Differences and distinctions
9.1 PHILOSOPHICAL DIFFERENCES
Although they are both founded in probability theory, traditional statistics and Bayesian statistics have fundamental philosophical differences in the way they treat uncertainty. Bayesian methods demand that uncertainty is quantified, whereas traditional methods accept the uncertainty and reason from that position. However, in practice our knowledge is somewhere between complete ignorance and precise probability, and both methods have ways of dealing with this in-between knowledge.
9.1.1 WHAT DO WE KNOW ABOUT THE WORLD?
We have seen that both traditional statistics and Bayesian statistics effectively start with the same underlying data, and in many circumstances yield ...