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Semiparametric Bayesian Techniques for Problems in Circular Data

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  • Kaushik Ghosh
  • Rao Jammalamadaka
  • Ram Tiwari

Abstract

In this paper, we consider the problems of prediction and tests of hypotheses for directional data in a semiparametric Bayesian set-up. Observations are assumed to be independently drawn from the von Mises distribution and uncertainty in the location parameter is modelled by a Dirichlet process. For the prediction problem, we present a method to obtain the predictive density of a future observation, and, for the testing problem, we present a method of computing the Bayes factor by obtaining the posterior probabilities of the hypotheses under consideration. The semiparametric model is seen to be flexible and robust against prior misspecifications. While analytical expressions are intractable, the methods are easily implemented using the Gibbs sampler. We illustrate the methods with data from two real-life examples.

Suggested Citation

  • Kaushik Ghosh & Rao Jammalamadaka & Ram Tiwari, 2003. "Semiparametric Bayesian Techniques for Problems in Circular Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(2), pages 145-161.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:2:p:145-161
    DOI: 10.1080/0266476022000023712
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    Cited by:

    1. Rodríguez, Carlos E. & Núñez-Antonio, Gabriel & Escarela, Gabriel, 2020. "A Bayesian mixture model for clustering circular data," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    2. McVinish, R. & Mengersen, K., 2008. "Semiparametric Bayesian circular statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4722-4730, June.

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