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A Bayesian Hierarchical Model for Classification with Selection of Functional Predictors
Author(s) -
Zhu Hongxiao,
Vannucci Marina,
Cox Dennis D.
Publication year - 2010
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2009.01283.x
Subject(s) - computer science , bayesian probability , gibbs sampling , functional data analysis , orthonormal basis , mixing (physics) , principal component analysis , bayesian hierarchical modeling , machine learning , functional principal component analysis , artificial intelligence , model selection , selection (genetic algorithm) , random effects model , markov chain monte carlo , data mining , bayesian inference , medicine , physics , meta analysis , quantum mechanics
Summary In functional data classification, functional observations are often contaminated by various systematic effects, such as random batch effects caused by device artifacts, or fixed effects caused by sample‐related factors. These effects may lead to classification bias and thus should not be neglected. Another issue of concern is the selection of functions when predictors consist of multiple functions, some of which may be redundant. The above issues arise in a real data application where we use fluorescence spectroscopy to detect cervical precancer. In this article, we propose a Bayesian hierarchical model that takes into account random batch effects and selects effective functions among multiple functional predictors. Fixed effects or predictors in nonfunctional form are also included in the model. The dimension of the functional data is reduced through orthonormal basis expansion or functional principal components. For posterior sampling, we use a hybrid Metropolis–Hastings/Gibbs sampler, which suffers slow mixing. An evolutionary Monte Carlo algorithm is applied to improve the mixing. Simulation and real data application show that the proposed model provides accurate selection of functional predictors as well as good classification.