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Recent years have seen an increased interest in the application of methodsand techniques commonly associated with machine learning and artificialintelligence to spatial statistics. Here, in a celebration of the ten-yearanniversary of the journal Spatial Statistics, we bring together normalizingflows, commonly used for density function estimation in machine learning, andspherical point processes, a topic of particular interest to the journal'sreadership, to present a new approach for modeling non-homogeneous Poissonprocess intensity functions on the sphere. The central idea of this frameworkis to build, and estimate, a flexible bijective map that transforms theunderlying intensity function of interest on the sphere into a simpler,reference, intensity function, also on the sphere. Map estimation can be doneefficiently using automatic differentiation and stochastic gradient descent,and uncertainty quantification can be done straightforwardly via nonparametricbootstrap. We investigate the viability of the proposed method in a simulationstudy, and illustrate its use in a proof-of-concept study where we model theintensity of cyclone events in the North Pacific Ocean. Our experiments revealthat normalizing flows present a flexible and straightforward way to modelintensity functions on spheres, but that their potential to yield a good fitdepends on the architecture of the bijective map, which can be difficult toestablish in practice.

Spherical Poisson Point Process Intensity Function Modeling and Estimation with Measure Transport