7. As outlined in Example 10.7, define a code for describing decision trees. Make sure that each code corresponds to a decision tree (for every sufficiently long sequence of bits, the initial segment of the sequence will describe a unique decision tree), and each decision tree has a code.
How does this code translate into a prior distribution on trees? In particular, how much does the likelihood of introducing a new split have to increase to offset the reduction in prior probability of the split (assuming that smaller trees are easier to describe than large trees in your code)?