- If we expect regular oscillation or time symmetric random walks, then I think we usually get H3 (integrated oscillation = high risk; the lack of risk in the past suggests that period of oscillation is long)
We can still get H4 if the amplitude of the oscillation or random walk decreases over time, right?
- If we expect rare, sudden changes then we get H3
Only if the sudden change has a sufficiently large magnitude, right?
We can still get H4 if the amplitude of the oscillation or random walk decreases over time, right?
The average needs to fall, not the amplitude. If weāre 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.
Only if the sudden change has a sufficiently large magnitude, right?
The large magnitude is an observationāwe 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.
The average needs to fall, not the amplitude. If weāre 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 observationāwe 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 ātransient deviationā rather than ārandom walkā or āregular oscillationā
Hi David,
We can still get H4 if the amplitude of the oscillation or random walk decreases over time, right?
Only if the sudden change has a sufficiently large magnitude, right?
The average needs to fall, not the amplitude. If weāre 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.
The large magnitude is an observationāwe 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.
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 ātransient deviationā rather than ārandom walkā or āregular oscillationā