Prior indifference is a distortion of Bayesian updating. While a correct update takes BR and increases or decreases it according to the likelihood of new evidence, Prior indifference triggers an inadvertent shift of the Base Rate to 50% before the update takes place. As a result, the update builds on Knightian uncertainty and Perfect ignorance, rather than on prior beliefs.
With meaningful, momentous and sometimes tragic consequences.
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@mihaljevic The point @mihaljevic is again Laplace's dictum: Extraordinary (improbable) claims require extraordinary (accurate) evidence. So an infection from a rare 1/1000 virus can only be supported by a test that is at least 99.9% accurate.
We shall clearly see it in the next post.
Here is the amazing paradox. Without the test, Bob would have reckoned he had a 0.1% probability of infection. With the test, after a positive result, that probability increased 19-fold: it went from 0.1% to 1.9%. But Bob thought it had gone all the way to 95%. He took the test because he wanted more evidence to lead him closer to the truth, but he ended up drifting far away from it. He would have stayed much closer to the truth if he had not taken the test: just like Othello, he was blinded by evidence.
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Dependence on prior beliefs is an inconvenient obstacle in the pursuit of truth. Ideally, we would like evidence to speak for itself, swamp priors and give us certainty. But when evidence is not so obliging, ignoring priors, or pretending they do not exist, is not the right course of action.
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Like all of us, Othello is a fallible Bayesian.
He has just learned from the wily Iago that the treasured handkerchief he had given to his beloved wife Desdemona has been discovered in the lodgings of his lieutenant Cassio.
How could this have happened? And how should he begin to make sense of such a troubling discovery?
https://t.co/ZkCXCf0soE
Nuovo video sul canale YouTube #MadeinItalyCEOs.
@VincePolidoro, Consigliere Esecutivo di @FirstCapitalSpA
L'intera conversazione รจ qui
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Con sottotitoli [CC] in italiano ed inglese.