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A Bayesian model for longitudinal circular data based on the projected normal distribution

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  • Nuñez-Antonio, Gabriel
  • Gutiérrez-Peña, Eduardo

Abstract

The analysis of short longitudinal series of circular data may be problematic and to some extent has not been fully developed. A Bayesian analysis of a new model for such data is presented. The model is based on a radial projection onto the circle of a particular bivariate normal distribution. Inference about the parameters of the model is based on samples from the corresponding joint posterior density, which are obtained using a Metropolis-within-Gibbs scheme after the introduction of suitable latent variables. The procedure is illustrated using both simulated data sets and a real data set previously analyzed in the literature.

Suggested Citation

  • Nuñez-Antonio, Gabriel & Gutiérrez-Peña, Eduardo, 2014. "A Bayesian model for longitudinal circular data based on the projected normal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 506-519.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:506-519
    DOI: 10.1016/j.csda.2012.07.025
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    References listed on IDEAS

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    1. Abe, Toshihiro & Pewsey, Arthur, 2011. "Symmetric circular models through duplication and cosine perturbation," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3271-3282, December.
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    3. Rueda, Cristina & Fernández, Miguel A. & Peddada, Shyamal Das, 2009. "Estimation of Parameters Subject to Order Restrictions on a Circle With Application to Estimation of Phase Angles of Cell Cycle Genes," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 338-347.
    4. Rinaldo Artes & Bent Jørgensen, 2000. "Longitudinal Data Estimating Equations for Dispersion Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(2), pages 321-334, June.
    5. Presnell, Brett & Rumcheva, Pavlina, 2008. "The mean resultant length of the spherically projected normal distribution," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 557-563, April.
    6. Pewsey, Arthur, 2008. "The wrapped stable family of distributions as a flexible model for circular data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1516-1523, January.
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