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A Predictive Study of Dirichlet Process Mixture Models for Curve Fitting

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  • Sara Wade
  • Stephen G. Walker
  • Sonia Petrone

Abstract

type="main" xml:id="sjos12047-abs-0001"> This paper examines the use of Dirichlet process mixtures for curve fitting. An important modelling aspect in this setting is the choice between constant and covariate-dependent weights. By examining the problem of curve fitting from a predictive perspective, we show the advantages of using covariate-dependent weights. These advantages are a result of the incorporation of covariate proximity in the latent partition. However, closer examination of the partition yields further complications, which arise from the vast number of total partitions. To overcome this, we propose to modify the probability law of the random partition to strictly enforce the notion of covariate proximity, while still maintaining certain properties of the Dirichlet process. This allows the distribution of the partition to depend on the covariate in a simple manner and greatly reduces the total number of possible partitions, resulting in improved curve fitting and faster computations. Numerical illustrations are presented.

Suggested Citation

  • Sara Wade & Stephen G. Walker & Sonia Petrone, 2014. "A Predictive Study of Dirichlet Process Mixture Models for Curve Fitting," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 580-605, September.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:3:p:580-605
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    File URL: http://hdl.handle.net/10.1111/sjos.12047
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    References listed on IDEAS

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    1. Gelfand, Alan E. & Kottas, Athanasios & MacEachern, Steven N., 2005. "Bayesian Nonparametric Spatial Modeling With Dirichlet Process Mixing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1021-1035, September.
    2. Fernando A. Quintana & Pilar L. Iglesias, 2003. "Bayesian clustering and product partition models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 557-574, May.
    3. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    4. 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.
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    Cited by:

    1. De Blasi, Pierpaolo & Martínez, Asael Fabian & Mena, Ramsés H. & Prünster, Igor, 2020. "On the inferential implications of decreasing weight structures in mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    2. 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.

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