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 p(D|\theta_i)=0 for all i\neq j, then, no matter how small the prior p(\theta_j)>0 is, the posterior p(\theta_j|D) must equal one.

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