[samch93]

I am surprised by how many people equal frequentist statistics with Neyman-Pearson hypothesis testing. In my opinion, the main difference between the two approaches being whether the parameters of a statistical model are considered as fixed or random, everything else follows from this.

On the subject of statistical education: The point I tried to make is that I think it is much easier to study first the likelihood, the central quantity of frequentist inference. One can then go to the Bayesian world simply by allowing the parameters to be random variables. Furthermore, as other commentors have pointed out, technical difficulties arise in the non-conjugate Bayesian setting when MCMC sampling has to be used. In my opinion, MCMC algorithms, convergence diagnostics, etc. are certainly not topics for an intro stats course.