Tree-Structured Bayesian Networks for Wrapped Cauchy Directional Distributions
Modelling the relationship between directional variables is a nearly unexplored field. The bivariate wrapped Cauchy distribution has recently emerged as the first closed family of bivariate directional distributions (marginals and conditionals belong to the same family). In this paper, we introduce a tree-structured Bayesian network suitable for modelling directional data with bivariate wrapped Cauchy distributions. We describe the structure learning algorithm used to learn the Bayesian network. We also report some simulation studies to illustrate the algorithms including a comparison with the Gaussian structure learning algorithm and an empirical experiment on real morphological data from juvenile rat somatosensory cortex cells.
KeywordsDirectional statistics Wrapped Cauchy distribution Tree-structure Bayesian networks
This work has been partially supported by the Spanish Ministry of Economy and Competitiveness through the TIN2013-41592-P and Cajal Blue Brain (C080020-09), by the Regional Government of Madrid through the S2013/ICE-2845-CASI-CAM-CM project. I.L. is supported by the Spanish Ministry of Education, Culture and Sport Fellowship (FPU13/01941). The authors thankfully acknowledge the Cortical Circuits Laboratory (CSIC-UPM) for the neurons dataset.
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