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Let's say you're trying to predict the probability of (H |E)

P(H) = 0,01

Let's say that you've found an instrument lying on the floor with a label on it saying "To be used to measure H). You know nothing about this instrument, neither if it's working or if it's broken, nothing about its hit and miss-rates etc. You can't know if the value it gives to you is reliable or not.

Still, you will have to use it to calculate the probability of (H) given the evidence(E).

Calculate the posterior probability using Bayes theorem.

P(H | E)?

What value would you set on P( E | -H) for this unknown instrument? 0,5?

Many thanks,

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    Is this an assignment? Why will you "have" to use it instead of just throwing it out? If you do use it, why wouldn't it be after testing it to find out its properties and relation to H, if any? And if H is a hypothesis how can it be "measured" by an instrument? The given setup is rather nonsensical. To sum up, what is the context of this question, and what is its philosophical content beyond a contrived calculational exercise?
    – Conifold
    Dec 26 '20 at 15:10
  • Thanks Conifold. This is about the philosophy of handling the unknown. Would you set P( E | -H) for this unknown instrument to be 0,5 or above? A great example are witnesses who say that they've encountered a miracle, their miss rate as instruments will always remain unknown. Dec 26 '20 at 15:28
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P(E | ~H) = P(E | H) = P(E) = 0.5 is a decent choice because it represents maximum uncertainty (and it means the instrument is useless). But in real life you're going to have some priors about the instrument that you could use to find a more specific estimate.

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