The coin was made in one of several ways. (Perhaps these ways are parametrized by the ratio of weights between the two sides of the coin.) You have a subjective probability distribution over this set W of possible ways in which the coin was made, according to which p(w) is the probability that the coin was made in way w. This distribution should come from a maximum entropy prior incorporating all your knowledge about the origin of the coin.
Furthermore, for each way w in W, you have a conditional probability p(H | w), which is your subjective probability that the coin will turn up Heads given that the coin was made in way w. This conditional probability distribution incorporates your physical knowledge about how weight ratios in coins influence the dynamics of their flipping.
Finally, you compute the unconditional probability p(H) that the coin will come up heads by summing up the values p(H | w) * p(w) over all ways w in W.
The coin was made in one of several ways. (Perhaps these ways are parametrized by the ratio of weights between the two sides of the coin.) You have a subjective probability distribution over this set W of possible ways in which the coin was made, according to which p(w) is the probability that the coin was made in way w. This distribution should come from a maximum entropy prior incorporating all your knowledge about the origin of the coin.
Furthermore, for each way w in W, you have a conditional probability p(H | w), which is your subjective probability that the coin will turn up Heads given that the coin was made in way w. This conditional probability distribution incorporates your physical knowledge about how weight ratios in coins influence the dynamics of their flipping.
Finally, you compute the unconditional probability p(H) that the coin will come up heads by summing up the values p(H | w) * p(w) over all ways w in W.
Ah, right, my beliefs about each particular kind of coin are also subjective. That’s a good answer, thanks.