I’d say the opposite. The more confusing the case the more important is to make it as simple as possible in order not to multiply possible sources of consufion.
Correctness implies one-dimensional measure and objectivity and then people start arguing what is “correct” probability in Sleeping Beauty.
Well, yes. Sleeping Beauty is actually a great example why you should be more careful with invoking betting, while trying to solve probability theory problems, as you may stumble into a case that doesn’t satisfy Kolmogorov Axioms without noticing it. I’ll talk more about it after I’ll have finished all the prerequisite posts. For now, it’s suffice to say that we can easily talk about different probabilities for Heads: on average awakening and on average experiment, just as we can talk about different betting schemes and the addition of betting scheme doesn’t make the problem clear in any way.
the law of large numbers is a value-laden bridge law.
I’m not sure what you mean by it. Law of large numbers is just a fact from probability theory, it doesn’t require utility functions or betting.
I’m not sure what you mean by it. Law of large numbers is just a fact from probability theory, it doesn’t require utility functions or betting.
I meant that the law is just a statement about probability, not about simulations confirming it. To conclude anything from simulations or any observations you need something more than just probability theory.
For now, it’s suffice to say that we can easily talk about different probabilities for Heads: on average awakening and on average experiment
Or on average odd awakening, if you only value half your days. Or on whatever awakening you need to define to minimize product of squared errors. I feel like the question confused people want answered is more like “can you get new knowledge about coin by awakening?”. But ok, looking forward to your next posts.
I’d say the opposite. The more confusing the case the more important is to make it as simple as possible in order not to multiply possible sources of consufion.
Well, yes. Sleeping Beauty is actually a great example why you should be more careful with invoking betting, while trying to solve probability theory problems, as you may stumble into a case that doesn’t satisfy Kolmogorov Axioms without noticing it. I’ll talk more about it after I’ll have finished all the prerequisite posts. For now, it’s suffice to say that we can easily talk about different probabilities for Heads: on average awakening and on average experiment, just as we can talk about different betting schemes and the addition of betting scheme doesn’t make the problem clear in any way.
I’m not sure what you mean by it. Law of large numbers is just a fact from probability theory, it doesn’t require utility functions or betting.
I meant that the law is just a statement about probability, not about simulations confirming it. To conclude anything from simulations or any observations you need something more than just probability theory.
Or on average odd awakening, if you only value half your days. Or on whatever awakening you need to define to minimize product of squared errors. I feel like the question confused people want answered is more like “can you get new knowledge about coin by awakening?”. But ok, looking forward to your next posts.