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Random density functions with common atoms and pairwise dependence

Author

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

Abstract

The construction of pairwise dependence between m random density functions each of which is modeled as a mixture of Dirichlet processes is considered. The key to this is how to create dependencies between random Dirichlet processes. A method previously used for creating pairwise dependence is adapted, with the simplification that all random Dirichlet processes share the same atoms. The main contention is that for dependent Dirichlet processes adopting common atoms is sufficient for prediction and density estimation purposes. In addition, it is possible to compute the L2 distances between all pairs of random probability measures.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:101:y:2016:i:c:p:236-249
    DOI: 10.1016/j.csda.2016.03.008
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    References listed on IDEAS

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    1. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    2. 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.
    3. 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.
    4. J. E. Griffin & M. Kolossiatis & M. F. J. Steel, 2013. "Comparing distributions by using dependent normalized random-measure mixtures," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(3), pages 499-529, June.
    5. 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.
    6. 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.
    7. David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323.
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    More about this item

    Keywords

    Bayesian nonparametric inference; Dependent Dirichlet process; L2 distance; Mixture of Dirichlet process; Pairwise dependence;
    All these keywords.

    JEL classification:

    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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