A outra...

A outra apresentacao de hoje, sexta, dia 06 de maio, será da Rosângela Loschi,

e ela vai apresentar o paper do JRSS-B de 2010

Hybrid Dirichlet mixture models for functional data

Sonia Petrone,

Bocconi University, Milan, Italy

Michele Guindani

University of New Mexico, Albuquerque, USA

and Alan E. Gelfand

Duke University, Durham, USA

Summary.

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

1and

their connection with Dirichlet process mixtures.

Keywords

: Bayesian non-parametrics; Dependent random partitions; Dirichlet process;Finite mixture models; Gaussian process; Labelling measures; Species sampling priors