Bayesian Nonparametric Models of Circular Variables Based on Dirichlet Process Mixtures of Normal Distributions

Abstract

This article introduces two new Bayesian nonparametric models for circular data based on Dirichlet process (DP) mixtures of normal distributions. The first model is a projected DP mixture of bivariate normals and the second approach is based on a wrapped DP mixture of normal distributions. We show how to carry out inference for these models based on a slice sampling scheme and introduce an approach to estimating a variant of the deviance information criterion which is appropriate in the context of latent variable models. Our models are then compared with both simulated and real data examples.

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Acknowledgments

The work of the first author was partially supported by Sistema Nacional de Investigadores, Mexico. Support from the Department of Statistics of the University Carlos III of Madrid is also gratefully acknowledged. The second and third authors were supported by MEC grant ECO2011-25706 and MEC grant ECO2012-38442 (respectively) from the Spanish Government. The authors are grateful to an associate editor and one anonymous referee for their helpful comments and suggestions on a previous version of paper.

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Correspondence to Gabriel Nuñez-Antonio.

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Nuñez-Antonio, G., Ausín, M.C. & Wiper, M.P. Bayesian Nonparametric Models of Circular Variables Based on Dirichlet Process Mixtures of Normal Distributions. JABES 20, 47–64 (2015). https://doi.org/10.1007/s13253-014-0193-y

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Keywords

  • Circular data
  • Deviance information criterion
  • Dirichlet process mixtures
  • Projected normal distribution
  • Wrapped normal distribution