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We present here two self-consistent implementations of a short-term earthquake probability (STEP) model that produces daily seismicity forecasts for the area of the Italian national seismic network. Both implementations combine a time-varying and a time-invariant contribution, for which we assume that the instrumental Italian earthquake catalog provides the best information. For the time-invariant contribution, the catalog is declustered using the clustering technique of the STEP model; the smoothed seismicity model is generated from the declustered catalog. The time-varying contribution is what distinguishes the two implementations: 1) for one implementation (STEP-LG), the original model parameterization and estimation is used; 2) for the other (STEP-NG), the mean abundance method is used to estimate aftershock productivity. In the STEP-NG implementation, earthquakes with magnitude up to ML= 6.2 are expected to be less productive compared to the STEP-LG implementation, whereas larger earthquakes are expected to be more productive. We have retrospectively tested the performance of these two implementations and applied likelihood tests to evaluate their consistencies with observed earthquakes. Both of these implementations were consistent with the observed earthquake data in space: STEP-NG performed better than STEP-LG in terms of forecast rates. More generally, we found that testing earthquake forecasts issued at regular intervals does not test the full power of clustering models, and future experiments should allow for more frequent forecasts starting at the times of triggering events

Building self-consistent, short-term earthquake probability (STEP) models: improved strategies and calibration procedures