How would I update my probabilities if I saw the opposite piece of evidence? What I’m trying to get at here is that “A” and “not A” can’t really be evidences for the same thing. And often it’s more obvious which way “not A” is pointing. A couple of examples:
I saw someone suggesting that maybe a certain Mr. Far Wright was secretly gay because, when the subject was broached, he had publicly expressed his dislike of homosexuality. There was even a wiki page (that I now can’t find) laying out the “law” that the more a person sounds like they hate gays the more likely they are to be gay. At first this sounded appealing*, but then I applied the “not A” test: “if Mr. Far Wright’s sexual orientation is unknown and I heard him publicly declare that he loved homosexual behavior, how would I update the probability that he is gay?” In that case, it seems clear that I’d update it towards him being gay. Therefore, it doesn’t really make sense that when Mr. Wright does that opposite—publicly declaring that he hates homosexual behavior—I also update my probability that he is gay.
Or another recent example I had from talking with someone about Mormonism. Someone said that not having the golden plates available for inspection wasn’t really evidence against Joseph Smith’s story because there were several good reasons why they weren’t available. I was about to concede when I realized that a world where the golden plates were observable would be strong evidence for Joseph Smith’s story so a world where they aren’t has to be at least weak evidence against his story. If A moves the probability quite a bit one way, not A has to at least minimally move the probability the other way.
*Sometimes, if all I can observe, is a denial, it is evidence that the person is guilty. For example, if I walked through the door and the first thing I heard was my toddler denying to my wife that he took the candy, it increases my probability that he did take candy. But too my wife—who already has the evidence that led her to make the accusation—a denial is evidence against him taking the candy (it increases the relative odds that his brother did it instead).
Did I keep all of my reasoning here correct? If not, there might be a better way to express the idea with a Bayesian network.
Not-A for publicly declaring that one hates homosexual behavior isn’t “publicly declaring that one loves homosexual behavior”. It’s just “not publicly declaring that one hates homosexual behavior”. Your A-or-not-A has to cover all the possibilities, including remaining silently at home, awkwardly evading questions about homosexuality, making positive statements about heterosexuality but none directly about homosexuality, etc.
Just to finish your thought: Because of this, it’s possible that “A” and “the opposite of A” actually can both raise your estimate of p(B), even though “A” and “not A” can’t, as BlueSun stated.
That’s the rebuttal I thought about too. In particular, the heuristic “if someone is vocal against gays, they are likely to be gay” (whether or not it’s true) may arise in practice from the heuristic “if someone is vocal about gays, whether for or against, they are likely to be gay”.
That’s the rebuttal I thought about too. In particular, the heuristic “if someone is vocal against gays, they are likely to be gay” (whether or not it’s true) may arise in practice from the heuristic “if someone is vocal about gays, whether for or against, they are likely to be gay”.
I had the impression it arose from the heuristic “If someone makes a verbal status attack a low effort way to handle it is to attempt to reverse it”. See also the ingenious reply to “X” that is “Your mom X”.
This is what I was trying to avoid with my asterisk, i.e., just talking about stealing candy does raise the probability they stole the candy. But once they’re talking, confessing raises the probability they did it so not confessing should lower it.
On reflection, when my original question was designed to help make situations clearer, using an example that I felt I had to asterisk probably wasn’t wise.
just talking about stealing candy does raise the probability they stole the candy. But once they’re talking, confessing raises the probability they did it so not confessing should lower it.
Even if this is so, the total evidence that they’re talking + they’re denying may still raise the probability they stole the candy.
We rarely know that people express strong opinions about homosexuals, without also knowing what their opinions are. The difference with your example of the candy is that your wife initiated the talk with your son; your son didn’t come forward himself and declare out of the blue, “I am against stealing candy!”
How would I update my probabilities if I saw the opposite piece of evidence? What I’m trying to get at here is that “A” and “not A” can’t really be evidences for the same thing. And often it’s more obvious which way “not A” is pointing. A couple of examples:
I saw someone suggesting that maybe a certain Mr. Far Wright was secretly gay because, when the subject was broached, he had publicly expressed his dislike of homosexuality. There was even a wiki page (that I now can’t find) laying out the “law” that the more a person sounds like they hate gays the more likely they are to be gay. At first this sounded appealing*, but then I applied the “not A” test: “if Mr. Far Wright’s sexual orientation is unknown and I heard him publicly declare that he loved homosexual behavior, how would I update the probability that he is gay?” In that case, it seems clear that I’d update it towards him being gay. Therefore, it doesn’t really make sense that when Mr. Wright does that opposite—publicly declaring that he hates homosexual behavior—I also update my probability that he is gay.
Or another recent example I had from talking with someone about Mormonism. Someone said that not having the golden plates available for inspection wasn’t really evidence against Joseph Smith’s story because there were several good reasons why they weren’t available. I was about to concede when I realized that a world where the golden plates were observable would be strong evidence for Joseph Smith’s story so a world where they aren’t has to be at least weak evidence against his story. If A moves the probability quite a bit one way, not A has to at least minimally move the probability the other way.
*Sometimes, if all I can observe, is a denial, it is evidence that the person is guilty. For example, if I walked through the door and the first thing I heard was my toddler denying to my wife that he took the candy, it increases my probability that he did take candy. But too my wife—who already has the evidence that led her to make the accusation—a denial is evidence against him taking the candy (it increases the relative odds that his brother did it instead).
Did I keep all of my reasoning here correct? If not, there might be a better way to express the idea with a Bayesian network.
Not-A for publicly declaring that one hates homosexual behavior isn’t “publicly declaring that one loves homosexual behavior”. It’s just “not publicly declaring that one hates homosexual behavior”. Your A-or-not-A has to cover all the possibilities, including remaining silently at home, awkwardly evading questions about homosexuality, making positive statements about heterosexuality but none directly about homosexuality, etc.
Just to finish your thought: Because of this, it’s possible that “A” and “the opposite of A” actually can both raise your estimate of p(B), even though “A” and “not A” can’t, as BlueSun stated.
That’s the rebuttal I thought about too. In particular, the heuristic “if someone is vocal against gays, they are likely to be gay” (whether or not it’s true) may arise in practice from the heuristic “if someone is vocal about gays, whether for or against, they are likely to be gay”.
I had the impression it arose from the heuristic “If someone makes a verbal status attack a low effort way to handle it is to attempt to reverse it”. See also the ingenious reply to “X” that is “Your mom X”.
This is what I was trying to avoid with my asterisk, i.e., just talking about stealing candy does raise the probability they stole the candy. But once they’re talking, confessing raises the probability they did it so not confessing should lower it.
On reflection, when my original question was designed to help make situations clearer, using an example that I felt I had to asterisk probably wasn’t wise.
Even if this is so, the total evidence that they’re talking + they’re denying may still raise the probability they stole the candy.
We rarely know that people express strong opinions about homosexuals, without also knowing what their opinions are. The difference with your example of the candy is that your wife initiated the talk with your son; your son didn’t come forward himself and declare out of the blue, “I am against stealing candy!”