The average needs to fall, not the amplitude. If we’re looking at risk in percentage points (rather than, say, logits, which might be a better parametrisation), small average implies small amplitude, but small amplitude does not imply small average.
Agreed. I meant that, if the risk is usually quite low (e.g. 0.001 % per century), but sometimes jumps to a high value (e.g. 1 % per century), the cumulative risk (over all time) may still be significantly below 100 % (e.g. 90 %) if the magnitude of the jumps decreases quickly, and risk does not stay high for long.
The large magnitude is an observation—we have seen risk go from quite low to quite high over a short period of time. If we expect such large magnitude changes to be rare, then we might expect the present conditions to persist.
Why should we expect the present conditions to persist if we expect large magnitude changes to be rare?
Because we are more likely to see no big changes than to see another big change.
if the risk is usually quite low (e.g. 0.001 % per century), but sometimes jumps to a high value (e.g. 1 % per century), the cumulative risk (over all time) may still be significantly below 100 % (e.g. 90 %) if the magnitude of the jumps decreases quickly, and risk does not stay high for long.
I would call this model “transient deviation” rather than “random walk” or “regular oscillation”
Thanks for the clarifications!
Agreed. I meant that, if the risk is usually quite low (e.g. 0.001 % per century), but sometimes jumps to a high value (e.g. 1 % per century), the cumulative risk (over all time) may still be significantly below 100 % (e.g. 90 %) if the magnitude of the jumps decreases quickly, and risk does not stay high for long.
Why should we expect the present conditions to persist if we expect large magnitude changes to be rare?
Because we are more likely to see no big changes than to see another big change.
I would call this model “transient deviation” rather than “random walk” or “regular oscillation”