If something would be equally certain in two cases it can fundamentally constitute no evidence at all, even in the Bayesian sense. Suppose the three alternatives are Honest administrators, business as Usual, and Deep state. We observe some Bribes. Then P(B|U)=P(B|D)=1 and P(B|H)=0. Given appropriate priors then, P(B)=P(U)+P(D). And therefore
P(D|B)=P(D)P(D)+P(U)
We haven’t really updated at all our odds of Deep state being the explanation instead of business as Usual. We have ruled out the Honest hypothesis but I didn’t have many illusions about that. It’s a fairly extreme perspective—you could get a tiny update if you posited that P(B|U) is slightly lower than 1 or whatever—but I think for all practical matters it does round up to this calculation.
Yes, if you assume that the probability of seeing an observation was 100% under your favorite model then seeing it doesn’t update you away from that model, but that assumption is obviously not true. (And I already conceded that the update is marginal!)
If something would be equally certain in two cases it can fundamentally constitute no evidence at all, even in the Bayesian sense. Suppose the three alternatives are Honest administrators, business as Usual, and Deep state. We observe some Bribes. Then P(B|U)=P(B|D)=1 and P(B|H)=0. Given appropriate priors then, P(B)=P(U)+P(D). And therefore
P(D|B)=P(D)P(D)+P(U)
We haven’t really updated at all our odds of Deep state being the explanation instead of business as Usual. We have ruled out the Honest hypothesis but I didn’t have many illusions about that. It’s a fairly extreme perspective—you could get a tiny update if you posited that P(B|U) is slightly lower than 1 or whatever—but I think for all practical matters it does round up to this calculation.
Yes, if you assume that the probability of seeing an observation was 100% under your favorite model then seeing it doesn’t update you away from that model, but that assumption is obviously not true. (And I already conceded that the update is marginal!)
I’d say the probability of seeing some resistance or corruption in virtually any administration is damn close to 100%.