We know the probability to a reasonable level of accuracy—eg consider acturial tables. This is different from things like Pascal’s wager where the actual probability may vary by many orders of magnitude from our best estimate.
This is different from things like Pascal’s wager where the actual probability may vary by many orders of magnitude from our best estimate.
According to the Bayesians, our best estimate is the actual probability. (According to the frequentists, the probabilities in Pascal’s wager are undefined.)
What parent means by “We know the probability to a reasonable level of accuracy—eg consider acturial tables” is that it is possible for a human to give a probability without having to do or estimate a very hairy computation to compute a prior probability (the “starting probability” before any hard evidence is taken into account). ADDED. In other words, it should have been a statement about the difficulty of the computation of the probability, not a statement about the existence of the probability in principle.
It should be a statement about the dependence of the probability on the priors. The more the probability depends on the priors, the less reliable it is.
We know the probability to a reasonable level of accuracy—eg consider acturial tables. This is different from things like Pascal’s wager where the actual probability may vary by many orders of magnitude from our best estimate.
According to the Bayesians, our best estimate is the actual probability. (According to the frequentists, the probabilities in Pascal’s wager are undefined.)
What parent means by “We know the probability to a reasonable level of accuracy—eg consider acturial tables” is that it is possible for a human to give a probability without having to do or estimate a very hairy computation to compute a prior probability (the “starting probability” before any hard evidence is taken into account). ADDED. In other words, it should have been a statement about the difficulty of the computation of the probability, not a statement about the existence of the probability in principle.
It should be a statement about the dependence of the probability on the priors. The more the probability depends on the priors, the less reliable it is.