The Super-thinned residuals (RT) test

Super-thinning is a residual analysis method for space-time point process models, which combines thinning and superposition. The observed earthquakes are each deleted with probability inversely proportional to the estimated intensity at that time and location. In addition, new simulated points are superposed, at a high rate where the modeled intensity is low and at a low rate where the modeled intensity is high. A single tuning parameter, k, controls the amount of thinning and superposition. The result, called super-thinned residuals, should be homogeneous Poisson, with approximately k points, if and only if the modeled rate is correct. Patterns, such as clustering, inhibition, or trends in the residuals indicate lack of fit of the model. Locations where one observes a significantly high number of points or unusually few points in the super-thinned residuals indicate places where the model appears to underestimate or overestimate, respectively, the rate of seismicity. In addition, if the total number of residuals is significantly greater or less than k, this indicates global underestimation or overestimation, respectively, of the rate by the model.