Can we be sure that he did not just assign a very strong prior distribution to the existence of Fifth Column? In that case, if we model Warren’s decision as binary hypothesis testing with a MAP rule, say, then maybe it occurred to Warren that the raw conditional probabilities satisfied this inequality P(no sabotage | imminent Fifth Column threat) < P(no sabotage | no imminent Fifth Column threat).
But perhaps, for Warren, P(imminent Fifth Column threat) >> P( no imminent Fifth Column threat).
In this scenario, he reasoned that it was so likely that there was a Fifth Column threat that it outweighed the ease with which (absence of Fifth Column) can account for (absence of sabotage), and led him to choose the hypothesis that a Fifth Column was a better explanation for lack of sabotage.
In that case, the issue becomes the strength in the prior belief. Similar reasoning can be applied to McCarthy, or to those suggesting we’re due for another terrorist attack.
I guess what I am saying is like this: maybe someone just believes we’re due for another terrorist attack very strongly (perhaps for irrational reasons, but reasons that have nothing to do with a witnessed lack of terrorist attacks). Then you present them with the evidence that no terrorist activity has been witnessed, say. Instead of this updating their prior to a better posterior that assigns less belief to imminence of terrorist attacks, they actually feel capable of explaining the absence of terrorist activities in light of their strong prior.
I do agree that it would then be nonsensical to take that conclusion and treat it like a new observation. As if: Fifth Column → they absolutely must exist and be planning something → invent a reason why strength of belief in prior is justified → Fifth Column’s existence explains absence of sabotage → further absence of sabotage now feeds back as ever-more-salient corroborating evidence of original prior.
Perhaps more focus should be placed on the role of the prior in all of this, rather than outright misinterpretations of evidence.
Can we be sure that he did not just assign a very strong prior distribution to the existence of Fifth Column? In that case, if we model Warren’s decision as binary hypothesis testing with a MAP rule, say, then maybe it occurred to Warren that the raw conditional probabilities satisfied this inequality P(no sabotage | imminent Fifth Column threat) < P(no sabotage | no imminent Fifth Column threat).
But perhaps, for Warren, P(imminent Fifth Column threat) >> P( no imminent Fifth Column threat).
In this scenario, he reasoned that it was so likely that there was a Fifth Column threat that it outweighed the ease with which (absence of Fifth Column) can account for (absence of sabotage), and led him to choose the hypothesis that a Fifth Column was a better explanation for lack of sabotage.
In that case, the issue becomes the strength in the prior belief. Similar reasoning can be applied to McCarthy, or to those suggesting we’re due for another terrorist attack.
I guess what I am saying is like this: maybe someone just believes we’re due for another terrorist attack very strongly (perhaps for irrational reasons, but reasons that have nothing to do with a witnessed lack of terrorist attacks). Then you present them with the evidence that no terrorist activity has been witnessed, say. Instead of this updating their prior to a better posterior that assigns less belief to imminence of terrorist attacks, they actually feel capable of explaining the absence of terrorist activities in light of their strong prior.
I do agree that it would then be nonsensical to take that conclusion and treat it like a new observation. As if: Fifth Column → they absolutely must exist and be planning something → invent a reason why strength of belief in prior is justified → Fifth Column’s existence explains absence of sabotage → further absence of sabotage now feeds back as ever-more-salient corroborating evidence of original prior.
Perhaps more focus should be placed on the role of the prior in all of this, rather than outright misinterpretations of evidence.