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Variational Bayesian functional PCA

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  • van der Linde, Angelika

Abstract

A Bayesian approach to analyze the modes of variation in a set of curves is suggested. It is based on a generative model thus allowing for noisy and sparse observations of curves. A Demmler-Reinsch(-type) basis is used to enforce smoothness of the latent ('eigen')functions. Inference, including estimation, error assessment and model choice, particularly the choice of the number of eigenfunctions and their degree of smoothness, is derived from a variational approximation of the posterior distribution. The proposed analysis is illustrated with simulated and real data.

Suggested Citation

  • van der Linde, Angelika, 2008. "Variational Bayesian functional PCA," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 517-533, December.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:517-533
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    References listed on IDEAS

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    Cited by:

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    2. M. Aguilera-Morillo & Ana Aguilera & Manuel Escabias & Mariano Valderrama, 2013. "Penalized spline approaches for functional logit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 251-277, June.
    3. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    4. Delicado, P., 2011. "Dimensionality reduction when data are density functions," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 401-420, January.
    5. Christian Acal & Ana M. Aguilera & Manuel Escabias, 2020. "New Modeling Approaches Based on Varimax Rotation of Functional Principal Components," Mathematics, MDPI, vol. 8(11), pages 1-15, November.
    6. Julia Wrobel & Vadim Zipunnikov & Jennifer Schrack & Jeff Goldsmith, 2019. "Registration for exponential family functional data," Biometrics, The International Biometric Society, vol. 75(1), pages 48-57, March.
    7. Kokoszka, Piotr & Miao, Hong & Petersen, Alexander & Shang, Han Lin, 2019. "Forecasting of density functions with an application to cross-sectional and intraday returns," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1304-1317.
    8. Jeff Goldsmith & Vadim Zipunnikov & Jennifer Schrack, 2015. "Generalized multilevel function-on-scalar regression and principal component analysis," Biometrics, The International Biometric Society, vol. 71(2), pages 344-353, June.

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