A projected normal copula model for hypertoroidal data
Conference
66th ISI World Statistics Congress
Format: WSC 2027: IPS Abstract
Keywords: bayesian inference, circular statistics, copula, directional data, interpretability
Abstract
In this talk, we introduce a family of probability distributions for the Bayesian analysis of hypertoroidal data. Our construction starts from a copula on the hypertorus, that is, a distribution on the hypertorus with uniform circular marginals, obtained by projecting a multivariate normal distribution under specific parameter constraints. The proposed family is then defined as a flexible extension of this copula, allowing for arbitrary univariate circular marginals. Unlike existing models derived via projection, the proposed family has the advantage that its parameters possess clear and intuitive interpretations. In terms of circular correlation, the proposed model allows for a full range of dependence between two variables, from independence to perfect positive or negative dependence in the limit. The bivariate case of the proposed copula has a closed-form density. The use of latent variables simplifies Bayesian estimation using Markov chain Monte Carlo algorithms. The usefulness of the proposed family is demonstrated through the analysis of a meteorological dataset on wind and wave directions in the Gulf of Mexico.