Regional Earthquake Likelihood Models II: Information Gains of Multiplicative Hybrids

Abstract

The Regional Earthquake Likelihood Models experiment in California tested the performance of earthquake likelihood models over a five-year period. First-order analysis showed a smoothed-seismicity model by Helmstetter et al. (2007) to be the best model. We construct optimal multiplicative hybrids involving the best individual model as a baseline and one or more conjugate models. Conjugate models are transformed using an order-preserving function. Two parameters for each conjugate model and an overall normalizing constant are fitted to optimize the hybrid model. Many two-model hybrids have an appreciable information gain (log probability gain) per earthquake relative to the best individual model. For the whole of California, the Bird and Liu (2007) ) and PI models as conjugates. The information gains of the best multiplicative hybrids are greater than those of additive hybrids constructed from the same set of models. The gains tend to be larger when the contributing models involve markedly different concepts or data. These results need to be confirmed by further prospective tests. Multiplicative hybrids will be useful for assimilating other earthquake-related observations into forecasting models and for combining forecasting models at all timescales.

A Spatiotemporal Clustering Model for the Third Uniform California Earthquake Rupture Forecast (UCERF3‐ETAS): Toward an Operational Earthquake Forecast

“…As mentioned, the model that specifies the longterm rate of smaller earthquakes in UCERF3-ETAS has demonstrated skill in the formal prospective tests conducted by the Collaboratory for the Study of Earthquake Predictability (CSEP, Helmstetter et al, 2007;Zechar et al, 2013;Helmstetter and Werner, 2014;Rhoades et al, 2014). However, we had to change these rates near several faults (via the ApplyGridSeisCorr parameter; Fig.…”

Accounting for Epistemic Uncertainty in PSHA: Logic Tree and Ensemble Modeling

“…The sample fθ z i ; ω i g can either stem from one or more logic trees or from a collection of models (hereafter, the term "model" means either an independent model or a final branch of a logic tree); the only requirement is that fθ z i ; ω i g represents an unbiased sample of the epistemic uncertainty. The models' output may be correlated, and the weight attached to each model should properly take into account not only the confidence on each model (based on expert opinion and/or on quantitative evaluation of the forecasting performances), but also the possible strong correlation with other models (Marzocchi et al, 2012;Rhoades et al, 2014).…”

Intermediate‐term forecasting of aftershocks from an early aftershock sequence: Bayesian and ensemble forecasting approaches

“…In addition to the forecasting from each magnitude frequency model, we also examine the performance of an ensemble forecasting that combines the two forecasts from these models. Ensemble forecasting has been implemented in some studies for probabilistic earthquake forecasting [e.g., Gerstenberger et al, ; Marzocchi et al, ; Helmstetter and Werner, ; Rhoades et al, ]. Akaike [] suggested that natural weighting of each forecast is proportional to the factor exp[ln L ( X learn ) − p ], where L ( X learn ) and p are the likelihood function and the number of model parameters, respectively.…”