  We propose a new method to test the effectiveness of a spatial point process
forecast based on a log-likelihood score for predicted point density and the
information gain for events that actually occurred in the test period. The
method largely avoids simulation use and allows us to calculate the information
score for each event or set of events as well as the standard error of each
forecast. As the number of predicted events increases, the score distribution
approaches the Gaussian law. The degree of its similarity to the Gaussian
distribution can be measured by the computed coefficients of skewness and
kurtosis. To display the forecasted point density and the point events, we use
an event concentration diagram or a variant of the Error Diagram (ED).
  We demonstrate the application of the method by using our long-term forecast
of seismicity in two western Pacific regions. We compare the ED for these
regions with simplified diagrams based on two-segment approximations. Since the
earthquakes in these regions are concentrated in narrow subduction belts, using
the forecast density as a template or baseline for the ED is a more convenient
display technique. We also show, using simulated event occurrence, that some
proposed criteria for measuring forecast effectiveness at EDs would be strongly
biased for a small event number.
