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A Predictive Study of Dirichlet Process Mixture Models for Curve Fitting
Author(s) -
Wade Sara,
Walker Stephen G.,
Petrone Sonia
Publication year - 2014
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12047
Subject(s) - covariate , mathematics , partition (number theory) , dirichlet distribution , computation , dirichlet process , statistics , mathematical optimization , algorithm , mathematical analysis , combinatorics , bayesian probability , boundary value problem
This paper examines the use of Dirichlet process mixtures for curve fitting. An important modelling aspect in this setting is the choice between constant and covariate‐dependent weights. By examining the problem of curve fitting from a predictive perspective, we show the advantages of using covariate‐dependent weights. These advantages are a result of the incorporation of covariate proximity in the latent partition. However, closer examination of the partition yields further complications, which arise from the vast number of total partitions. To overcome this, we propose to modify the probability law of the random partition to strictly enforce the notion of covariate proximity, while still maintaining certain properties of the Dirichlet process. This allows the distribution of the partition to depend on the covariate in a simple manner and greatly reduces the total number of possible partitions, resulting in improved curve fitting and faster computations. Numerical illustrations are presented.