Figure 2

Distribution of the number of events and of likelihoods for ETAS simulations. Contour plot of probability density as a function of time interval T _i of the number of events and likelihood for the first ETAS Japanese simulated catalog. (a) Contour plot of probabilities $q_n^i$ predicted by Poisson hypothesis Hyp₂. Solid black line marks the observed number of events. Dashed black lines mark the 2.5th and 97.5th percentiles of distribution. (b) The same as (a) but for the distribution expected by ETAS model. Specifically, dotted lines mark the values $P_{\text{ETAS},i}^{\Omega }\left[2.5\%\right]$ and $P_{\text{ETAS},i}^{\Omega }\left[97.5\%\right]$. (c) Contour plot of PDF of log-likelihoods L(Ω _i |Λ) predicted by Poisson hypothesis Hyp₂ (Equation 4). Solid black line marks the observed log-likelihoods. Dashed black lines mark the 5.0th percentile expected by Poisson distribution. (d) The same as (c) but for the CLF (see Equation 8). Solid black line marks the observed values CLF_ETAS,i. Dotted black line marks the percentile $P_{\text{ETAS},i}^{\text{CLF}}\left[5.0\%\right]$.