Bayesian Regression Analysis for Dependent Data with an Elliptical Shape

Abstract

This paper proposes a parametric hierarchical model for functional data with an elliptical shape, using a Gaussian process prior to capturing the data dependencies that reflect systematic errors while modeling the underlying curved shape through a von Mises–Fisher distribution. The model definition, Bayesian inference, and MCMC algorithm are discussed. The effectiveness of the model is demonstrated through the reconstruction of curved trajectories using both simulated and real-world examples. The discussion in this paper focuses on two-dimensional problems, but the framework can be extended to higher-dimensional spaces, making it adaptable to a wide range of applications.