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

  • Gabriel Nuñez-AntonioEmail author
  • María Concepción Ausín
  • Michael P. Wiper


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.


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



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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Copyright information

© International Biometric Society 2014

Authors and Affiliations

  • Gabriel Nuñez-Antonio
    • 1
    Email author
  • María Concepción Ausín
    • 2
  • Michael P. Wiper
    • 2
  1. 1.Departamento de MatemáticasUniversidad Autónoma Metropolitana – Unidad IztapalaMéxicoMexico
  2. 2.Department of StatisticsUniversidad Carlos III de MadridGetafeSpain

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