This might be a minor or a major nitpick, depending on your point of view: Laplace rule works only if the repeated trials are thought to be independent of one another. That is why you cannot use it to predict sunrise: even without accurate cosmological model, it’s quite clear that the ball of fire rising up in the sky every morning is always the same object. But what prior you use after that information is another story...
That entirely depends on your cosmological model, and in all cosmological models I know, the sun is a definite and fixed object, so usually P(sunrise)=1−P(apocalypse)
The premise seems to be that there is no model, you’re seeing the sun for the first time. Presumably there are also no starts, planets, moons in the sky, and no telescopes or other tools that would help you build a decent cosmological model.
In that situation you may still realize that there is one thing rotating around another and deduce that P(sunrise) = 1-P(apocalypse). Unless you happen to live in the Arctic, or your planet is rotating in some weird ways, or it’s moving in a weird orbit, or etc.
My point is that estimating P(sunrise) is not trivial, the number can’t just be pulled out of the air. I don’t see anything better than Laplace rule, at least initially. You said it doesn’t work, so I’m asking you, what does work?
Take a prior over all potential turing machines, take the number of all the agents simulated by those turing machines (times their respective turing machines prior probability) that have had the same sensory experience that you remember and that see a sunrise tomorrow, divide by the number of agents (multiplied by the prior for their respective turing machine) that have had the same sensory experience and do not see a sunrise. Done. Trivial.
This might be a minor or a major nitpick, depending on your point of view: Laplace rule works only if the repeated trials are thought to be independent of one another. That is why you cannot use it to predict sunrise: even without accurate cosmological model, it’s quite clear that the ball of fire rising up in the sky every morning is always the same object. But what prior you use after that information is another story...
How do you evaluate P(sun will rise tomorrow) then?
That entirely depends on your cosmological model, and in all cosmological models I know, the sun is a definite and fixed object, so usually P(sunrise)=1−P(apocalypse)
The premise seems to be that there is no model, you’re seeing the sun for the first time. Presumably there are also no starts, planets, moons in the sky, and no telescopes or other tools that would help you build a decent cosmological model.
In that situation you may still realize that there is one thing rotating around another and deduce that P(sunrise) = 1-P(apocalypse). Unless you happen to live in the Arctic, or your planet is rotating in some weird ways, or it’s moving in a weird orbit, or etc.
My point is that estimating P(sunrise) is not trivial, the number can’t just be pulled out of the air. I don’t see anything better than Laplace rule, at least initially. You said it doesn’t work, so I’m asking you, what does work?
A much, much easier think that still works is P(sunrise) = 1, which I expect is what ancient astronomers felt about.
Take a prior over all potential turing machines, take the number of all the agents simulated by those turing machines (times their respective turing machines prior probability) that have had the same sensory experience that you remember and that see a sunrise tomorrow, divide by the number of agents (multiplied by the prior for their respective turing machine) that have had the same sensory experience and do not see a sunrise. Done. Trivial.