14 Missing Data and Other Opportunities
A big advantage of Bayesian inference is that it obviates the need to be clever. For example, there's a classic probability puzzle known as Bertrand's box paradox.165 The version that I prefer involves pancakes. Suppose I cook three pancakes. The first pancake is burnt on both sides (BB). The second pancake is burnt on only one side (BU). The third pancake is not burnt at all (UU). Now I serve you—at random-one of these pancakes, and the side facing up on your plate is burnt. What is the probability that the other side is also burnt?
This is a hard problem, if we rely upon intuition. Most people say “one-half,” but that is quite wrong. And with no false modesty, my intuition is no better. But I have learned ...
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