Hmm… this isn’t exactly a Bayesian update, though.
Bayesian update: you have prior probabilities for theories A, B, C, D; you get new evidence for D, and you use Bayes’ rule to decide how to move posterior probability to D.
Oz: you have prior probabilities for theories A, B, and C; you hear a new theory D that you hadn’t previously considered, and you recalculate the influence of previous evidence to see how much credence you should give D.
This quote isn’t a pure example of the distinction between “getting new evidence” and “considering a new theory”, since obviously “my friends believe in D” is also new evidence, but there seems to be more of the latter than the former going on.
It’s weird that we don’t seem to have a term describing what kind of update the “considering a new theory” process is. It’s not something that would ever be done by an ideal Bayesian agent with infinite computing resources, but it’s unavoidable for us finite types.
Oz: you have prior probabilities for theories A, B, and C; you hear a new theory D that you hadn’t previously considered, and you recalculate the influence of previous evidence to see how much credence you should give D.
This seems slightly off both in terms of what (the writer intends us to infer) is going on in Oz’s head, and what ought to be going on. First, it seems that Oz may have considered vampires or other supernatural explanations, but dismissed them using the absurdity heuristic, or perhaps what we can call the “Masquerade heuristic”—that’s where people who live in a fictional world full of actual vampires and demons and whatnot nevertheless heurise as though they lived in ours. (Aside: Is ‘heurise’ a reasonable verbing of “use heuristics?”) Upon hearing that his friends take the theory seriously (plus perhaps whatever context caused them to make these remarks) he reconsiders without the absurdity penalty.
Second, what should be going on is that Oz has theories A, B, C with probabilities adding up to 1-epsilon, where epsilon is the summed probability of “All those explanations which I haven’t had time to explicitly consider as theories”. Just because he’s never explicitly formulated D and formally assigned a probability to it, doesn’t mean it doesn’t have an implicit one. Once it is picked out of hypothesis space, he can detach it from the other previously unconsidered theories, formally assign an initial probability much smaller than epsilon, and update from there. Of course this is not realistic as a matter of human psychology, but what I’m arguing is that “I never thought of theory X before” does not actually demonstrate that “Oh yeah, theory X makes a lot of sense” is not a Bayesian update. It just means that the updater hasn’t had the processing power to fully enumerate the space of available theories.
Hmm… this isn’t exactly a Bayesian update, though.
Bayesian update: you have prior probabilities for theories A, B, C, D; you get new evidence for D, and you use Bayes’ rule to decide how to move posterior probability to D.
Oz: you have prior probabilities for theories A, B, and C; you hear a new theory D that you hadn’t previously considered, and you recalculate the influence of previous evidence to see how much credence you should give D.
This quote isn’t a pure example of the distinction between “getting new evidence” and “considering a new theory”, since obviously “my friends believe in D” is also new evidence, but there seems to be more of the latter than the former going on.
It’s weird that we don’t seem to have a term describing what kind of update the “considering a new theory” process is. It’s not something that would ever be done by an ideal Bayesian agent with infinite computing resources, but it’s unavoidable for us finite types.
This seems slightly off both in terms of what (the writer intends us to infer) is going on in Oz’s head, and what ought to be going on. First, it seems that Oz may have considered vampires or other supernatural explanations, but dismissed them using the absurdity heuristic, or perhaps what we can call the “Masquerade heuristic”—that’s where people who live in a fictional world full of actual vampires and demons and whatnot nevertheless heurise as though they lived in ours. (Aside: Is ‘heurise’ a reasonable verbing of “use heuristics?”) Upon hearing that his friends take the theory seriously (plus perhaps whatever context caused them to make these remarks) he reconsiders without the absurdity penalty.
Second, what should be going on is that Oz has theories A, B, C with probabilities adding up to 1-epsilon, where epsilon is the summed probability of “All those explanations which I haven’t had time to explicitly consider as theories”. Just because he’s never explicitly formulated D and formally assigned a probability to it, doesn’t mean it doesn’t have an implicit one. Once it is picked out of hypothesis space, he can detach it from the other previously unconsidered theories, formally assign an initial probability much smaller than epsilon, and update from there. Of course this is not realistic as a matter of human psychology, but what I’m arguing is that “I never thought of theory X before” does not actually demonstrate that “Oh yeah, theory X makes a lot of sense” is not a Bayesian update. It just means that the updater hasn’t had the processing power to fully enumerate the space of available theories.
Does Oz already know that he’s a werewolf at this point? That would seem to bring “vampires exist” into the realm of plausible hypotheses.