Abstract This paper presents advanced applications of hierarchical space–time point-process models (HIST-PPM) through recent implementation examples based on the seismicity-analysis software developed and published by the author and collaborators. The model enhances the precision of earthquake forecasting by incorporating spatial interpolation using Delaunay triangulation meshes, which—unlike kernel smoothing—naturally reproduce locally varying and anisotropic spatial patterns of seismic activity without the need for ad hoc bandwidth selection. Characteristic parameters—such as changes in spatial density over transformed time and variations in the b -value of Gutenberg–Richter’s law—are captured flexibly and in detail across both time and space, owing to a model structure in which these parameters vary linearly within each triangular element. The estimation procedure employs empirical Bayesian maximum a posteriori (MAP) estimation, enabling stable inference in high-dimensional parameter spaces while effectively avoiding overfitting. In particular, the hierarchical space–time ETAS (HIST-ETAS) model, which incorporates spatial anisotropy and regional characteristics, not only enhances the reliability of short-term earthquake forecasts but also supports mid- to long-term spatial assessments of seismic activity by estimating background seismicity. Moreover, it can be applied to seismic monitoring by visualizing spatial variations in aftershock activity intensity. In addition, the spatiotemporal detection rate model—developed to address the incompleteness of earthquake catalogs, particularly those involving small earthquakes—enables unbiased estimation of seismic activity in both real-time and long-term settings. These technological advancements offer a practical and effective foundation for developing future multi-layered earthquake forecasting systems. Graphical Abstract
Yosihiko Ogata (2026) studied this question.