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Dependent mixtures of Dirichlet processes

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  • Hatjispyros, Spyridon J.
  • Nicoleris, Theodoros
  • Walker, Stephen G.

Abstract

An approach to modeling dependent nonparametric random density functions is presented. This is based on the well known mixture of Dirichlet process model. The idea is to use a technique for constructing dependent random variables, first used for dependent gamma random variables. While the methodology works for an arbitrary number of dependent random densities, with each pair having their own dependent structure, the mathematics and estimation algorithm is focused on two dependent random density functions. Simulations and a real data example are presented.

Suggested Citation

  • Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2011. "Dependent mixtures of Dirichlet processes," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2011-2025, June.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:6:p:2011-2025
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    References listed on IDEAS

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    1. Griffin, J.E. & Steel, M.F.J., 2006. "Order-Based Dependent Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 179-194, March.
    2. Hatjispyros, S.J. & Yannacopoulos, A.N., 2005. "A random dynamical system model of a stylized equity market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 583-612.
    3. David B. Dunson & Natesh Pillai & Ju‐Hyun Park, 2007. "Bayesian density regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 163-183, April.
    4. Peter Müller & Fernando Quintana & Gary Rosner, 2004. "A method for combining inference across related nonparametric Bayesian models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 735-749, August.
    5. Hatjispyros, S.J. & Nicoleris, Theodoros & Walker, Stephen G., 2007. "Parameter estimation for random dynamical systems using slice sampling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 71-81.
    6. David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323.
    7. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2009. "A Bayesian nonparametric study of a dynamic nonlinear model," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3948-3956, October.
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    Cited by:

    1. Billio, Monica & Casarin, Roberto & Rossini, Luca, 2019. "Bayesian nonparametric sparse VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 97-115.
    2. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2016. "Random density functions with common atoms and pairwise dependence," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 236-249.
    3. Federico Bassetti & Roberto Casarin & Francesco Ravazzolo, 2018. "Bayesian Nonparametric Calibration and Combination of Predictive Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 675-685, April.
    4. Leisen, Fabrizio & Casarin, Roberto & Bassetti, Federico, 2011. "Beta-product Poisson-Dirichlet Processes," DES - Working Papers. Statistics and Econometrics. WS 12160, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Lijoi, Antonio & Nipoti, Bernardo & Prünster, Igor, 2014. "Dependent mixture models: Clustering and borrowing information," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 417-433.
    6. Hatjispyros, Spyridon J. & Merkatas, Christos & Nicoleris, Theodoros & Walker, Stephen G., 2018. "Dependent mixtures of geometric weights priors," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 1-18.
    7. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    8. Matteo Iacopini & Luca Rossini, 2019. "Bayesian nonparametric graphical models for time-varying parameters VAR," Papers 1906.02140, arXiv.org.
    9. Weixuan Zhu & Fabrizio Leisen, 2015. "A multivariate extension of a vector of two-parameter Poisson-Dirichlet processes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 89-105, March.
    10. Antonio Lijoi & Bernardo Nipoti & Igor Prünster, 2013. "Dependent mixture models: clustering and borrowing information," DEM Working Papers Series 046, University of Pavia, Department of Economics and Management.
    11. González, Jorge & Barrientos, Andrés F. & Quintana, Fernando A., 2015. "Bayesian nonparametric estimation of test equating functions with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 222-244.
    12. Leisen, Fabrizio & Zhu, W., 2013. "A multivariate extension of a vector of Poisson- Dirichlet processes," DES - Working Papers. Statistics and Econometrics. WS ws132220, Universidad Carlos III de Madrid. Departamento de Estadística.

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