Bayesian shape analysis of the complex Bingham distribution

• We develop a full Bayesian analysis for planar landmark data arising from a complex Bingham.
• A novel MCMC method to sample the eigenvalues and eigenvectors of the complex-valued Hermitian parameter matrix is designed.
• A new conjugate prior for the complex Bingham distribution is developed.

Previous shape analysis of landmark data arising from a complex Bingham distribution involved frequentist statistical estimation, and Bayesian MAP estimation. In this paper, we develop a full Bayesian analysis for planar landmark data arising from a complex Bingham. A novel MCMC method to sample the eigenvalues and eigenvectors of the complex-valued Hermitian parameter matrix is designed. Additionally, a new conjugate prior for the complex Bingham distribution is developed. Illustrative analysis using simulated and actual landmark data demonstrate the methods.