Over a number of years I taught the standard, classical, theory of statistics to a large number of
students, most of whom appeared to have similar difficulties to those I had myself encountered in
understanding the nature of the conclusions that this theory comes to. However, the mere fact that
students have difficulty with a theory does not prove it wrong. More importantly, I found the theory
did not improve with better acquaintance, and I went on studying Bayesian theory. It turned out that
there were real differences in the conclusions arrived at by classical and Bayesian statisticians, and
so the former was not just a special case of the latter corresponding to a conventional choice of prior
beliefs. On the contrary, there was a strong disagreement between statisticians as to the conclusions to
be arrived at in certain standard situations, of which I will cite three examples for now.
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