0.00002 would be one in five hundred thousand, but with the percent sign it’s one in fifty million.
Indeed, even on basic Bayesianism, volatility is fine as long as the averages work out
I agree with this as far as the example given, but I want to push back on oscillation (in the sense of regularly going from one estimate to another) being Bayesian. In particular, the odds you should put on assigning 20% in the future, then 30% after that, then 20% again, then 30% again, and so on for ten up-down oscillations, shouldn’t be more than half a percent, because each 20 → 30 jump can be at most 2⁄3 probable and each 30 → 20 jump at most 7⁄8 (and (23⋅78)10≈0.0047).
So it’s fine to think that you’ve got a decent chance of having all kinds of credences in the future, but thinking “I’ll probably feel one of two ways a few times a week for the next year” is not the kind of belief a proper Bayesian would have. (Not that I think there’s an obvious change to one’s beliefs you should try to hammer in by force, if that’s your current state of affairs, but I think it’s worth flagging that something suboptimal is going on when this happens.)
0.00002 would be one in five hundred thousand, but with the percent sign it’s one in fifty million.
I agree with this as far as the example given, but I want to push back on oscillation (in the sense of regularly going from one estimate to another) being Bayesian. In particular, the odds you should put on assigning 20% in the future, then 30% after that, then 20% again, then 30% again, and so on for ten up-down oscillations, shouldn’t be more than half a percent, because each 20 → 30 jump can be at most 2⁄3 probable and each 30 → 20 jump at most 7⁄8 (and (23⋅78)10≈0.0047).
So it’s fine to think that you’ve got a decent chance of having all kinds of credences in the future, but thinking “I’ll probably feel one of two ways a few times a week for the next year” is not the kind of belief a proper Bayesian would have. (Not that I think there’s an obvious change to one’s beliefs you should try to hammer in by force, if that’s your current state of affairs, but I think it’s worth flagging that something suboptimal is going on when this happens.)
Re: “0.00002 would be one in five hundred thousand, but with the percent sign it’s one in fifty million.”—thanks, edited.
Re: volatility—thanks, that sounds right to me, and like a potentially useful dynamic to have in mind.