What prior are you using for Knox? The pre-murder “chances a nice, pretty upper-middle class American girl would be involved in a murder in the next year” or the “chances the nice, pretty, upper-middle class American girl was involved in murder, given that her roommate was stabbed to death?
The major difference is going to end up being that Meredith Kercher was actually murdered and Willingham’s children were not.
What prior are you using for Knox? The pre-murder “chances a nice, pretty upper-middle class American girl would be involved in a murder in the next year” or the “chances the nice, pretty, upper-middle class American girl was involved in murder, given that her roommate was stabbed to death?
I’ve been kicking myself for months for not having done a better job of making the point that it shouldn’t matter: so long as you take into account all of the relevant information, Bayes’ theorem says nothing about the order in which you process the information.
What we label “prior probability” in everyday contexts like this is just an arbitrary matter of convenience: “priors” are in fact posteriors based on information not explicitly mentioned—and that information is still there, whether we mention it or not.
Thus, for example, if you assign a high “prior” to Amanda Knox’s guilt because of Meredith Kercher’s death, you still have to lower the probability (to something around the “pretty middle-class female honor student” range) upon learning that Kercher’s death was caused by Rudy Guede—the screening off effect doesn’t go away just because you decided to call that state of knowledge the “prior”; it just acquires the label of “evidence of innocence.”
(Just to be clear, I’m not suggesting you don’t realize this; I just think the point needs to be reinforced.)
What prior are you using for Knox? The pre-murder “chances a nice, pretty upper-middle class American girl would be involved in a murder in the next year” or the “chances the nice, pretty, upper-middle class American girl was involved in murder, given that her roommate was stabbed to death?
The major difference is going to end up being that Meredith Kercher was actually murdered and Willingham’s children were not.
I’ve been kicking myself for months for not having done a better job of making the point that it shouldn’t matter: so long as you take into account all of the relevant information, Bayes’ theorem says nothing about the order in which you process the information.
What we label “prior probability” in everyday contexts like this is just an arbitrary matter of convenience: “priors” are in fact posteriors based on information not explicitly mentioned—and that information is still there, whether we mention it or not.
Thus, for example, if you assign a high “prior” to Amanda Knox’s guilt because of Meredith Kercher’s death, you still have to lower the probability (to something around the “pretty middle-class female honor student” range) upon learning that Kercher’s death was caused by Rudy Guede—the screening off effect doesn’t go away just because you decided to call that state of knowledge the “prior”; it just acquires the label of “evidence of innocence.”
(Just to be clear, I’m not suggesting you don’t realize this; I just think the point needs to be reinforced.)