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Geometric Stick-Breaking Processes for Continuous-Time Nonparametric Modeling

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  • Ramses H. Mena

    ()

  • Matteo Ruggiero
  • Stephen G. Walker

Abstract

This paper is concerned with the construction of a continuous parameter sequence of random probability measures and its application for modeling random phenomena evolving in continuous time. At each time point we have a random probability measure which is generated by a Bayesian nonparametric hierarchical model, and the dependence structure is induced through a Wright-Fisher diffusion with mutation. The sequence is shown to be a stationary and reversible diffusion taking values on the space of probability measures. A simple estimation procedure for discretely observed data is presented and illustrated with simulated and real data sets.

Suggested Citation

  • Ramses H. Mena & Matteo Ruggiero & Stephen G. Walker, 2009. "Geometric Stick-Breaking Processes for Continuous-Time Nonparametric Modeling," ICER Working Papers - Applied Mathematics Series 26-2009, ICER - International Centre for Economic Research.
  • Handle: RePEc:icr:wpmath:26-2009
    as

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    File URL: http://www.biblioecon.unito.it/biblioservizi/RePEc/icr/wp2009/ICERwp26-09.pdf
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    References listed on IDEAS

    as
    1. Antonio Lijoi & Igor Pruenster & Stephen G. Walker, 2008. "Bayesian nonparametric estimators derived from conditional Gibbs structures," ICER Working Papers - Applied Mathematics Series 06-2008, ICER - International Centre for Economic Research.
    2. Lancelot F. James & Antonio Lijoi & Igor PrĂ¼nster, 2009. "Posterior Analysis for Normalized Random Measures with Independent Increments," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 76-97.
    3. Hanson T. & Johnson W.O., 2002. "Modeling Regression Error With a Mixture of Polya Trees," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1020-1033, December.
    4. James, Lancelot F., 2003. "A simple proof of the almost sure discreteness of a class of random measures," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 363-368, December.
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    More about this item

    Keywords

    Bayesian non-parametric inference; continuous time dependent random measure; Markov process; measure-valued process; stationary process; stick-breaking process;

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