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Title: A Bayesian network model for linear-circular data Authors:  Ignacio Leguey - Universidad Politecnica de Madrid (Spain)
Concha Bielza - Universidad Politecnica de Madrid (Spain)
Pedro Larranaga - Universidad Politecnica de Madrid (Spain)
Shogo Kato - Institute of Statistical Mathematics (Japan) [presenting]
Abstract: In numerous academic fields, it is common that multivariate data include circular observations. Because of the periodic nature of circular observations, a direct application of ordinary Bayesian network techniques could lead to an erroneous result in analysis. We propose a tree-structured Bayesian network model for linear-circular data, namely, data comprising of multiple linear and circular observations. The proposed model is defined using marginals and conditionals of the following three bivariate models: the bivariate normal distribution, a bivariate wrapped Cauchy distribution, and an existing bivariate distribution on the cylinder. There is an efficient algorithm for random generation of the presented Bayesian network model. The mutual information for the joint distributions of parent and child variables can be expressed in a simple and closed form. Maximum likelihood estimation of the parameters is efficient for the marginals and conditionals related to parent and child variables. There are closed-form expressions for the method of moments estimators of the parameters. The presented Bayesian network model can be estimated based on the mutual information via Chow Liu algorithm. A simulation study and an application of the proposed model are given.