A geometrical interpretation of independence and exchangeability leads to understanding the failure of de Finetti's theorem for a finite exchangeable sequence. In particular an exchangeable sequence of length r which can be extended to an exchangeable sequence of length k is almost a mixture of independent experiments, the error going to zero like 1/k.

From the outside, Bayesian statistics may seem like a closed little corner of probability. Once a prior is specified you compute! From the inside the field is filled with problems, conceptual and otherwise. This paper surveys some of what remains to be done and gives examples of the work in progress via a Bayesian peek into Feller volume I.