Facing Missing Observations in Data—A New Approach for Estimating Strength of Earthquakes on the Pacific Coast of Southern Mexico Using Random Censoring

Abstract

We introduced a novel spatial model based on the distribution of generalized extreme values (GEV) to analyze the maximum intensity levels of earthquakes with incomplete data (randomly censored) on the Pacific coast of southern Mexico using a random censorship approach. Spatiotemporal trends were modeled through a non-stationary GEV model. We used a multivariate smoothing function as a linear predictor of GEV parameters to approximate nonlinear trends. The model was fitted using a flexible semi-parametric Bayesian approach and the parameters are estimated via Markov chain Monte-Carlo (MCMC). Through a rigorous simulation study, we showed the robustness of both the model and the estimation method used. Maps of the location parameter on the spatial plane for different periods of time show the existence of local variations in the extreme values of seismicity in the study area. The results indicate strong evidence of an increase in the magnitude of earthquakes over time. A spatial map of risk with maximum intensity of earthquakes in a period of 25 years was elaborated.