Don has asked me to evaluate his forecast for Mammoth Lakes as
we would a typical forecast using the Jones technique and Monte Carlo
random simulations.
The specific daily prediction calls for an earthquake of 2.5-4.0 on a certain
day - the 21st of May, 2000. The window length of this prediction
is therefore 1 day and events with magnitude 2.5-4.0 will be
considered. The background period taken is usually one year prior
to the current date. This tests the prediction against current
seismicity in the area. Since May 21, 2000 there have been 38 days
on which an earthquake with 2.5<=ML<=4.0 has occurred within 32 km
of the predicted epicenter (23 days on which a Ml>=2.8 has occurred).
Because the distribution of these events is non-uniform we run
100 monte carlo random simulations to find the random distribution
of these Ml 2.5 days. We find that on average about 36.5 days would
have a random event of Ml>=2.5 and 22.5 days would have at least
one random event of Ml>=2.8. The probability that an event will
occur on a given day with Ml>=2.5 is then 36.5/365 = 0.1, in other
words odds of about 1 in 10. The probability that an event will
occur on a given day with Ml>=2.8 is 0.06 or odds of 1 in 16. The
second is near statistical significance, the first slightly less
than significance. In both cases, however, odds of 1 in 10 mean
that given 10 random guesses, you would be wrong 9 times, odds
of 1 in 16 means you would be wrong 15 of 16 times, right on only
one guess.