78. Bird, P. [2018] Ranking some global forecasts with the
Kagan information score, *Seismol. Res. Lett., 89*(4), 1272-1276, doi:
10.1785/0220180029.

**Abstract**. The *Kagan*
[2009] information score *I*_{1} is a simple metric for the
relative success of the map patterns of any seismicity forecasts with the same
spatial extent and the same earthquake-selection rules. Because it does
not require declustering of either the forecast or the test catalog, it is
particularly appropriate for forecasts of total seismicity. Three years
of prospective testing have given consistent rankings of four global models of
shallow seismicity, demonstrating the expected superiority of the Global
Earthquake Activity Rate model v.1 (GEAR1) hybrid forecast relative to its
smoothed seismicity and tectonic parent forecasts. Accumulation of *I*_{1}
scores and their covariances over a number of consecutive test periods
naturally leads to estimated significance of each ranking, so continuing
testing is desirable.

** P.S.** For a full explanation of these models (especially
GEAR1), see my paper #69

Figure 1. Example of *I*_{1}
scoring of long-term forecast Global Earthquake Activity Rate model v.1 (GEAR1)
in the year 2016. Epicentroid rate densities (top color bar) are
converted to base-2 logarithms of the dimensionless ratio of rate densities
(see equation 1). This value (bottom color bar), sampled at the test earthquake
epicentroid, is its contribution to the *I*_{1} score; the
final score is obtained by averaging over all 196 test earthquakes. CMT,
Centroid Moment Tensor.

Figure 2. Cumulative distribution
functions (CDFs) of per-earthquake contributions to *I*_{1}
(equation 1; here referred to as *x*), before averaging, for each of the
four global models in 2016. Each CDF has 196 steps, for the 196 test
earthquakes in that year. Better performance is indicated by a CDF curve
which is further to the right. This graph shows that, in 2016, GEAR1
outperformed the other models along most parts of the curve, with two
exceptions: SHIFT_GSRM2f was better in one low-seismicity region (1.9 < *x*
< 2.7), and smoothed seismicity was better in the highest-seismicity regions
(*x* > 6.3). Abbreviations: SHIFT, Seismic Hazard Inferred from
Tectonics; GSRM, Global Strain Rate Map.