All Times EDT
Keywords: spatial statistics, machine learning, kernel methods
Comparison of spatial point patterns is of practical importance in a number of scientific fields including ecology, epidemiology, and criminology. For example, such comparisons may reveal differential effects of the environment on plant species spread, uncover spatial variation in disease risk, or detect seasonal differences in crime locations. We introduce an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to spatial point processes. The main advantages of the proposed approach are that it can be applied to both single and replicated pattern comparisons, and that neither bootstrap nor permutation procedures are needed to obtain or calibrate the p-values, making it especially useful in big data settings. Two applications to real world data will be presented.