Approximate wrapped normal pdf excludes independent translations?

[rees-c]

Thanks authors for your great work in this repo. I was looking at your wrapped normal pdf function, and assuming x and p_ are 3-dimensional, it seems as though the wrapping is only done over translations of the form [T,T,T] instead of [Tx,Ty,Tz] for integers T, Tx, Ty, Tz. I would think [Tx,Ty,Tz] would be more accurate - seems like a minor detail but I was hoping you could comment on it. Thanks!

[jiaor17]

Hi,
Thanks for your interest! If I understand correctly, you’re suggesting directly modeling a full 3D wrapped normal distribution rather than composing three independent 1D wrapped normals. That is a quite nice point and I have made updates to the codes in the 'multivariant_dev' branch to approximate the 3D wrapped normal by accumulating probability density over a 3D meshgrid rather than along separate 1D intervals. While results show no significant change compared to the original implementation, I believe the 3D approximation better aligns with the real distribution.

[rees-c]

Thanks @jiaor17 for your prompt response and experiment! Interesting to hear that the results are unchanged.