The Wikipedia page explains how a frequentist can get the answer ⅓, but it doesn’t explain how a Bayesian can get that answer. That’s what’s missing.
I’m still hoping for a reference for “the Bayesian rules of forgetting”. If these rules exist, then we can check to see if they give the answer ⅓ in the Sleeping Beauty case. That would go a long way to convincing a naive Bayesian.
I do not think it is missing—since a Bayesian can ask themselves at what odds they would accept a bet on the coin coming up heads—just as easily as any other agent can.
What is missing is an account involving Bayesian forgetting. It’s missing because that is a way of solving the problem which makes little practical sense.
Now, it might be an interesting exercise to explore the rules of Bayesian forgetting—but I don’t think it can be claimed that that is needed to solve this problem—even from a Bayesian perspective. Bayesians have more tools available to them than just Bayes’ Law.
FWIW, Bayesian forgetting looks somewhat managable. Bayes’ Law is a reversible calculation—so you can just un-apply it.
The Wikipedia page explains how a frequentist can get the answer ⅓, but it doesn’t explain how a Bayesian can get that answer. That’s what’s missing.
I’m still hoping for a reference for “the Bayesian rules of forgetting”. If these rules exist, then we can check to see if they give the answer ⅓ in the Sleeping Beauty case. That would go a long way to convincing a naive Bayesian.
I do not think it is missing—since a Bayesian can ask themselves at what odds they would accept a bet on the coin coming up heads—just as easily as any other agent can.
What is missing is an account involving Bayesian forgetting. It’s missing because that is a way of solving the problem which makes little practical sense.
Now, it might be an interesting exercise to explore the rules of Bayesian forgetting—but I don’t think it can be claimed that that is needed to solve this problem—even from a Bayesian perspective. Bayesians have more tools available to them than just Bayes’ Law.
FWIW, Bayesian forgetting looks somewhat managable. Bayes’ Law is a reversible calculation—so you can just un-apply it.