When Holmes meets Bayes

Please read him as him/her. ‘Man’ refers to mankind/humanity in general.

Like many people, in the past 2 weeks I too am disturbed when I think about what could have happened to the missing Malaysian flight MH370. On Saturday the 15th of March, Malaysia Prime Minister communicated that evidence is consistent with someone acting deliberately from inside the plane and I could not help notice the shift in direction since then. The focus is now high on its pilots, crewmembers and passengers. The dearth of a solid meaningful clue has understandably made the search difficult and if it stays, I’m worried Sherlock Holmes might get to solve this with help from Thomas Bayes.

Bayesian inference in is a useful tool in statistics to help manage uncertainties. Mathematically, Bayes’ theorem gives the relationship between the probabilities of event A and B, P(A) and P(B), and the conditional probabilities of A given B and B given A, P(A|B) and P(B|A). In its most common form, it is:

13_Bayes

However, in real life, Bayesian inference could get ‘belief shattering’ when Holmes begins to use the same. In an investigation involving uncertainties and humans (like the missing MH370), without Holmes in the picture, the Bayesian way of solving it would be to find the probability of the underlying event occurring, given that the men involved are innocent. The premise or the prior knowledge held is simple i.e. the involved men are innocent to start with.

However, the Bayesian inference by Holmes is different. Holmes believes when one has excluded the impossible, whatever remains however improbable has to be the truth. Holmes tries to solve the problem by attempting to calculate the probability of one’s innocence given all the evidence. The premise or the prior knowledge that Holmes focuses on is the probability of getting such an evidence itself out of earlier such occurrences involving innocent men.

With the search entering the 11th day, I’m trying hard to believe in a miracle. I hope the entire episode gets explained through facts very soon. I hope Holmes does not have to go far into theorizing this mystery.

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