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Hypothesis testing and earthquake prediction
Pages 3772-3775

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From page 3772...
... In this example, we could consider the null hypothesis to be that earthquakes result from a Poisson process with a rate of r = 1.5/yr; the probability that at least one qualifying earthquake would occur at random is Single Prediction The simplest definition of earthquake prediction involves specification in advance of the time interval, region, and magnitude range in which a future earthquake is predicted to occur. To be meaningful, all of these ranges should be defined in such a way that any future earthquake could be objectively judged to be either inside or outside the range.
From page 3773...
... Most strong earthquakes occur within a fairly small fraction of the map, so that some success could be achieved simply by declaring TIPs at random times in the more active parts of the earth. A true test of the M8 algorithm requires a good null hypothesis that accounts for the spatial variability of earthquake occurrence.
From page 3774...
... The function ~ is often referred to in the statistical literature as the "conditional intensity," but I will use the notation "conditional rate density" to avoid confusion with the seismic intensity. The term "conditional" is used because earthquake prediction usually refers to a temporal increase in earthquake likelihood inferred from the existence of some special geophysical circumstance.
From page 3775...
... Choices for the smoothing kernel, the time interval, and the magnitude distribution may determine how well the null hypothesis represents future seismicity, just as similar decisions will affect the performance of the test hypothesis. In many areas of the world, available earthquake catalogs are insufficiently complete to allow an accurate estimate of the background rate.


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