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Understanding that large earthquakes can be violent to human beings, a wide variety of seismicity forecasting models are proposed. To perform useful comparisons among these point process models, graphical residual methods are proposed because they visualize and highlight when and where a given model does not agree closely with either the observed seismicity or another model. In this paper, we work with the one-day observational and forecasting earthquake data from Southern California in the entire year of 2017. Our goal is to utilized Voronoi analysis and Super-thinned analysis to evaluate and compare the Epidemic- Type Aftershock Sequence model (ETAS) and the Modified Nonparametric Hawkes Point Process model (Modified MISD). Essentially, our results suggest that the Modified MISD Model returns comparatively better predictions and better goodness of fit.

Understanding that large earthquakes can be violent to human beings, a wide variety of seismicity forecasting models are proposed. To perform useful comparisons among these point process models, graphical residual methods are proposed because they visualize and highlight when and where a given model does not agree closely with either the observed seismicity or another model. In this paper, we work with the one-day observational and forecasting earthquake data from Southern California in the entire year of 2017. Our goal is to utilized Voronoi analysis and Super-thinned analysis to evaluate and compare the Epidemic- Type Aftershock Sequence model (ETAS) and the Modified Nonparametric Hawkes Point Process model (Modified MISD). Essentially, our results suggest that the Modified MISD Model returns comparatively better predictions and better goodness of fit.

Network data often take the form of repeated interactions between senders and receivers tabulated over time. A primary question to ask of such data is which traits and behaviors are predictive of interaction. To answer this question, a model is introduced for treating directed interactions as a multivariate point process: a Cox multiplicative intensity model using covariates that depend on the history of the process. Consistency and asymptotic normality are proved for the resulting partial-likelihood-based estimators under suitable regularity conditions, and an efficient fitting procedure is described. Multicast interactions--those involving a single sender but multiple receivers--are treated explicitly. The resulting inferential framework is then employed to model message sending behavior in a corporate e-mail network. The analysis gives a precise quantification of which static shared traits and dynamic network effects are predictive of message recipient selection.