Hi all;

Here's a test;

Read the quotes listed below and then tell me if you agree that a random distribution is the correct null hypothesis to use in evaluating predictions.

Roger

Article #1 quote
http://geology.fullerton.edu/faculty/dbowman/nsf2001textframe.html
Based on the number of events and the quality of the curve fits it was shown that the null hypothesis, that purely random clustering could generate the observed acceleration in seismicity, could be rejected at greater than 95% confidence.

Article #2 quote
http://scec.ess.ucla.edu/~yfrong/research/china/proposal.htm
3.1.2 Statistical testing
Statistical testing is a powerful key to examine the reliability of a forecast.
Since the earthquake potentials are formulated in terms of the number of
qualifying earthquakes that each area would experience given the space and time
windows, from this point of view, it is easy to test the forecast statistically.
However, if we want to do a rigorous forward testing, we have to wait until the
forecasting time is matured. For small earthquakes , it can be done in a few
years, since these events are frequent. But testing for larger events will take
much longer, and such a test is very important because the relationship of small
to large earthquake rates is fundamental to each hypothesis. Obviously, this
long time scale brings us big difficulty for testing the hypothesis.
Retrospective testing is not adequate, but it is important nevertheless. We must
show that each hypothesis is at least consistent with past data, and
retrospective testing helps to identify issues for prospective testing. In this
study, the earthquake catalog between Jan. 1950 to Dec. 1999 is used to estimate
the earthquake potential. We can apply a ˇ°pseudo-forwardˇ± test by testing the
forecast against the earthquakes occurred after Dec. 1999.
We employ two different tests to evaluate the forecast based on smoothed
seismicity. In each case, we define a statistic (a measurable feature of the
earthquake catalog), simulate synthetic records for the hypotheses, compute the
defined statistic for both the observed and simulated earthquake records, and
compare the observed statistic with the simulated values. To test the
consistency of a hypothesis with the data, we ask if the observed statistic
falls safely within the range of values for records simulated assuming that
hypothesis. If so, we judge that the observed catalog ˇ°looks likeˇ± those that
satisfy the hypothesis by construction; otherwise we reject the hypothesis as an
explanation for the observed record. To simulate earthquake records consistent
with a given hypothesis, we generate a suite of random numbers between 0 to1.
Then we compare those numbers with the rate of earthquakes that the forecast
provides. The test is based only on the first quake in each area. Clustering is
not built into the model, but the test recognizes clustering in a very
approximate way, because it does not count aftershocks in a given cell as if
they were fresh quakes. Thus, if the random number is less than the rate, we
consider there is one earthquake occurs in that area in the synthetic catalog.
Otherwise, we assume there is no earthquake in the area. We will apply a
two-tailed test at the 95% confidence level, rejecting a hypothesis if the
observed number of events is either too small or too large compared to the
predicted value. Therefore, we will reject a hypothesis if fewer than 2.5% or
more than 97.5% of the simulations have number of earthquakes less than or equal
to the observed value.

Article #3 quote
http://www.ingv.it/~wwwpaleo/pantosti/abstracts/EGSConsole.htm
Sets of paleoseimologically dated earthquakes have been established for some faults in
the Mediterranean area: the Irpinia fault in southern Italy, the Fucino fault in
central Italy, The El Asnam fault in Algeria and the Skinos fault in central
Greece. By using the age of the paleoearthquakes with their associated
uncertainty we have computed, through a Montecarlo procedure, the probability
that the observed interevent times come from a uniform random distribution (null
hypothesis). This probability is estimated approximately equal to 8.4% for the
Irpinia fault, 0.5% for the Fucino fault, 49% for the El Asnam fault and 42% for
the Skinos fault. So, the null Poisson hypothesis can be rejected with a
confidence level of 99.5% for the Fucino fault, but it can be rejected only with
a confidence level between 90% and 95% for the Irpinia fault, while it can not
be rejected for the other two cases.

Article #4 quote
http://www.seismo.demon.co.uk/Nov7th/stark.html
Starks's AbstractThe Null Hypothesis
Philip B. Stark
Department of Statistics
University of California
Berkeley, CA 94720-3860
USA
email: stark@stat.berkeley.edu

The hypothesis that an earthquake prediction scheme works is often tested by
examining a null hypothesis, that the "successful" predictions can be explained
by chance coincidence. The details of the probability model for coincidental,
successful predictions are important, but insufficient attention is drawn to
them. For example, if the chance model under the null hypothesis is that
earthquakes occur according to a Poisson process in space and time, with known,
spatially varying intensity, the null hypothesis could be rejected not because
the prediction scheme is successful, but because earthquakes do not follow that
probability law (for example, because of precursors and aftershocks). An example
where such a "straw man" null hypothesis leads to erroneous conclusions about
the success of a prediction scheme will be presented, along with other
geophysical examples.
An alternative approach is to consider the seismicity to be fixed, and to
compare the success rate of the prediction scheme in question to that of a
random prediction scheme. Because the probability model for the random
prediction scheme is under the control of the experimenter, the chance of an
erroneous rejection of the null hypothesis can be calculated.
The random rule should be causal; i.e., it can use information from the past
only in predicting future events. Subject to that restriction, any function of
the seismicity (or other variables) is acceptable. This approach also
corresponds to the intuitive idea that, to be useful, a prediction scheme should
perform better than a naive rule, such as predicting that large events will have
aftershocks.

Atricle #5 quote
Hypothesis testing and earthquake prediction
DAVID D. JACKSON
Southern California Earthquake Center, University of California, Los Angeles, CA 90095-1567
http://www.nap.edu/books/0309058376/html/3772.html

One can then compare the observed earthquake record (in this case, the occurrence or not of a qualifying earthquake) with the probabilities for either case according to a ‘‘null hypothesis,’’ that earthquakes occur at random, at a rate determined by past behavior. In this example, we could consider the null hypothesis to be that earthquakes result from a Poisson process with a rate of r 5 1.5yyr; the probability that at least one qualifying earthquake would occur at random is

p0 5 1 2 exp(2r*t).
For r 5 1.5yyr and t 5 1 yr,p0 5 0.78.

What can be said if a prediction is not satisfied? In principle, one could reject the prediction and the theory behind it. In practice, few scientists would completely reject a theory for one failure, no matter how embarrassing. In some cases, a probability is attached to a simple prediction; for the Parkfield, California, long-term prediction (1), this probability was taken to be 0.95. In such a case the conclusions that can be drawn from success depend very much on the background probability, and only weak conclusions can be drawn from failure. In the Parkfield case, the predicted event was never rigorously defined, but clearly no qualifying earthquake occurred during the predicted time interval (1983–1993). The background rateof Parkfield earthquakes is usually taken to be 1y22 yr; for t 5 10 yr, p0 5 0.37. Thus, a qualifying earthquake, had it
occurred, would not have been sufficient evidence to reject the Poissonian null hypothesis.

Article #6 quote
http://www.nature.com/nature/debates/earthquake/
Rather than debating whether or not reliable and accurate earthquake
prediction is possible, we should instead be debating the extent to which
earthquake occurrence is stochastic. Since it appears likely that earthquake
occurrence is at least partly stochastic (or effectively stochastic), efforts at
achieving deterministic prediction seem unwarranted.

We should instead be searching for reliable statistical methods for
quantifying the probability of earthquake occurrence as a function of space,
time, earthquake size, and previous seismicity. The case study approach to
earthquake prediction research should be abandoned in favour of the objective
testing of unambiguously formulated hypotheses. In view of the lack of proven
forecasting methods, scientists should exercise caution in issuing public
warnings regarding future seismic hazards. Finally, prediction proponents should
refrain from using the argument that prediction has not yet been proven to be
impossible as justification for prediction research.

Robert J. Geller
Department of Earth and Planetary Physics,
Graduate School of Science,
Tokyo University,
Bunkyo, Tokyo 113-0033,
Japan.
bob@global.geoph.s.u-tokyo.ac.jp