Convolutional Neural Networks for Inhomogeneous Neyman Scott Cox Process With Application in Earthquake Risk Prediction

Spatial point process is used to analyze the distribution of objects locations within geographic space, such as earthquake epicenters. Neyman Scott Cox Process (NSCP) is one model that can analyze spatial point process that has a cluster pattern. The likelihood form of NSCP model is difficult to evaluate analytically, so parameter estimation can be done using methods such as Composite Likelihood and Minimum Contrast Estimation. Neural networks offer great potential for modeling nonlinear relationships between points in space without requiring explicit assumptions about spatial dependence. Convolutional Neural Network (CNN) has proven to be effective in various applications especially for image analysis. This study explores CNN for parameter estimation in NSCP model with several covariate variables. The results show that although composite likelihood and minimum contrast methods provide different parameter estimate but they produce similar spatial intensity patterns. CNN model trained on historical earthquake data and covariates, achieves low prediction errors, with MSE 0.00045 and RMSE 0.0213, and able to identify high risk zones in northern Sulawesi and Halmahera. Overall, the methods produce consistent intensity patterns, with the highest risk areas being in northern Sulawesi and Maluku such as Manado, Ternate and Banda Sea south of Seram. The similarity of these pattern confirms that the inhomogeneity structure of data represented by spatial covariates, has a significant impact on earthquake occurrence, particularly in Sulawesi and Maluku regions.