Shifted Inverse stereographic normal distributions as flexible distribution family on the hypertorus
Abstract: Circular data arises in various fields including robotics, biology, geology and material sciences. Modelling such data requires flexible distribution families on the hypertorus. Common choices are the von Mises and the wrapped normal distributions. In this work we investigate the \textit{inverse stereographic normal distribution} as an interesting and computationally appealing alternative. We demonstrate its flexibility and practical applicability by fitting mixtures of shifted inverse stereographic normal distributions via gradient descent to dihedral data of protein backbones characterizing the conformational landscape of folding. Furthermore, we prove that the inverse stereographic normal distribution is unimodal if and only if all eigenvalues of the covariance matrix are less than or equal to $0.5$.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Trevor_Campbell1
Submission Number: 2074
Loading