Overview

Module for Kernel-Density Estimation (KDE) on unit sphere. Created for ¹.

Uses a Fisher distribution (i.e. Fisher-Von-Mises with p=3) as kernel function. No bandwidth selection. Calculation can be performed in chunks to reduce max. memory requirements.

Coordinates

Coordinates on the sphere must be specified in spherical polar coordinates. The polar angle (theta) must be in the range [0,PI], with 0 at the north pole, and the azimuthal angle (phi) should be in range [0,2*PI]. Both should be in radians.

Requirements

The base module only requires numpy. To run the unit tests, matplotlib and scipy are required.

Unit tests

There are two unit tests. The first tests that the Fisher kernel is correctly normalized. The second computes the KDE estimate for a uniform distribution and compares the MISE to the known MISE: for the uniform distribution on the sphere, the MISE can be computed analytically. The parameters for the unit tests are set directly in the scripts.

Footnotes

1. Russell M.B., Johnson, C.L., Gilchrist, S.A.: 2024,"Investigating the Spatial Relationship of Shield Volcanism with Coronae on Venus",55th Lunar and Planetary Science Conference,3040, URL: https://ui.adsabs.harvard.edu/abs/2024LPICo3040.2582R ↩