### A Bayesian interpretation of Holmesian deduction

#### by Yi Zhang

An interesting point I’ve read from book “Doing Bayesian Data Analysis“, is the Bayesian interpretation of the famous deduction from Sherlock Holmes: ” How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?”. In other words,

How often have I said to you that when for all , then, no matter how small the prior is, the posterior must equal one.

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Some people consider it isn’t deduction but induction because all is based on generalization of events) But I wrote Sherlock Holmes too and remember that originally it is called this way.