# How Useful Are Strain Rates for Estimating the Long-Term Spatial Distribution of Earthquakes?
## 3 Results  
### Hybrid Models  
IGPE estimates and 95% confidence intervals of the hybrid models with BSS for the fitting period (1987-2006), forward testing period (2012-2015), and reverse testing period (1951-1986) are presented in Figure 3. Corresponding results with GSS and HWS are presented in Figures 4 and 5, respectively. The IGPEs are relative to the SUP baseline model. To compare the IGPEs of two hybrid models, one needs to obtain the differences between their log-likelihoods for the target earthquakes and perform a \(T\)-test on those differences. In this study, we have only presented \(T\)-tests for comparing each hybrid model to the baseline model. The combination of covariates contributing to each hybrid is indicated by a model number composite. This composite combines the baseline model identifier with those of the selected covariates: \"1\" for SUP, \"2\" for PPI, \"3\" for PMF, \"4\" for FLT, and \"5\" for strain rate covariate (BSS, GSS, or HWS). Table 1 contains the name, acronym, and identifier for the baseline model and covariates. For example, the composite \"123\" represents a hybrid with SUP as baseline and PPI and PMF as covariates. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Covariate or Model Name** & **Acronym** & **Identifier** \\ \hline Stationary uniform Poisson baseline model & SUP & \({}^{\prime\prime}1^{\prime\prime}\) \\ Proximity to plate interface covariate & PPI & \({}^{\prime\prime}2^{\prime\prime}\) \\ Proximity to mapped faults covariate & PMF & \({}^{\prime\prime}3^{\prime\prime}\) \\ Fault in cell covariate (binary) & FLT & \({}^{\prime\prime}4^{\prime\prime}\) \\ Beavan shear strain rate covariate & BSS & \({}^{\prime\prime}5^{\prime\prime}\) \\ Global shear strain rate covariate & GSS & \({}^{\prime\prime}5^{\prime\prime}\) \\ Haines and Wallace shear strain rate covariate & HWS & \({}^{\prime\prime}5^{\prime\prime}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Name, acronym, and identifier for the baseline model and covariates. Figure 4: Information gain per earthquake (IGPE) of hybrid models relative to SUP baseline model with the GSS strain rate covariate. The combination of covariates contributing to each hybrid is indicated by the model number, which is a composite of the numbers corresponding to the baseline model and selected covariates, as follows: 1-SUP; 2-PPI; 3-PMF; 4-FLT; 5-GSS. **(a)** Fitting period (1987–2006); **(b)** Forward testing period (2012–2015); **(c)** Reverse testing period (1951–1986). Error bars are 95% confidence intervals. Figure 3: Information gain per earthquake (IGPE) of hybrid models relative to SUP baseline model with the Beavan shear strain rate (BSS) covariate. The combination of covariates contributing to each hybrid is indicated by the model number, which is a composite of the numbers corresponding to the baseline model and selected covariates, as follows: 1-SUP; 2-PPI; 3-PMF; 4-FLT; 5-BSS. **(a)** Fitting period (1987–2006); **(b)** Forward testing period (2012–2015); **(c)** Reverse testing period (1951–1986). Error bars are 95% confidence intervals. Results for the fitting and forward testing period with the BSS covariate were previously reported by [PERSON] et al. [11] and showed that the IGPE was higher for all hybrid models including BSS than for all models not including BSS. Here, with modified non-strain-rate covariates for the fitting period (Figure 3a), all hybrids including BSS (composites containing \"5\") have IGPE > 1.1. The largest IGPE is 1.48 for \"1345\". On the other hand, all hybrids excluding BSS have IGPE < 1.1. For these, the largest IGPE is 1.00 for \"134\". When the BSS covariate is replaced by either GSS (Figure 4a) or HWS (Figure 5a), the results for the fitting period are different. With BSS, \"15\" (SUP + BSS) has the largest IGPE amongst all the simple hybrids. However, with GSS and HWS, \"13\" (SUP + PMF) outperforms \"15\". However, similar to BSS, the largest IGPE values for GSS and HWS are obtained for \"1345\" (1.08 and 1.01, respectively).