Hybrid Dirichlet mixture models for functional data

Sonia Petrone, Michele Guindani and Alan E. Gelfand

Journal Of The Royal Statistical Society Series B, 2009, vol. 71, issue 4, pages 755-782

Abstract: In functional data analysis, curves or surfaces are observed, up to measurement error, at a finite set of locations, for, say, a sample of "n" individuals. Often, the curves are homogeneous, except perhaps for individual-specific regions that provide heterogeneous behaviour (e.g. 'damaged' areas of irregular shape on an otherwise smooth surface). Motivated by applications with functional data of this nature, we propose a Bayesian mixture model, with the aim of dimension reduction, by representing the sample of "n" curves through a smaller set of canonical curves. We propose a novel prior on the space of probability measures for a random curve which extends the popular Dirichlet priors by allowing local clustering: non-homogeneous portions of a curve can be allocated to different clusters and the "n" individual curves can be represented as recombinations (hybrids) of a few canonical curves. More precisely, the prior proposed envisions a conceptual hidden factor with "k"-levels that acts locally on each curve. We discuss several models incorporating this prior and illustrate its performance with simulated and real data sets. We examine theoretical properties of the proposed finite hybrid Dirichlet mixtures, specifically, their behaviour as the number of the mixture components goes to ∞ and their connection with Dirichlet process mixtures. Copyright (c) 2009 Royal Statistical Society.

Date: 2009

Downloads: (external link)
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9868.2009.00708.x link to full text (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:bla:jorssb:v:71:y:2009:i:4:p:755-782

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=1369-7412

Access Statistics for this article

Journal Of The Royal Statistical Society Series B is edited by C. Robert and A. T. A. Wood

More articles in Journal Of The Royal Statistical Society Series B from Royal Statistical Society
Series data maintained by Christopher F. Baum ().