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I like the concept, it's a cool way of introducing Bayesian probabilities! The conclusion strikes me as overly confident, though. It implies that if we had 100
by ced 12y ago
I like the concept, it's a cool way of introducing Bayesian probabilities!
The conclusion strikes me as overly confident, though. It implies that if we had 100 Han Solo's, we are very confident that about 3/4 of them are going to make it through. This comes about because it uses this:
We're going to say that C3PO has records of two people surviving and 7,440 people ending their trip through the asteroid field in a glorious explosion.
as data for Han's odds of making it. But 100 out-of-shape people dying on the ascent of Mount Everest does not tell us anything about the odds for someone who is very fit.
I would rather model that there is no one true probability of making it through - it's going to be dependent on the pilot. Mediocre pilots might have odds in the neighborhoud of 1/3720, but there is presumably a lot of variance depending on skill, and my prior belief is that Han would wind up in the upper end of the distribution.
- sukilot 12y agoHow is your model different from the blog post? Yours sounds like a paraphrase. Do you disagree that Han is more likely to survive more difficult challenges than easier ones?
- ced 12y agoThe blog post has the right idea, but the wrong equations. If we take C3PO's statement to mean: We're going to say that C3PO has records of two people surviving and 7,440 people ending their trip through the asteroid field in a glorious explosion. Then the big question is how skill-dependent the challenge is. Is it like swimming across the English channel, or is it random like surviving the Niagara Falls in a barrel? There exists a distribution of survival rates as a function of skill level, we just don't know what it is. We could assume a sigmoid form. C3PO's statement gives us some constraint on what the parameters of the sigmoid are, but not enough. We could make some further assumptions and get an answer, but the results will depend strongly on the specific assumptions. In other words: we don't know the answer. https://xkcd.com/384/ https://xkcd.com/384/
- xaetium 12y agoI often find myself wondering if the major problem with any given statistical analysis is whether Bayesian inference ought to have been used at all.