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Bayesian nonparametric functional data analysis through density estimation

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  • Abel Rodríguez
  • David B. Dunson
  • Alan E. Gelfand

Abstract

In many modern experimental settings, observations are obtained in the form of functions and interest focuses on inferences about a collection of such functions. We propose a hierarchical model that allows us simultaneously to estimate multiple curves nonparametrically by using dependent Dirichlet process mixtures of Gaussian distributions to characterize the joint distribution of predictors and outcomes. Function estimates are then induced through the conditional distribution of the outcome given the predictors. The resulting approach allows for flexible estimation and clustering, while borrowing information across curves. We also show that the function estimates we obtain are consistent on the space of integrable functions. As an illustration, we consider an application to the analysis of conductivity and temperature at depth data in the north Atlantic. Copyright 2009, Oxford University Press.

Suggested Citation

  • Abel Rodríguez & David B. Dunson & Alan E. Gelfand, 2009. "Bayesian nonparametric functional data analysis through density estimation," Biometrika, Biometrika Trust, vol. 96(1), pages 149-162.
  • Handle: RePEc:oup:biomet:v:96:y:2009:i:1:p:149-162
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    File URL: http://hdl.handle.net/10.1093/biomet/asn054
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    References listed on IDEAS

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    Cited by:

    1. Navarrete, Carlos A. & Quintana, Fernando A., 2011. "Similarity analysis in Bayesian random partition models," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 97-109, January.
    2. Jensen, Mark J & Maheu, John M, 2013. "Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis," MPRA Paper 52132, University Library of Munich, Germany.
    3. Shotwell, Matthew S., 2013. "profdpm: An R Package for MAP Estimation in a Class of Conjugate Product Partition Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i08).
    4. XuanLong Nguyen & Alan Gelfand, 2014. "Bayesian nonparametric modeling for functional analysis of variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(3), pages 495-526, June.
    5. Lian, Heng & Choi, Taeryon & Meng, Jie & Jo, Seongil, 2016. "Posterior convergence for Bayesian functional linear regression," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 27-41.

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