Here is another illustration of how catastrophe-censoring gives bad results.
Suppose you ask me when I expect (say) the first human to set foot on another planet. And suppose I think that this is likely to happen in 50 years’ time if everything goes well, but that there’s some class of Bad Thing that might happen that would delay it—economic disaster, pandemic, environmental collapse, etc. Now, imagine what happens as we ramp up the severity I think this Bad Thing would have, while keeping everything else constant. My estimate of that date will get later and later, as it obviously should … until the point where the Bad Thing counts as a catastrophe, when (if we’re conditioning on no catastrophe) suddenly my estimated date gets much earlier because now the possible worlds where the Bad Thing happens are being excluded from consideration.
(With a more realistic model of Bad Things, rather than a nice monotonic increase followed by an absurd backward jump we get some more complicated curve that eventually turns downward. But it’s the same problem.)
Here is another illustration of how catastrophe-censoring gives bad results.
Suppose you ask me when I expect (say) the first human to set foot on another planet. And suppose I think that this is likely to happen in 50 years’ time if everything goes well, but that there’s some class of Bad Thing that might happen that would delay it—economic disaster, pandemic, environmental collapse, etc. Now, imagine what happens as we ramp up the severity I think this Bad Thing would have, while keeping everything else constant. My estimate of that date will get later and later, as it obviously should … until the point where the Bad Thing counts as a catastrophe, when (if we’re conditioning on no catastrophe) suddenly my estimated date gets much earlier because now the possible worlds where the Bad Thing happens are being excluded from consideration.
(With a more realistic model of Bad Things, rather than a nice monotonic increase followed by an absurd backward jump we get some more complicated curve that eventually turns downward. But it’s the same problem.)