bayesianism, even when is contradictory with Popper ideas is a relevant method of inference and I can say that is the best method to phylogenetic analysis at the moment.
Bernardo J, Smith A (2000). Bayesian Theory. John Wiley & Sons, West Sussex, England.
Mayo, D. G. (1996). Error and the growth of experimental knowledge. University of Chicago Press.
Rossi, P, Allenby, G, McCulloch, R. (2005). Bayesian Statistics and Marketing. John Wiley & Sons, West Sussex, England.