On Bayesian Philosophy, Confidence vs. Credibility
for frequentists, a probability is a measure of the frequency of repeated events
→ parameters are fixed (but unknown), and data are random for Bayesians,
a probability is a measure of the degree of certainty about values
→ parameters are random and data are fixed
Bayesians: Given our observed data, there is a 95% probability that the true value of θ falls within the credible region
vs.
Frequentists: There is a 95% probability that when I compute a confidence interval
from data of this sort, the true value of θ will fall within it.