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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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    Citations

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    Cited by:

    1. Mark J. Jensen & John M. Maheu, 2018. "Risk, Return and Volatility Feedback: A Bayesian Nonparametric Analysis," JRFM, MDPI, vol. 11(3), pages 1-29, September.
    2. Silvia Montagna & Surya T. Tokdar & Brian Neelon & David B. Dunson, 2012. "Bayesian Latent Factor Regression for Functional and Longitudinal Data," Biometrics, The International Biometric Society, vol. 68(4), pages 1064-1073, December.
    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. Ryo Kato & Takahiro Hoshino, 2020. "Semiparametric Bayesian multiple imputation for regression models with missing mixed continuous–discrete covariates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 803-825, June.
    6. Adriano Zanin Zambom & Julian A. A. Collazos & Ronaldo Dias, 2019. "Functional data clustering via hypothesis testing k-means," Computational Statistics, Springer, vol. 34(2), pages 527-549, June.
    7. 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.
    8. Jaeeun Yu & Jinsu Park & Taeryon Choi & Masahiro Hashizume & Yoonhee Kim & Yasushi Honda & Yeonseung Chung, 2021. "Nonparametric Bayesian Functional Meta-Regression: Applications in Environmental Epidemiology," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(1), pages 45-70, March.
    9. Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Multiple Imputation for Regression Models with Missing Mixed Continuous-Discrete Covariates," Discussion Paper Series DP2018-15, Research Institute for Economics & Business Administration, Kobe University.
    10. Roy, Arkaprava & Ghosal, Subhashis, 2022. "Optimal Bayesian smoothing of functional observations over a large graph," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    11. 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.
    12. Bruno Scarpa & David B. Dunson, 2014. "Enriched Stick-Breaking Processes for Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(506), pages 647-660, June.

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