Despite the difficulty of exact Bayesian inference in complex mathematical models, the essence of Bayesian reasoning is frequently used in everyday life. One example has been immortalized in the words of Sherlock Holmes to his friend Dr. Watson: “How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?” (Arthur Conan Doyle, The Sign of Four, 1890, Ch. 6). This reasoning is actually a consequence of Bayesian belief updating, as expressed in Equation 4.4. Let me re-state it this way: “How often have I said to you that when p(D|θ_i ) = 0 for all i!=j, then, no matter how small the prior p(θ_j ) > 0 is, the posterior p(θ_j |D) must equal one.” Somehow it sounds better the way Holmes said it.

--Kruschke 2010, Doing Bayesian Data Analysis, pg56-57