Exploration-Based Statistical Learning for Selecting Kernel Density Estimates of Spatial Point Patterns

Abstract

This paper addresses the use of nonparametric kernel density estimation (KDE) to estimate point-based data density in spatial modeling using Geographic Information Systems (GIS). The paper highlights challenges in selecting the appropriate settings for generating the best fitting KDE surfaces and validating their accuracy, as many GIS packages lack sufficient tools for this purpose. The paper focuses on providing guidelines for choosing the best bivariate KDE surface to approximate point patterns, using principles of machine learning for evaluation of the accuracy of KDE using internal and external metrics. Performance evaluation is based on the mass-preservation property of spatial point processes with the introduction of metrics such as residuals, cross-validation errors, and out-of-sample errors. These approaches are demonstrated on statistical data for violent crime in Lithuania but can be applied to other datasets with spatial point patterns.