Nonparametric Bayes kernel-based priors for functional data analysis

Richard F. MacLehose, David B. Dunson

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We focus on developing nonparametric Bayes methods for collections of dependent random functions, allowing individual curves to vary flexibly while adaptively borrowing information. A prior is proposed, which is expressed as a hierarchical mixture of weighted kernels placed at unknown locations. The induced prior for any individual function is shown to fall within a reproducing kernel Hilbert space. We allow flexible borrowing of information through the use of a hierarchical Dirichlet process prior for the random locations, along with a functional Dirichlet process for the weights. Theoretical properties are considered and an efficient MCMC algorithm is developed, relying on stick-breaking truncations. The methods are illustrated using simulation examples and an application to reproductive hormone data.

Original languageEnglish (US)
Pages (from-to)611-629
Number of pages19
JournalStatistica Sinica
Volume19
Issue number2
StatePublished - Apr 1 2009

Keywords

  • Dirichlet process
  • Functional data analysis
  • Kernel smoothing
  • Mixture model
  • RKHS
  • Random curve

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