"From earlier pages, this will be harder than it..."


by Dewi Morgan Sep 25 2018

When you have your guards search her, and they find a dagger, then \(according to students of Bayes' rule\) you should update your beliefs in the same way you update your belief in the Diseasitis setting — where there is a large population with an objective frequency of sickness — despite the fact that this maybe\-assassin is a unique case\. According to a Bayesian, your brain can track the probabilities of different possibilities regardless, even when there are no large populations and objective frequencies anywhere to be found, and when you update your beliefs using evidence, you're not "eliminating people from consideration," you're eliminating probability mass from certain possible worlds represented in your own subjective belief state\.

From earlier pages, this will be harder than it initially appears.

Say that, on hearing there was a dagger, the king also ponders what other things an assassin might carry. Poisons, for sure - an assassin would have them like 6:1 odds at least, and a non-assassin would be surely no more than 0.02:1.

Listening devices, for spying and stuff. Probably 4:1 and 0.02:1 again.

Naive Bayesian analysis would say that doctors, with their knives and stethoscopes and drugs, would be carrying tools with odds of 9 * 6 * 4 : 1 = 216 : 1 if they were an assassin, and 0.02 * 0.02 * 0.3 = 0.00012 : 1 if they were not.

It's very easy to forget that "updated odds" are also "updated conditions". The king has not updated his odds of that person being an assassin; they have replaced their odds of "the person" being an assassin, with some new odds of "the person with the knife" being an assassin.

Subsequent odds need to be added in that light. The need to accurately track the decreasing weight of subsequent pieces of evidence feels like it is unlikely to be intuitively grasped by most.