9:30 AM - 9:45 AM
[SSS03-03] Evaluating earthquake forecasting models with likelihood based marginal and conditional scores
Keywords:point-process model, earthquake forecasting, forecast evaluation, likelihood
Vere-Jones (1998, Computational Geoscience) proposed the general process of earthquake probability forecasting by using point-process models: First, the entire forecasting period is divided into many small time intervals with length Δt. Second, for each time interval seismicity is simulated by using the forecasting model and observations in the past. Then, the probability of earthquake occurrence is the proportion of the simulations with events occurring in all the simulations. He also proposed the likelihood based binary and Poisson scores for evaluating the forecast performance against some reference models.
To evaluate different aspects in the forecasting performance of a model or a method, in CSEP testing centers, the N-, M-, R-, S-, and T-tests have been adopted to test different aspects of the earthquake forecasts in a gridded space-time range. Likelihood based topical scores was proposed by Ogata et al (2015, BSSA) using the Poisson assumptions together with an assumption on each cell of approximation. In this talk, I will show how to use the point-process likelihood directly to evaluate different aspects of the forecast performance: marginal and conditional scores. These scores include: Numbers, occurrence times, occurrence locations, event magnitudes, correlation among different space-time-magnitude cells.
The results show:
For a fully specified point process model like the ETAS model, the correspondence of N-, T-, L-, and M-tests can be implemented in a rigorous manner according to the likelihood function. We should take special care when calculating the ratio between two small probabilities. Gridding in space, such as in the CSEP tests, unnecessarily increases the complexity of the testing problem. Giving it and evaluating spatial forecasting performance directly the marginal likelihood seems to be a more promising option.
To evaluate different aspects in the forecasting performance of a model or a method, in CSEP testing centers, the N-, M-, R-, S-, and T-tests have been adopted to test different aspects of the earthquake forecasts in a gridded space-time range. Likelihood based topical scores was proposed by Ogata et al (2015, BSSA) using the Poisson assumptions together with an assumption on each cell of approximation. In this talk, I will show how to use the point-process likelihood directly to evaluate different aspects of the forecast performance: marginal and conditional scores. These scores include: Numbers, occurrence times, occurrence locations, event magnitudes, correlation among different space-time-magnitude cells.
The results show:
For a fully specified point process model like the ETAS model, the correspondence of N-, T-, L-, and M-tests can be implemented in a rigorous manner according to the likelihood function. We should take special care when calculating the ratio between two small probabilities. Gridding in space, such as in the CSEP tests, unnecessarily increases the complexity of the testing problem. Giving it and evaluating spatial forecasting performance directly the marginal likelihood seems to be a more promising option.