Diffusion Smoothing for Spatial Point Patterns

Traditional kernel methods for estimating the spatially-varying density of points in a spatial point pattern may exhibit unrealistic artefacts, addition to familiar problems bias and over- or under-smoothing. Performance can be improved by using diffusion smoothing, which smoothing is heat on domain. This paper develops into practical statistical methodology two-dimensional data. We clarify advantages disadvantages over Gaussian smoothing. Adaptive where bandwidth spatially-varying, performed adopting rate: this avoids technical with adaptive has substantially better performance. introduce new form lagged arrival times, good performance robustness. Applications archaeology epidemiology are demonstrated. The implemented open-source R code.