General Content

Deviance residuals are a model comparison tool, useful for both spatial and space-time point process models. Deviance residuals compare the log-likelihood between two models, within each bin. With deviance residuals one can see which forecast is performing better bin-by-bin. A residual greater than zero indicates places where model 1 if preferred, and a residual less than zero indicates places where model 2 is preferred. Summing up all of the deviance residuals provides a likelihood ratio score which indicates which forecast is performing better overall.

Pearson residuals can be used for both spatial and space-time point process models. The Pearson residual is a normalized version of the raw residual, which is defined simply as the number of points in a bin minus the expected number of points in that bin.

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 weighted L-function is a spatial test of goodness-of-fit of a spatial point process model. It is a centered and weighted version of Ripley's K-function, which is a popular statistic used to detect clustering or inhibition in spatial point patterns. The null hypothesis for the unweighted version assumes that the spatial point process is homogeneous Poisson, i.e. completely spatially random.

CSEP Testing Center Requirements for Model Submission

Please refer to the http://northridge.usc.edu/trac/csep/wiki/CSEPModelRequirements for online documentation.

Please contact John Yu (johnyu at usc dot edu) to request a login to the CSEP development server for model installation.