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Given a partially explored tree (represented by a set of nodes which are limit of exploration), we would like to know the best node from which to explore further. The Fano metric (named after [[Robert Fano]]) allows one to calculate from which is the best node to explore further. This metric is optimal given no other constraints (e.g. memory).
For a [[binary symmetric channel]] (with error probability <math>p</math>) the Fano metric can be derived via [[Bayes' theorem]]. We are interested in following the most likely path <math>P_i</math> given an explored state of the tree <math>X</math> and a received sequence <math>{\mathbf r}</math>. Using the language of [[probability]] and [[Bayes' theorem]] we want to choose the maximum over <math>i</math> of:
:<math>\Pr(P_i|X,{\mathbf r}) \propto \Pr({\mathbf r}|P_i,X)\Pr(P_i|X)</math>
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