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Solution: Bayes and the Othello Problem – in a nutshell.

April 3, 2019

Solution to Exercise

The hypothesis is that Desdemona is being unfaithful to Othello.

The Bayesian probability of Desdemona’s guilt is:

ab/[ab+c(1-a)]

where a = 0.05 (the prior subjective probability of Desdemona’s guilt)

b = 0.5 (the subjective probability that Othello would have found the keepsake in Cassio’s lodgings if she was being unfaithful to him)

c = 0.1 (the subjective probability that Othello would have found the keepsake in Cassio’s lodgings if she was not being unfaithful to him)

Substituting into Bayes’ equation gives:

New probability = 0.05 x 0.5 / [0.05 x 0.5 + 0.1 (1 – 0.05) = 0.025 / (0.025 + 0.095) = 20.83%.

A reduction in a or b, or both, would reduce the subjective probability of Desdemona’s guilt in Othello’s eyes, while a reduction in c would increase it.

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