The spatial variability of the magnitude–frequency distribution is important to improve earthquake forecasting capabilities at different time scales. Here, we develop a novel approach, based on the weighted maximum‐likelihood estimation, to build a spatial model for the $b$‐value parameter of the Gutenberg–Richter law and its uncertainty, also for earthquake catalogs with a time‐varying completeness magnitude. Then, we also provide a guideline based on the Bayes factor to measure the importance of the $b$‐value spatial variability with respect to a model having a spatially uniform $b$‐value. Finally, we apply the procedure to a new Italian instrumental earthquake catalog from 1960 to 2019 to investigate the $b$‐value spatial variability over the Italian territory.

We consider a seismicity forecast experiment conducted during the last 4 yr. At the beginning of each year, three models make a 1-yr forecast of the distribution of large earthquakes everywhere on the Earth. The forecasts are generated and the observations are collected in the Collaboratory for the Study of Earthquake Predictability (CSEP). We apply CSEP likelihood measures of consistency and comparison to see how well the forecasts match the observations, and we compare results from some intuitive reference models. These results illustrate some undesirable properties of the consistency tests: the tests can be extremely sensitive to only a few earthquakes, and yet insensitive to seemingly obvious flaws—a naïve hypothesis that large earthquakes are equally likely everywhere is not always rejected. The results also suggest that one should check the assumptions of the so-called T and W comparison tests, and we illustrate some methods to do so. As an extension of model assessment, we explore strategies to combine forecasts, and we discuss the implications for operational earthquake forecasting. Finally, we make suggestions for the next generation of global seismicity forecast experiments.

We introduce a novel approach to estimate the temporal variation of the b-value parameter of the Gutenberg–Richter law, based on the weighted likelihood approach. This methodology allows estimating the b-value based on the full history of the available data, within a data-driven setting. We test this methodology against the classical “rolling window” approach using a high-definition Italian seismic catalogue as well as a global catalogue of high magnitudes. The weighted likelihood approach outperforms competing methods, and measures the optimal amount of past information relevant to the estimation.

We develop a long‐term (a few decades or longer) earthquake rate forecast for Italy based on smoothed seismicity for incorporation in the 2017–2018 Italian Probabilistic Seismic Hazard Maps (IPSHM). Because the earthquake rate models from previous IPSHM were computed using source zones that were drawn around seismicity and tectonic provinces, the present model will be the first introduction of the smoothed seismicity method into the IPSHM. Smoothed seismicity models are constructed from both historical CPTI15 (Catalogo Parametrico dei Terremoti Italiani, 1000–2014) and instrumental (1981–2016) earthquake catalogs and use both fixed and adaptive smoothing methods. We compute spatial likelihood values comparing the spatial distribution of observed earthquakes with a suite of trial earthquake rate models to optimize smoothing parameters and catalogs. Then we produce an ensemble model using two different smoothing models (adaptive and fixed) and two earthquake catalogs (historical and instrumental), which are weighted equally through a logic‐tree approach to improve the forecast capability. We also compare our optimized smoothed seismicity models with the best two models of the Italian Collaboratory for the Study of Earthquake Predictability (CSEP) experiment and retrospectively test them with the CSEP methodology. We observed that the ensemble model performs slightly better than the optimized fixed and the adaptive smoothing seismicity models obtained in this study and the best time‐independent model of the CSEP Italian experiment. The preferred ensemble model forecasts an annual rate of 1.47 $M≥5.0$ earthquakes, with higher rates mainly concentrating along the Apennines chain, eastern Alps, Calabria, and northeast Sicily. Finally, six ensemble models are created from the different smoothing methods using different weights through a logic‐tree approach to estimate the uncertainty associated with the model.

Volcanic activity typically switches between high-activity states with many eruptions and low-activity states with few or no eruptions. We present a simple two-regime physics-informed statistical model that allows interpreting temporal modulations in eruptive activity. The model enhances comprehension and comparison of different volcanic systems and enables homogeneous integration into multivolcano hazard assessments that account for potential changes in volcanic regimes. The model satisfactorily fits the eruptive history of the three active volcanoes in the Neapolitan area, Italy (Mt. Vesuvius, Campi Flegrei, and Ischia) which encompass a wide range of volcanic behaviors. We find that these volcanoes have appreciably different processes for triggering and ending high-activity periods connected to different dominant volcanic processes controlling their eruptive activity, with different characteristic times and activity rates (expressed as number of eruptions per time interval). Presently, all three volcanoes are judged to be in a low-activity state, with decreasing probability of eruptions for Mt. Vesuvius, Ischia, and Campi Flegrei, respectively.

The estimation of the magnitude of completeness for a seismic catalog is the starting point for most of the seismological statistical analyses. It is important, in particular, for the estimation of the Gutenberg–Richter (GR) law parameters. This law corresponds to an exponential distribution of the magnitudes. The recent studies have shown that the proper method to estimate the completeness is to check the exponentiality of the data. Here, we try to improve this method using a simple random variable transformation, which makes the method more robust in the case of catalogs with magnitudes coming from exponential distributions with different parameters, that is, catalogs with different b‐values of the GR law.