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Longitudinal functional principal component modelling via Stochastic Approximation Monte Carlo
Author(s) -
Martinez Josue G.,
Liang Faming,
Zhou Lan,
Carroll Raymond J.
Publication year - 2010
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.10062
Subject(s) - markov chain monte carlo , frequentist inference , principal component analysis , monte carlo method , maxima and minima , functional principal component analysis , bayesian probability , computer science , mathematics , statistical physics , mathematical optimization , bayesian inference , statistics , physics , mathematical analysis
The authors consider the analysis of hierarchical longitudinal functional data based upon a functional principal components approach. In contrast to standard frequentist approaches to selecting the number of principal components, the authors do model averaging using a Bayesian formulation. A relatively straightforward reversible jump Markov Chain Monte Carlo formulation has poor mixing properties and in simulated data often becomes trapped at the wrong number of principal components. In order to overcome this, the authors show how to apply Stochastic Approximation Monte Carlo (SAMC) to this problem, a method that has the potential to explore the entire space and does not become trapped in local extrema. The combination of reversible jump methods and SAMC in hierarchical longitudinal functional data is simplified by a polar coordinate representation of the principal components. The approach is easy to implement and does well in simulated data in determining the distribution of the number of principal components, and in terms of its frequentist estimation properties. Empirical applications are also presented. The Canadian Journal of Statistics 38: 256–270; 2010 © 2010 Statistical Society of Canada